diff --git a/docs/LowerBound_Dist_Profile_Derivation.ipynb b/docs/LowerBound_Dist_Profile_Derivation.ipynb new file mode 100644 index 000000000..e93c9cccf --- /dev/null +++ b/docs/LowerBound_Dist_Profile_Derivation.ipynb @@ -0,0 +1,2305 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0e440d53", + "metadata": {}, + "source": [ + "# Intro" + ] + }, + { + "cell_type": "markdown", + "id": "d8ebe111", + "metadata": {}, + "source": [ + "In this notebook, we would like to derive the eq(2) of the paper [VALMOD](https://arxiv.org/pdf/2008.13447.pdf).\n", + "\n", + "**Notation:** $T_{i,m} = T[i:i+m]$, a subsequence of `T` that starts at index `i` and has length `m`. " + ] + }, + { + "cell_type": "markdown", + "id": "5f999789", + "metadata": {}, + "source": [ + "**The idea goes as follows:**
\n", + "\"Given the distance profile of $T_{j,m}$, how can we find a lower bound for distance profile of $T_{j,m+k}$\", where $T_{j,m+k}$ represents a sequence that starts from the same index `j` with length `m+k`? In other words, can we find **Lower Bound (LB)** for $d(T_{j,m+k}, T_{i,m+k})$ only by help of $T_{j,m}$, $T_{i,m}$, and $T_{j,m+k}$? (So, the last `k` elements of $T_{i,m+k}$ are unknown)" + ] + }, + { + "cell_type": "markdown", + "id": "3b5c8c5a", + "metadata": {}, + "source": [ + "## Non-normalized distance" + ] + }, + { + "cell_type": "markdown", + "id": "1f7e294e", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " d^{(m+k)}_{j,i} ={}& \n", + " \\sqrt[\\leftroot{5}\\uproot{5}p]{\n", + " \\sum\\limits_{t=0}^{m+k-1}{\n", + " \\bigg\\lvert{\n", + " T[i+t] - T[j+t]\n", + " }\\bigg\\rvert\n", + " }^{p}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\sqrt[\\leftroot{5}\\uproot{5}p]{\n", + " \\sum\\limits_{t=0}^{m-1}{\n", + " \\bigg\\lvert{\n", + " T[i+t] - T[j+t]\n", + " }\\bigg\\rvert\n", + " }^{p}\n", + " +\n", + " \\sum\\limits_{t=m}^{m+k-1}{\n", + " \\bigg\\lvert{\n", + " T[i+t] - T[j+t]\n", + " }\\bigg\\rvert\n", + " }^{p}\n", + " }\n", + " \\\\\n", + " \\geq{}&\n", + " \\sqrt[\\leftroot{5}\\uproot{5}p]{\n", + " \\sum\\limits_{t=0}^{m-1}{\n", + " \\bigg\\lvert{\n", + " T[i+t] - T[j+t]\n", + " }\\bigg\\rvert\n", + " }^{p}\n", + " }\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "5a4d2b3a", + "metadata": {}, + "source": [ + "Therefore:" + ] + }, + { + "cell_type": "markdown", + "id": "dc578dbd", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " d^{(m+k)}_{j,i} \\geq{}&\n", + " d^{(m)}_{j,i}\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "b51f7143", + "metadata": {}, + "source": [ + "In other words, we can simply use the p-norm distance between $T_{i,m}$ and $T_{j,m}$ as the lower-bound value for the distance between $T_{i,m+k}$ and $T_{j,m+k}$." + ] + }, + { + "cell_type": "markdown", + "id": "0b539ca8", + "metadata": {}, + "source": [ + "## Normalized distance" + ] + }, + { + "cell_type": "markdown", + "id": "91ab346f", + "metadata": {}, + "source": [ + "In z-normalized distance, one should note that $d^{(m+k)}_{j,i} \\geq d^{(m)}_{j,i}$ is not necessarily correct. In other words, the distance between two subsequences does not necessarily increase by making them longer. However, it seems there is a very nice relationship between $d_{j,i}^{(m)}$ and the lower-bound value of $d_{j,i}^{(m+k)}$." + ] + }, + { + "cell_type": "markdown", + "id": "d60acabc", + "metadata": {}, + "source": [ + "### Derving Equation (2)" + ] + }, + { + "cell_type": "markdown", + "id": "1d3734ed", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " d^{(m+k)}_{j,i} ={}& \n", + " \\sqrt{\\sum\\limits_{t=0}^{m+k-1}{{\n", + " \\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{i,m+k}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m+k}}\\right)\n", + " }^{2}}} \n", + " \\\\\n", + " d^{(m+k)}_{j,i} ={}& \n", + " \\sqrt{\n", + " \\sum\\limits_{t=0}^{m-1}{{\n", + " \\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{i,m+k}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m+k}}\\right)\n", + " }^{2}}\n", + " +\n", + " \\sum\\limits_{t=m}^{m+k-1}{{\n", + " \\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{i,m+k}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m+k}}\\right)\n", + " }^{2}}\n", + " } \n", + " \\\\\n", + " \\geq{}&\n", + " \\sqrt{\\sum\\limits_{t=0}^{m-1}{{\n", + " \\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{i,m+k}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m+k}}\\right)\n", + " }^{2}}}\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "72a47d5c", + "metadata": {}, + "source": [ + "So, the Lower-Bound (LB) value for $d_{j,i}^{(m+k)}$ can be obtained by minimizing the right-hand side:" + ] + }, + { + "cell_type": "markdown", + "id": "ade9e7e4", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " LB ={}& \n", + " \\min \\sqrt{\\sum\\limits_{t=0}^{m-1}{{\n", + " \\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{i,m+k}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m+k}}\\right)\n", + " }^{2}}} \n", + " \\\\\n", + " ={}&\n", + " \\min \\sqrt{\\sum\\limits_{t=0}^{m-1}{{\n", + " \\left[\\frac{1}{\\sigma_{j,m+k}}\n", + " \\left(\n", + " \\frac{T[i+t] - \\mu_{i,m+k}}{\\frac{\\sigma_{i,m+k}}{\\sigma_{j,m+k}}} - \\frac{T[j+t] - \\mu_{j,m+k}}{1}\n", + " \\right)\n", + " \\right]\n", + " }^{2}}}\n", + " \\\\\n", + " ={}&\n", + " \\min \\sqrt{\n", + " \\sum\\limits_{t=0}^{m-1}{{\n", + " \\left[\n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m}}\n", + " \\frac{1}{\\sigma_{j,m+k}}\n", + " \\left(\n", + " \\frac{T[i+t] - \\mu_{i,m+k}}{\\frac{\\sigma_{i,m+k}}{\\sigma_{j,m+k}}} \n", + " - \n", + " \\frac{T[j+t] - \\mu_{j,m+k}}{1}\n", + " \\right)\n", + " \\right]\n", + " }^{2}\n", + " }\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\min \\sqrt{\n", + " \\sum\\limits_{t=0}^{m-1}{{\n", + " \\left[\n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + " \\left(\n", + " \\frac{T[i+t] - \\mu_{i,m+k}}{\\sigma_{j,m}\\frac{\\sigma_{i,m+k}}{\\sigma_{j,m+k}}} \n", + " - \n", + " \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\n", + " \\right)\n", + " \\right]\n", + " }^{2}\n", + " }\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}} \\times \\min \\sqrt{\\sum\\limits_{t=0}^{m-1}{\\left(\\frac{T[i+t] - \\mu_{i,m+k}}{\\frac{\\sigma_{j,m} \\sigma_{i,m+k}}{\\sigma_{j,m+k}}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\\right)^{2}}} \\quad(1)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "d410ec5a", + "metadata": {}, + "source": [ + "**Note:** that the unknown variables are $\\mu_{i,m+k}$ and $\\sigma_{i,m+k}$. Also, note that all $\\mu$ and $\\sigma$ values are **constant** regardless of them being known or unknown.
\n", + "\n", + "We subtitute $\\mu_{i,m+k}$ with $\\mu^{'}$, and $\\frac{\\sigma_{j,m} \\sigma_{i,m+k}}{\\sigma_{j,m+k}}$ with $\\sigma^{'}$. Note that the unknown variables are now $\\mu^{'}$ and $\\sigma^{'}$.
\n", + "\n", + "Also, we define $\\alpha_{t}$ as:" + ] + }, + { + "cell_type": "markdown", + "id": "2ade7583", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\alpha_{t} \\triangleq{}& \n", + " {\n", + " \\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}} \\quad (2)\n", + " } \n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "5fe5c9e3", + "metadata": {}, + "source": [ + "Therefore, we have:" + ] + }, + { + "cell_type": "markdown", + "id": "a293197c", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " LB ={}& \n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + " \\sqrt{\\min \\sum \\limits_{t=0}^{m-1} {\\alpha_t^{2}}} \n", + " \\\\\n", + " ={}&\n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + " \\sqrt{\\min f(\\mu^{'}, \\sigma^{'})} \\quad (3)\n", + " \\\\\n", + " f(\\mu^{'}, \\sigma^{'}) ={}&\n", + " \\sum \\limits_{t=0}^{m-1} {\\alpha_t^{2}} \\quad (4)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "e7564257", + "metadata": {}, + "source": [ + "**To find extrema points, we first need to find the critical point(s) by solving the single system of equations below.** In other words, we are looking for $\\mu^{'}$ and $\\sigma^{'}$ that satisfies both equations below:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "c2de39a8", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{\\partial{f}}{\\partial{\\mu^{'}}} = 0 \\quad (5)\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} = 0 \\quad (6)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "a3656f16", + "metadata": {}, + "source": [ + "**Solving $\\frac{\\partial{f}}{\\partial{\\mu^{'}}} = 0$:**" + ] + }, + { + "cell_type": "markdown", + "id": "8b7c8a81", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{\\partial{f}}{\\partial{\\mu^{'}}} ={}& \n", + " \\sum \\limits_{t=0}^{m-1}{\n", + " \\frac{\\partial{(\\alpha_{t}^{2})}}{\\partial{\\mu^{'}}}\n", + " }\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\mu^{'}}} ={}& \n", + " \\sum \\limits_{t=0}^{m-1}{\n", + " 2\\frac{\\partial{(\\alpha_{t})}}{\\partial{\\mu^{'}}}\\alpha_{t}\n", + " }\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\mu^{'}}} ={}&\n", + " \\sum \\limits_{t=0}^{m-1} {\n", + " 2\\left(\n", + " \\frac{-1}{\\sigma^{'}}\n", + " \\right)\n", + " \\alpha_{t}} \n", + " \\\\\n", + " 0 ={}&\n", + " \\frac{-2}{\\sigma^{'}}\\sum \\limits_{t=0}^{m-1}{\\alpha_{t}}\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "6ef98f3f", + "metadata": {}, + "source": [ + "Please note that $\\sigma^{'}$ is constant and thus it was factered out of the summation.
\n", + "This gives us:" + ] + }, + { + "cell_type": "markdown", + "id": "cdc74b21", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sum \\limits_{t=0}^{m-1}{\\alpha_{t}} = 0 \\quad (7)\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "0aad71e0", + "metadata": {}, + "source": [ + "**Exapanding (7):**" + ] + }, + { + "cell_type": "markdown", + "id": "0d3f4dfa", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sum \\limits_{t=0}^{m-1} \\alpha_{t} ={}& \n", + " 0\n", + " \\\\\n", + " \\sum \\limits_{t=0}^{m-1} {\\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}} ={}& \n", + " 0\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}}\\left(\\sum \\limits_{t=0}^{m-1}T[i+t] - \\sum \\limits_{t=0}^{m-1} \\mu^{'}\\right) - \n", + " \\frac{1}{\\sigma_{j,m}}\\left(\\sum \\limits_{t=0}^{m-1}T[j+t] - \\sum \\limits_{t=0}^{m-1} \\mu_{j,m+k}\\right) ={}& \n", + " 0\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}}\\left(m\\mu_{i,m} - m\\mu^{'}\\right) - \n", + " \\frac{1}{\\sigma_{j,m}}\\left(m\\mu_{j,m} - m\\mu_{j,m+k}\\right) ={}& \n", + " 0\n", + " \\\\\n", + " \\sigma_{j,m}\\left(\\mu_{i,m} - \\mu^{'}\\right) - \n", + " \\sigma^{'}\\left(\\mu_{j,m} - \\mu_{j,m+k}\\right) ={}& \n", + " 0\n", + " \\\\\n", + " \\sigma_{j,m} \\mu^{'} + \n", + " \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)\\sigma^{'} - \\sigma_{j,m}\\mu_{i,m} ={}& \n", + " 0 \\quad (8)\n", + "\\end{align} \n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "393ddb8f", + "metadata": {}, + "source": [ + "**Solving $\\frac{\\partial{f}}{\\partial{\\sigma^{'}}} = 0$:**" + ] + }, + { + "cell_type": "markdown", + "id": "4eae27d8", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}& \n", + " \\sum \\limits_{t=0}^{m-1}{\n", + " \\frac{\\partial{(\\alpha_{t}^{2})}}{\\partial{\\sigma^{'}}}\n", + " }\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}& \n", + " \\sum \\limits_{t=0}^{m-1}{\n", + " 2\\frac{\\partial{(\\alpha_{t})}}{\\partial{\\sigma^{'}}}\\alpha_{t}\n", + " }\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}&\n", + " \\sum \\limits_{t=0}^{m-1} {\n", + " 2 \\left(\n", + " \\frac{-\\left({T[i+t] - \\mu^{'}}\\right)}{\\sigma^{'2}}\n", + " \\right)\n", + " \\alpha_{t}} \n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\\sum \\limits_{t=0}^{m-1}{\\left({T[i+t] - \\mu^{'}}\\right) \\alpha_{t}}\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\\sum \\limits_{t=0}^{m-1}{\\left({T[i+t]\\alpha_{t} - \\mu^{'}\\alpha_{t}}\\right)}\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\n", + " {\\left(\n", + " \\sum \\limits_{t=0}^{m-1}{T[i+t]\\alpha_{t}} \n", + " - \n", + " \\sum \\limits_{t=0}^{m-1}{\\mu^{'}\\alpha_{t}}\n", + " \\right)\n", + " }\n", + " \\\\\n", + " \\frac{\\partial{f}}{\\partial{\\sigma^{'}}} ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\n", + " {\\left(\n", + " \\sum \\limits_{t=0}^{m-1}{T[i+t]\\alpha_{t}} \n", + " - \n", + " \\mu^{'}\\sum \\limits_{t=0}^{m-1}{\\alpha_{t}}\n", + " \\right)\n", + " }\n", + " \\\\\n", + " 0 ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\n", + " {\\left(\n", + " \\sum \\limits_{t=0}^{m-1}{T[i+t]\\alpha_{t}} \n", + " - \n", + " \\mu^{'}\\cdot 0\n", + " \\right)\n", + " }\n", + " \\\\\n", + " 0 ={}&\n", + " \\frac{-2}{\\sigma^{'2}}\n", + " {\n", + " \\sum \\limits_{t=0}^{m}{T[i+t]\\alpha_{t}} \n", + " }\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1340817b", + "metadata": {}, + "source": [ + "Note: In the calculations above, we substituted 0 for $\\sum \\limits_{t=0}^{m-1}{\\alpha_{t}}$ according to eq(7)." + ] + }, + { + "cell_type": "markdown", + "id": "c3b80336", + "metadata": {}, + "source": [ + "And, this gives:" + ] + }, + { + "cell_type": "markdown", + "id": "c398718a", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sum \\limits_{t=0}^{m-1}{T[i+t]\\alpha_{t}} ={}&\n", + " 0 \\quad (9)\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "4a34e737", + "metadata": {}, + "source": [ + "**Expanding (9):**" + ] + }, + { + "cell_type": "markdown", + "id": "de3f6023", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sum \\limits_{t=0}^{m-1} T[i+t] \\left(\\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\\right) = 0\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1ce7c9be", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t-1] \n", + " \\left(\n", + " \\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}}\n", + " \\right)\n", + " - \n", + " \\sum\\limits_{t=0}^{m-1}T[i+t-1] \n", + " \\left(\n", + " \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\n", + " \\right)\n", + " ={}& 0\n", + " \\\\\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t] \n", + " \\left(\n", + " T[i+t] - \\mu^{'}\n", + " \\right)\n", + " - \n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t-1] \n", + " \\left(\n", + " T[j+t] - \\mu_{j,m+k}\n", + " \\right)\n", + " ={}& 0\n", + " \\\\\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t]T[i+t]\n", + " -\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t]\\mu^{'}\n", + " \\right) \n", + " - \\\\\n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left(\n", + " {\\sum\\limits_{t=0}^{m-1}T[i+t]T[j+t] \n", + " -\\sum \\limits_{t=0}^{m-1}T[i+t]\\mu_{j,m+k}\n", + " }\n", + " \\right) \n", + " ={}& \n", + " 0\n", + " \\\\\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left(\n", + " \\sum \\limits_{t=0}^{m-1}T[i+t]T[i+t]\n", + " -\n", + " \\mu^{'}\\sum\\limits_{t=0}^{m-1} T[i+t]\n", + " \\right) \n", + " - \\\\\n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}T[i+t]T[j+t]\n", + " -\n", + " \\mu_{j,m+k}\\sum \\limits_{t=0}^{m-1}T[i+t]\n", + " \\right) \n", + " ={}& \n", + " 0 \\quad (*)\n", + "\\end{align} \n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "0c839937", + "metadata": {}, + "source": [ + "Now, recall that the pearson correlation $\\rho_{ij}$ between two subsequences starting at locations $i$ and $j$, respectively, and both of length $m$ is defined as follows:" + ] + }, + { + "cell_type": "markdown", + "id": "82bc9b8e", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align}\n", + "\\rho_{ij} ={}&\n", + " \\frac{\n", + " COV(T_{i,m}T_{j,m})}{\n", + " \\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " E\\left[\n", + " (T_{i,m} - \\mu_{i,m})(T_{j,m} - \\mu_{j,m})\n", + " \\right]}\n", + " {\n", + " \\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\frac{1}{m}\\sum\\limits_{t=0}^{m-1}\n", + " (T[i+t] - \\mu_{i,m})(T[j+t] - \\mu_{j,m})\n", + " }\n", + " {\n", + " \\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]T[j+t] \n", + " -\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " \\mu_{i,m}T[j+t]\n", + " -\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " \\mu_{j,m}T[i+t]\n", + " +\n", + " \\sum\\limits_{t=0}^{m-1}\\mu_{i,m}\\mu_{j,m}\n", + " }{\n", + " m\\sigma_{i,m}\\sigma_{j,,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]T[j+t] \n", + " -\n", + " \\mu_{i,m}\\sum\\limits_{t=0}^{m-1}\n", + " T[j+t]\n", + " -\n", + " \\mu_{j,m}\\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]\n", + " +\n", + " \\sum\\limits_{t=0}^{m-1}\\mu_{i,m}\\mu_{j,m}\n", + " }{\n", + " m\\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]T[j+t] \n", + " -\n", + " \\mu_{i,m}\\cdot m\\mu_{j,m}\n", + " -\n", + " \\mu_{j,m}\\cdot m\\mu_{i,m}\n", + " +\n", + " m\\mu_{i,m}\\mu_{j,m}\n", + " }{\n", + " m\\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]T[j+t] \n", + " -\n", + " m\\mu_{i,m}\\mu_{j,m}\n", + " }{\n", + " m\\sigma_{i,m}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4880c751", + "metadata": {}, + "source": [ + "We can rearrange the pearson correlation equation as follows:
\n", + "$\\sum \\limits_{t=0}^{m-1}T[i+t]T[j+t] = m\\rho\\sigma_{i,m}\\sigma_{j,m} + m\\mu_{i,m}\\mu_{j,m}$ (\\*\\*)" + ] + }, + { + "cell_type": "markdown", + "id": "a01fd0cc", + "metadata": {}, + "source": [ + "**Therefore, with help of (\\*\\*), we continue our calculation from eq(\\*):**" + ] + }, + { + "cell_type": "markdown", + "id": "1543b1f4", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left[\n", + " \\left(\n", + " m\\rho_{ii}\\sigma_{i,m}\\sigma_{i,m} + m\\mu_{i,m}\\mu_{i,m}\n", + " \\right)\n", + " - \n", + " \\mu^{'} \\cdot m\\mu_{i,m}\n", + " \\right] \n", + " - \n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left[\n", + " \\left(\n", + " m\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " + \n", + " m\\mu_{i,m}\\mu_{j,m}\n", + " \\right)\n", + " - \n", + " \\mu_{j,m+k} \\cdot m\\mu_{i,m}\n", + " \\right]\n", + " ={}& 0\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "3ab1a478", + "metadata": {}, + "source": [ + "In the calculations above, we subsituted 1 for $\\rho_{ii}$ as the Pearson Correlation of a subsequence with itself is 1." + ] + }, + { + "cell_type": "markdown", + "id": "182b8064", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left[\n", + " \\left(\n", + " m\\cdot1\\cdot\\sigma_{i,m}^{2} + m\\mu_{i,m}^{2}\n", + " \\right)\n", + " - \n", + " \\mu^{'} \\cdot m\\mu_{i,m}\n", + " \\right] \n", + " - \n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left[\n", + " \\left(\n", + " m\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " + \n", + " m\\mu_{i,m}\\mu_{j,m}\n", + " \\right)\n", + " - \n", + " \\mu_{j,m+k} \\cdot m\\mu_{i,m}\n", + " \\right]\n", + " ={}& 0\n", + " \\\\\n", + " \\frac{1}{\\sigma^{'}\\sigma_{j,m}}\n", + " \\left[\n", + " \\sigma_{j,m}\\left(\n", + " m\\sigma_{i,m}^{2} \n", + " + \n", + " m\\mu_{i,m}^{2} \n", + " - \n", + " \\mu^{'} \\cdot m\\mu_{i,m}\n", + " \\right) \n", + " - \n", + " \\sigma^{'}\\left(\n", + " {m\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " +\n", + " m\\mu_{i,m}\\mu_{j,m} \n", + " -\n", + " \\mu_{j,m+k} \\cdot m\\mu_{i,m}}\n", + " \\right)\n", + " \\right] ={}& 0\n", + " \\\\\n", + " \\frac{m}{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\left[\n", + " \\sigma_{j,m}\\left(\n", + " \\sigma_{i,m}^{2} \n", + " + \n", + " \\mu_{i,m}^{2} \n", + " - \n", + " \\mu^{'} \\mu_{i,m}\n", + " \\right) \n", + " - \n", + " \\sigma^{'}\\left(\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " +\n", + " \\mu_{i,m}\\mu_{j,m}\n", + " -\n", + " \\mu_{j,m+k} \\mu_{i,m}}\n", + " \\right)\n", + " \\right]\n", + " ={}& 0\n", + " \\\\\n", + " \\sigma_{j,m}\\left(\n", + " \\sigma_{i,m}^{2} \n", + " + \n", + " \\mu_{i,m}^{2} \n", + " - \n", + " \\mu^{'} \\mu_{i,m}\n", + " \\right) \n", + " - \n", + " \\sigma^{'}\\left(\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " +\n", + " \\mu_{i,m}\\mu_{j,m}\n", + " -\n", + " \\mu_{j,m+k} \\mu_{i,m}}\n", + " \\right)\n", + " ={}& 0\n", + " \\\\\n", + " \\sigma_{j,m}\\left(\n", + " \\sigma_{i,m}^{2} \n", + " + \n", + " \\mu_{i,m}^{2}\n", + " \\right)\n", + " - \n", + " \\sigma_{j,m} \\cdot\n", + " \\mu^{'} \\mu_{i,m}\n", + " - \n", + " \\sigma^{'}\\left(\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " +\n", + " \\mu_{i,m}\\mu_{j,m}\n", + " -\n", + " \\mu_{j,m+k} \\mu_{i,m}}\n", + " \\right)\n", + " ={}& 0\n", + " \\\\\n", + " - \\sigma_{j,m}\\left(\n", + " \\sigma_{i,m}^{2} \n", + " + \n", + " \\mu_{i,m}^{2}\n", + " \\right)\n", + " + \n", + " \\sigma_{j,m} \\cdot\n", + " \\mu^{'} \\mu_{i,m}\n", + " + \n", + " \\sigma^{'}\\left(\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} \n", + " +\n", + " \\mu_{i,m}\\mu_{j,m}\n", + " -\n", + " \\mu_{j,m+k} \\mu_{i,m}}\n", + " \\right)\n", + " ={}& 0\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1d37830b", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\mu_{i,m}\\sigma_{j,m}\\mu^{'} + (\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m} - \\mu_{i,m}\\mu_{j,m+k})\\sigma^{'} - \\sigma_{j,m}(\\mu_{i,m}^{2} + \\sigma_{i,m}^{2}) = 0 \\quad (10)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "6adaea06", + "metadata": {}, + "source": [ + "**Now, it is time to solve equations (8) and (10), provided below:**" + ] + }, + { + "cell_type": "markdown", + "id": "6ac05b5f", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "\\sigma_{j,m} \\mu^{'} + \n", + " \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)\\sigma^{'} - \\sigma_{j,m}\\mu_{i,m} \n", + " ={}& 0 \\quad(8)\n", + " \\\\\n", + " \\mu_{i,m}\\sigma_{j,m}\\mu^{'} + (\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m} - \\mu_{i,m}\\mu_{j,m+k})\\sigma^{'} - \\sigma_{j,m}(\\mu_{i,m}^{2} + \\sigma_{i,m}^{2}) \n", + " ={}& 0 \\quad(10)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "b2322ecc", + "metadata": {}, + "source": [ + "Note that in the system of equations above, the unknown variables are $\\mu^{'}$ and $\\sigma^{'}$, and the remaining ones are known." + ] + }, + { + "cell_type": "markdown", + "id": "e40d711e", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "-\\mu_{i,m}\\left[\n", + " \\sigma_{j,m} \\mu^{'} \n", + " + \n", + " \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)\\sigma^{'} \n", + " - \n", + " \\sigma_{j,m}\\mu_{i,m} \n", + " \\right]\n", + " ={}& 0 \\quad(8')\n", + " \\\\\n", + " \\mu_{i,m}\\sigma_{j,m}\\mu^{'} + (\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m} - \\mu_{i,m}\\mu_{j,m+k})\\sigma^{'} - \\sigma_{j,m}(\\mu_{i,m}^{2} + \\sigma_{i,m}^{2}) \n", + " ={}& 0 \\quad(10)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "4dfc6b45", + "metadata": {}, + "source": [ + "$(8')+(10)$ gives:" + ] + }, + { + "cell_type": "markdown", + "id": "c798dc6b", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "-\\mu_{i,m}\\sigma_{j,m} \\mu^{'} - \n", + " \\mu_{i,m}\\mu_{j,m}\\sigma^{'} + \\mu_{i,m}\\mu_{j,m+k}\\sigma^{'} \n", + " + \\sigma_{j,m}\\mu_{i,m}^{2} +\n", + " \\mu_{i,m}\\sigma_{j,m}\\mu^{'} + \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}\\sigma^{'} + \\mu_{i,m}\\mu_{j,m}\\sigma^{'} - \\mu_{i,m}\\mu_{j,m+k}\\sigma^{'} - \\sigma_{j,m}\\mu_{i,m}^{2} - \\sigma_{j,m}\\sigma_{i,m}^{2}\n", + " ={}& 0\n", + " \\\\\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}\\sigma^{'} - \\sigma_{j,m}\\sigma_{i,m}^{2} \n", + " ={}& 0\n", + " \\\\\n", + " \\sigma_{i,m}\\sigma_{j,m}\n", + " \\left(\n", + " \\rho_{ij}\\sigma^{'} - \\sigma_{i,m}\n", + " \\right)\n", + " ={}&\n", + " 0\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "3627a49a", + "metadata": {}, + "source": [ + "Hence:" + ] + }, + { + "cell_type": "markdown", + "id": "de0702cf", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sigma^{'} = \\frac{\\sigma_{i,m}}{\\rho_{ij}} \\quad (11)\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "ed3f7802", + "metadata": {}, + "source": [ + "Note that we assumed $\\sigma_{i,m}$ and $\\sigma_{j,m}$ cannot be zero. Also, since standard deviations are positive, eq(11) is valid only if $\\rho_{ij} \\gt 0$." + ] + }, + { + "cell_type": "markdown", + "id": "91752bef", + "metadata": {}, + "source": [ + "And, subsituting eq(11) in eq(8):" + ] + }, + { + "cell_type": "markdown", + "id": "631d7d57", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "\\sigma_{j,m} \\mu^{'} + \n", + " \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)(\\frac{\\sigma_{i,m}}{\\rho_{ij}}) - \\sigma_{j,m}\\mu_{i,m} \n", + " ={}& 0 \n", + " \\\\\n", + " \\frac{1}{\\sigma_{j,m}}\\left[\n", + " \\sigma_{j,m} \\mu^{'} + \n", + " \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)(\\frac{\\sigma_{i,m}}{\\rho_{ij}}) - \\sigma_{j,m}\\mu_{i,m} \n", + " \\right]\n", + " ={}& 0 \n", + " \\\\\n", + " \\mu^{'} + \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right)(\\frac{\\sigma_{i,m}}{\\rho_{ij}\\sigma_{j,m}}) - \\mu_{i,m} \n", + " ={}& 0 \n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "335173da", + "metadata": {}, + "source": [ + "Hence:" + ] + }, + { + "cell_type": "markdown", + "id": "8efc2627", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\mu^{'} = \\mu_{i,m} - \\frac{\\sigma_{i,m}}{\\rho_{ij}\\sigma_{j,m}} \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right) \\quad(12)\n", + "\\end{align}\n", + "$$\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "4278ff7e", + "metadata": {}, + "source": [ + "**Therefore, the critical point of function $f(\\mu^{'},\\sigma^{'})$ is:**" + ] + }, + { + "cell_type": "markdown", + "id": "e0104b24", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\sigma^{'} ={}& \n", + " \\frac{\\sigma_{i,m}}{\\rho_{ij}} \\quad (11)\n", + " \\\\\n", + " \\mu^{'} ={}& \n", + " \\mu_{i,m} - \\frac{\\sigma_{i,m}}{\\rho_{ij}\\sigma_{j,m}} \\left(\\mu_{j,m} - \\mu_{j,m+k}\\right) \\quad(12)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "b266cfb2", + "metadata": {}, + "source": [ + "**NOTE:** It is important to note that eq(11) and eq(12) are favorable to us as they give the $\\mu^{'}$ and $\\sigma^{'}$ of the critical point of `f` as a function of known parameters $\\mu_{i,m}$, $\\sigma_{i,m}$, $\\mu_{j,m}$, $\\sigma_{j,m}$, $\\rho_{ij}$, and $\\mu_{j,m+k}$. Therefore, we can calculate the lower-bound LB as a function of the aforementioned parameters. \n", + "\n", + "**NOTE:** It is worthwhile to reiterate the fact that the solution is valid when $\\rho_{ij} \\gt 0$. (We will discuss $\\rho_{ij} \\leq 0$ later...)" + ] + }, + { + "cell_type": "markdown", + "id": "a0e36dfc", + "metadata": {}, + "source": [ + "Now that we calculated the values $\\mu^{'}$ and $\\sigma^{'}$ of the crtical point, we need to plug them in the function $f(.)$ to find the extremum value. However, using these values directly in function $f(.)$ might make the calculation difficult. Therefore, we prefer to use higher-level equations (7) and (9) to first simplify $f_{min}(.)$. \n", + "\n", + "**NOTE:** we have been solving the single system of equations (5) and (6). Therefore, the calculated values $\\mu^{'}$(11) and $\\sigma^{'}$(12) should satisfy all equations (5), (6), (7), (8), (9), and (10) discovered throughout the solution.
" + ] + }, + { + "cell_type": "markdown", + "id": "92abd2a2", + "metadata": {}, + "source": [ + "**Start with equation (4):**" + ] + }, + { + "cell_type": "markdown", + "id": "b51d32b2", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f(\\mu^{'},\\sigma^{'}) ={}&\n", + " \\sum \\limits_{t=0}^{m-1}\\alpha_{t}^{2}\n", + " \\\\\n", + " ={}&\n", + " \\sum \\limits_{t=0}^{m-1}\\alpha_{t} \\cdot \\alpha_{t}\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "7afe0a3d", + "metadata": {}, + "source": [ + "And, we replace one of $\\alpha_{t}$ with its equivalent term provided in eq(2)..." + ] + }, + { + "cell_type": "markdown", + "id": "bfb10bce", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f_{min}(\\mu^{'},\\sigma^{'}) ={}&\n", + " \\sum\\limits_{t=0}^{m-1}{\n", + " {\\alpha_{t}\n", + " \\left(\n", + " \\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\n", + " \\right)\n", + " }}\n", + " \\\\\n", + " ={}&\n", + " {\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]\\alpha_{t} \n", + " - \n", + " \\sum\\limits_{t=0}^{m-1}\n", + " \\mu^{'}\\alpha_{t}\n", + " \\right)\n", + " - \\frac{1}{\\sigma_{j,m}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[j+t]\\alpha_{t} \n", + " - \n", + " \\sum\\limits_{t=0}^{m-1}\n", + " \\mu_{j,m+k}\\alpha_{t}\n", + " \\right)\n", + " } \n", + " \\\\ \n", + " ={}&\n", + " {\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}\n", + " T[i+t]\\alpha_{t} \n", + " - \n", + " \\mu^{'}\\sum\\limits_{t=0}^{m-1}\\alpha_{t}\n", + " \\right)\n", + " - \n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}T[j+t]\\alpha_{t} \n", + " - \n", + " \\mu_{j,m+k}\\sum\\limits_{t=0}^{m-1}\\alpha_{t}\n", + " \\right)\n", + " } \n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "4a9e3f03", + "metadata": {}, + "source": [ + "And, now with help of eq(7), $\\sum\\limits_{t=0}^{m-1}{\\alpha_{t}}=0$, and the eq(9), $\\sum\\limits_{t=0}^{m-1}{T[i+t]\\alpha_{t}}=0$, we will have:" + ] + }, + { + "cell_type": "markdown", + "id": "650cae87", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f_{min}(\\mu^{'},\\sigma^{'}) ={}&\n", + " {\n", + " \\frac{1}{\\sigma^{'}}\n", + " \\left(\n", + " 0 - \\mu^{'} \\cdot 0\n", + " \\right) \n", + " - \n", + " \\frac{1}{\\sigma_{j,m}}\n", + " \\left(\n", + " \\sum\\limits_{t=0}^{m-1}T[j+t]\\alpha_{t} - \\mu_{j,m+k}\\cdot 0\n", + " \\right)\n", + " } \n", + " \\\\ \n", + " ={}&\n", + " {\n", + " - \\frac{1}{\\sigma_{j,m}} \\sum\\limits_{t=0}^{m-1}T[j+t]\\alpha_{t}\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {\n", + " - \\frac{1}{\\sigma_{j,m}} \n", + " \\sum\\limits_{t=0}^{m-1}{\\left[\n", + " T[j+t]\\left(\n", + " \\frac{T[i+t] - \\mu^{'}}{\\sigma^{'}} - \\frac{T[j+t] - \\mu_{j,m+k}}{\\sigma_{j,m}}\n", + " \\right)\n", + " \\right]\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {\n", + " - \\frac{1}{\\sigma_{j,m}} \n", + " \\sum\\limits_{t=0}^{m-1}{\n", + " \\left(\n", + " \\frac{T[i+t]T[j+t] - \\mu^{'}T[j+t]}{\\sigma^{'}} - \\frac{T[j+t]T[j+t] - \\mu_{j,m+k}T[j+t]}{\\sigma_{j,m}}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{1}{\\sigma_{j,m}} \n", + " {\n", + " \\left(\n", + " \\frac{\\sum\\limits_{t=0}^{m-1}T[i+t]T[j+t] - \\mu^{'}\\sum\\limits_{t=0}^{m-1}T[j+t]}{\\sigma^{'}} \n", + " - \n", + " \\frac{\\sum\\limits_{t=0}^{m-1}T[j+t]T[j+t] - \\mu_{j,m+k}\\sum\\limits_{t=0}^{m-1}T[j+t]}{\\sigma_{j,m}}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "9f2ca2da", + "metadata": {}, + "source": [ + "And, now with help of the fact that $\\sum{T} = m\\mu$ and also the Pearon Correlation equation (\\*\\*)..." + ] + }, + { + "cell_type": "markdown", + "id": "35db152a", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f_{min}(\\mu^{'},\\sigma^{'}) ={}& \n", + " {- \\frac{1}{\\sigma_{j,m}} \n", + " {\n", + " \\left(\n", + " \\frac{(m\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + m\\mu_{i,m}\\mu_{j,m}) - \\mu^{'} \\cdot m\\mu_{j,m}}{\\sigma^{'}} \n", + " - \n", + " \\frac{(m\\rho_{jj}\\sigma_{j,m}^{2} + m\\mu_{j,m}^{2}) - \\mu_{j,m+k} \\cdot m\\mu_{j,m}}{\\sigma_{j,m}}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{1}{\\sigma_{j,m}} \n", + " {\n", + " \\left[\n", + " \\frac{\n", + " m\\left(\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m} - \\mu^{'} \\cdot \\mu_{j,m}\n", + " \\right)\n", + " }{\n", + " \\sigma^{'}\n", + " } \n", + " - \n", + " \\frac{\n", + " m\\left(\n", + " 1\\cdot\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m+k} \\cdot \\mu_{j,m}\n", + " \\right)\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\n", + " \\right]\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma^{'}} \n", + " {\n", + " \\left(\n", + " {\\sigma_{j,m}(\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m} - \\mu_{j,m}\\mu^{'})} \n", + " - \n", + " {\\sigma^{'}(\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m}\\mu_{j,m+k})}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma^{'}} \n", + " {\n", + " \\left(\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}^{2} + \\mu_{i,m}\\mu_{j,m}\\sigma_{j,m} - \\mu_{j,m}\\sigma_{j,m}\\mu^{'}} \n", + " - \n", + " {\\sigma^{'}(\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m}\\mu_{j,m+k})}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "cfd5a617", + "metadata": {}, + "source": [ + "And, now we are at a good position to plug in the values $\\mu^{'}$(11) and $\\sigma^{'}$(12):" + ] + }, + { + "cell_type": "markdown", + "id": "f3e25620", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f_{min}(\\mu^{'},\\sigma^{'}) ={}& \n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\n", + " (\\frac{\\sigma_{i,m}}{\\rho_{ij}})\n", + " } \n", + " {\n", + " \\left[\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}^{2} + \n", + " \\mu_{i,m}\\mu_{j,m}\\sigma_{j,m} - \n", + " \\mu_{j,m}\\sigma_{j,m}\\left({\n", + " \\mu_{i,m} - \\frac{\\sigma_{i,m}}{\\rho_{ij}\\sigma_{j,m}}(\\mu_{j,m}-\\mu_{j,m+k})\n", + " }\n", + " \\right)} \n", + " - \n", + " {(\\frac{\\sigma_{i,m}}{\\rho_{ij}})(\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m}\\mu_{j,m+k})}\n", + " \\right]\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m\\rho_{ij}}{\\sigma_{j,m}^{2}\\sigma_{i,m}} \n", + " {\n", + " \\left[\n", + " {\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}^{2} \n", + " + \n", + " \\mu_{i,m}\\mu_{j,m}\\sigma_{j,m} \n", + " - \n", + " {\n", + " \\mu_{j,m}\\sigma_{j,m}\\mu_{i,m} \n", + " + \n", + " \\frac{\\sigma_{i,m}}{\\rho_{ij}\\sigma_{j,m}}{\\mu_{j,m}\\sigma_{j,m}}(\\mu_{j,m}-\\mu_{j,m+k})\n", + " }\n", + " } \n", + " - \n", + " {\\frac{\\sigma_{i,m}}{\\rho_{ij}}(\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m}\\mu_{j,m+k})}\n", + " \\right]\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma_{i,m}} \n", + " {\n", + " \\left[\n", + " {\\rho_{ij}^{2}\\sigma_{i,m}\\sigma_{j,m}^{2} \n", + " + \n", + " \\rho_{ij}\\mu_{i,m}\\mu_{j,m}\\sigma_{j,m} \n", + " - \n", + " {\n", + " \\rho_{ij}\\mu_{j,m}\\sigma_{j,m}\\mu_{i,m} \n", + " + \n", + " \\mu_{j,m}\\sigma_{i,m}(\\mu_{j,m}-\\mu_{j,m+k})\n", + " }\n", + " } \n", + " - \n", + " {\\sigma_{i,m}(\\sigma_{j,m}^{2} + \\mu_{j,m}^{2} - \\mu_{j,m}\\mu_{j,m+k})}\n", + " \\right]\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma_{i,m}} \n", + " {\n", + " \\left(\n", + " {\\rho_{ij}^{2}\\sigma_{i,m}\\sigma_{j,m}^{2} \n", + " + \n", + " \\rho_{ij}\\mu_{i,m}\\mu_{j,m}\\sigma_{j,m} \n", + " - \n", + " {\n", + " \\rho_{ij}\\mu_{j,m}\\sigma_{j,m}\\mu_{i,m} \n", + " + \n", + " \\mu_{j,m}\\sigma_{i,m}\\mu_{j,m} - \\mu_{j,m}\\sigma_{i,m}\\mu_{j,m+k}\n", + " }\n", + " }\n", + " - \n", + " {\\sigma_{i,m}\\sigma_{j,m}^{2} - \\sigma_{i,m}\\mu_{j,m}^{2} + \\sigma_{i,m}\\mu_{j,m}\\mu_{j,m+k}}\n", + " \\right)\n", + " }\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma_{i,m}}\n", + " \\left( \n", + " {\\rho_{ij}^{2}\\sigma_{i,m}\\sigma_{j,m}^{2} \n", + " - \n", + " \\sigma_{i,m}\\sigma_{j,m}^{2} \n", + " }\n", + " \\right)\n", + " } \n", + " \\\\\n", + " ={}&\n", + " {- \\frac{m}{\\sigma_{j,m}^{2}\\sigma_{i,m}}\n", + " (\\rho_{ij}^{2} - 1)\n", + " \\sigma_{i,m}\\sigma_{j,m}^{2}\n", + " }\n", + " \\\\\n", + " ={}&\n", + " m(1-\\rho_{ij}^{2}) \\quad (13)\n", + "\\end{align} \n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "64dc1027", + "metadata": {}, + "source": [ + "**Finally, with eq(3), the lower-bound `LB` for distance profile of `T[j:j+m+k]` is as follows:**" + ] + }, + { + "cell_type": "markdown", + "id": "98db40a5", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " LB ={}& \n", + " \\frac{\n", + " \\sigma_{j,m}\n", + " }{\\sigma_{j,m+k}\n", + " } \\sqrt{m (1 - \\rho_{ij}^{2})} \\quad \\text{if} \\, \\rho > 0 \\quad (14)\n", + " \\\\\n", + " \\\\\n", + " \\rho_{ij} ={}& \n", + " \\frac{\\sum \\limits_{t=0}^{m-1}T[i+t]T[j+t] - m\\mu_{i,m}\\mu_{j,m} }{m\\sigma_{i,m}\\sigma_{j,m}}\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "8cbad624", + "metadata": {}, + "source": [ + "**Note:**
\n", + "* Note that eq(12) is valid only for $\\rho_{ij} > 0$. Therefore, we can use the formula (14) to calculate $LB$ only if $\\rho_{ij} > 0$. \n", + "* The pearson correlation, $\\rho_{ij}$, can be also obtained with help of $ED_{z-norm}$ between subsequences `T[i:i+m]` and `T[j:j+m]`.\n", + "\n", + "In fact: $d_{i,j}^{(m)} = \\sqrt{2m(1-\\rho_{ij})}$, where $d_{i,j}^{(m)}$ is the z-norm euclidean distance between two sequences of length `m` that start at index `i` and `j`.\n", + "\n", + "**Pending...**
\n", + "* We need to analyze the behavior of function `f` to verify that this local minimum is actually the global minimum for this function (more on this later after we derive LB for case $\\rho_{ij} \\leq 0$.)" + ] + }, + { + "cell_type": "markdown", + "id": "a5370108", + "metadata": {}, + "source": [ + "### Derving Equation (2): Continued\n", + "**How about LB for the case $\\rho_{ij} \\leq 0$?**" + ] + }, + { + "cell_type": "markdown", + "id": "fc19b2dd", + "metadata": {}, + "source": [ + "So far, we have derived the first sub-function of the piecewise function provided in the eq(2) of the paper VALMOD, that is LB for $\\rho_{ij} \\gt 0$.
\n", + "Now, we would like to derive the second sub-function, where LB is defined for $\\rho_{ij} \\leq 0$." + ] + }, + { + "cell_type": "markdown", + "id": "a4f11acc", + "metadata": {}, + "source": [ + "We start with eq(4), $f(\\mu^{'}, \\sigma^{'}) = \\sum \\limits_{t=0}^{m-1} {\\alpha_t^{2}}$, and we replace $\\alpha_{t}$ with its equivalent term, see eq(2). Therefore:" + ] + }, + { + "cell_type": "markdown", + "id": "1aac6ab8", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "f(\\mu^{'},\\sigma^{'}) ={}& \n", + " \\sum \\limits_{t=0}^{m-1}\n", + " \\left(\n", + " \\frac{\n", + " T[i+t] - \\mu^{'}\n", + " }{\n", + " \\sigma^{'}\n", + " } \n", + " - \n", + " \\frac{\n", + " T[j+t] - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\n", + " \\right)^{2}\n", + " \\quad (15)\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "bf007040", + "metadata": {}, + "source": [ + "Inside the summation, we use the formula: $(A \\pm B)^{2} = A^{2} + B^{2} \\pm 2AB$" + ] + }, + { + "cell_type": "markdown", + "id": "f8d24612", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f(\\mu^{'},\\sigma^{'}) ={}& \n", + " \\sum \\limits_{t=0}^{m-1}\n", + " \\left[\n", + " \\left(\n", + " \\frac{\n", + " T[i+t] - \\mu^{'}\n", + " }{\n", + " \\sigma^{'}\n", + " }\\right)^{2}\n", + " +\n", + " \\left(\n", + " \\frac{\n", + " T[j+t] - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\n", + " \\right)^{2}\n", + " -\n", + " 2\n", + " \\left(\\frac{\n", + " T[i+t] - \\mu^{'}\n", + " }{\n", + " \\sigma^{'}\n", + " }\\right)\n", + " \\left(\\frac{\n", + " T[j+t] - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\n", + " \\right)\n", + " \\right]\n", + " \\\\\n", + " \\\\\n", + " ={}&\n", + " \\sum \\limits_{t=0}^{m-1}\n", + " \\left[\n", + " \\left(\n", + " \\frac{\n", + " T[i+t]^{2} + \\mu^{'2} - 2T[i+t]\\mu^{'}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\\right)\n", + " +\n", + " \\left(\n", + " \\frac{\n", + " T[j+t]^{2} + \\mu_{j,m+k}^{2} - 2 T[j+t]\\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " \\right)\n", + " -\n", + " 2\n", + " \\left(\\frac{\n", + " T[i+t]T[j+t] \n", + " - T[i+t]\\mu_{j,m+k}\n", + " - T[j+t]\\mu^{'}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\right)\n", + " \\right]\n", + " \\\\\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sum \\limits_{t=0}^{m-1}T[i+t]^{2} + \\sum \\limits_{t=0}^{m-1}\\mu^{'2} - 2\\mu^{'}\\sum \\limits_{t=0}^{m-1}T[i+t]\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " \\sum \\limits_{t=0}^{m-1}T[j+t]^{2} + \\sum \\limits_{t=0}^{m-1}\\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\sum \\limits_{t=0}^{m-1}T[j+t]}{\\sigma_{j,m}^{2}}\n", + " -\n", + " 2\n", + " \\frac{\n", + " \\sum \\limits_{t=0}^{m-1}T[i+t]T[j+t] \n", + " - \\mu_{j,m+k}\\sum \\limits_{t=0}^{m-1}T[i+t]\n", + " - \\mu^{'}\\sum \\limits_{t=0}^{m-1}T[j+t]\n", + " + \\sum \\limits_{t=0}^{m-1}\\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "c1cbd849", + "metadata": {}, + "source": [ + "With help of Pearson Correlation equation (\\*\\*), we have:" + ] + }, + { + "cell_type": "markdown", + "id": "bb5a2896", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "f(\\mu^{'},\\sigma^{'}) ={}& \n", + " \\frac{\n", + " (m\\rho_{ii}\\sigma_{i,m}^{2} + m\\mu_{i,m}^{2}) + m\\mu^{'2} - 2\\mu^{'}\\cdot m\\mu_{i,m}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " (m\\rho_{jj}\\sigma_{j,m}^{2} + m\\mu_{j,m}^{2}) + m\\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\cdot m\\mu_{j,m}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\n", + " \\frac{\n", + " (m\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + m\\mu_{i,m}\\mu_{j,m}) \n", + " - \\mu_{j,m+k}\\cdot m\\mu_{i,m}\n", + " - \\mu^{'} \\cdot m\\mu_{j,m}\n", + " + m\\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "f54b458f", + "metadata": {}, + "source": [ + "Recall that $\\rho_{ii}=1$ and $\\rho_{jj}=1$. Therefore:" + ] + }, + { + "cell_type": "markdown", + "id": "755955af", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "f(\\mu^{'},\\sigma^{'}) ={}& \n", + " m\\left[\n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + \\mu_{i,m}^{2} + \\mu^{'2} - 2\\mu^{'}\\mu_{i,m}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " \\sigma_{j,m}^{2} + \\mu_{j,m}^{2} + \\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\mu_{j,m}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\n", + " \\frac{\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\right]\n", + " \\\\\n", + " \\\\\n", + " ={}&\n", + " m\\left[\n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + \\mu_{i,m}^{2} + \\mu^{'2} - 2\\mu^{'}\\mu_{i,m}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\left(1\n", + " +\n", + " \\frac{\n", + " \\mu_{j,m}^{2} + \\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\mu_{j,m}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " \\right)\n", + " -\n", + " 2\n", + " \\frac{\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\right]\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "96db6201", + "metadata": {}, + "source": [ + "Hence:" + ] + }, + { + "cell_type": "markdown", + "id": "4359532f", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f(\\mu^{'},\\sigma^{'}) ={}& \n", + " m \\left[1 + g(\\mu^{'},\\sigma^{'})\\right] \\quad (16) \n", + " \\\\\n", + " g(\\mu^{'},\\sigma^{'}) ={}& \n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + \\mu_{i,m}^{2} + \\mu^{'2} - 2\\mu^{'}\\mu_{i,m}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " \\mu_{j,m}^{2} + \\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\mu_{j,m}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\n", + " \\frac{\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " } \\quad(17)\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "d73539ec", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " g(\\mu^{'},\\sigma^{'}) ={}& \n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + \\mu_{i,m}^{2} + \\mu^{'2} - 2\\mu^{'}\\mu_{i,m}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " \\mu_{j,m}^{2} + \\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\mu_{j,m}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\n", + " \\frac{\n", + " \\rho_{ij}\\sigma_{i,m}\\sigma_{j,m} + \\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\\\\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + (\\mu_{i,m}^{2} + \\mu^{'2} - 2\\mu^{'}\\mu_{i,m})\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " (\\mu_{j,m}^{2} + \\mu_{j,m+k}^{2} - 2\\mu_{j,m+k}\\mu_{j,m})\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\n", + " \\left(\n", + " \\frac{\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}}{\\sigma^{'}\\sigma_{j,m}}\n", + " +\n", + " \\frac{\\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " }\n", + " \\right)\n", + " \\\\\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + (\\mu_{i,m}-\\mu^{'})^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " (\\mu_{j,m} - \\mu_{j,m+k})^{2}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\\frac{\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}}{\\sigma^{'}\\sigma_{j,m}}\n", + " -\n", + " 2\\frac{\\mu_{i,m}\\mu_{j,m}\n", + " - \\mu_{j,m+k}\\mu_{i,m}\n", + " - \\mu^{'} \\mu_{j,m}\n", + " + \\mu^{'}\\mu_{j,m+k}\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " } \n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2} + (\\mu_{i,m}-\\mu^{'})^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{\n", + " (\\mu_{j,m} - \\mu_{j,m+k})^{2}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2\\frac{\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}}{\\sigma^{'}\\sigma_{j,m}}\n", + " -\n", + " 2\\frac{(\\mu_{i,m}-\\mu^{'})(\\mu_{j,m}\n", + " - \\mu_{j,m+k})\n", + " }{\n", + " \\sigma^{'}\\sigma_{j,m}\n", + " } \n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " \\frac{(\\mu_{i,m}-\\mu^{'})^{2}}{\\sigma^{'2}}\n", + " +\n", + " \\frac{\n", + " (\\mu_{j,m} - \\mu_{j,m+k})^{2}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " +\n", + " 2\\frac{-\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}}{\\sigma^{'}\\sigma_{j,m}}\n", + " -\n", + " 2(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}})(\n", + " \\frac{\\mu_{j,m}\n", + " - \\mu_{j,m+k}}{\\sigma_{j,m}})\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " 2\\frac{-\\rho_{ij}\\sigma_{i,m}\\sigma_{j,m}}{\\sigma^{'}\\sigma_{j,m}}\n", + " +\n", + " \\left[\n", + " \\frac{(\\mu_{i,m}-\\mu^{'})^{2}}{\\sigma^{'2}}\n", + " +\n", + " \\frac{\n", + " (\\mu_{j,m} - \\mu_{j,m+k})^{2}\n", + " }{\n", + " \\sigma_{j,m}^{2}\n", + " }\n", + " -\n", + " 2(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}})(\n", + " \\frac{\\mu_{j,m}\n", + " - \\mu_{j,m+k}}{\\sigma_{j,m}})\n", + " \\right]\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " 2\\frac{-\\rho_{ij}\\sigma_{i,m}}{\\sigma^{'}}\n", + " +\n", + " \\left[\n", + " (\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}})^{2}\n", + " +\n", + " (\\frac{\n", + " \\mu_{j,m} - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " })^{2}\n", + " -\n", + " 2(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}})(\n", + " \\frac{\\mu_{j,m}\n", + " - \\mu_{j,m+k}}{\\sigma_{j,m}})\n", + " \\right]\n", + " \\\\\n", + " ={}&\n", + " \\frac{\n", + " \\sigma_{i,m}^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " 2\\frac{-\\rho_{ij}\\sigma_{i,m}}{\\sigma^{'}}\n", + " +\n", + " \\left[\n", + " \\left(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}}\\right)\n", + " -\n", + " \\left(\\frac{\n", + " \\mu_{j,m} - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\\right)\n", + " \\right]^{2} \\quad (18)\n", + " \\\\\n", + " \\geq{}&\n", + " 2\\frac{(-\\rho_{ij})\\sigma_{i,m}}{\\sigma^{'}} \\quad (19)\n", + " \\\\\n", + " \\geq{}&\n", + " 0\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1f8c0fb5", + "metadata": {}, + "source": [ + "NOTE: Since $\\rho_{i,j} \\leq 0$, the second term becoms non-negative. Therefore:" + ] + }, + { + "cell_type": "markdown", + "id": "d435f4fc", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " g(\\mu^{'},\\sigma^{'}) \\geq{}& 0\n", + " \\\\\n", + " 1 + g(\\mu^{'},\\sigma^{'}) \\geq{}& 1\n", + " \\\\\n", + " m\\left[1 + g(\\mu^{'},\\sigma^{'})\\right] \\geq{}& m\n", + " \\\\\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "125c27bc", + "metadata": {}, + "source": [ + "Therefore, according to eq(16), $f(\\mu^{'},\\sigma^{'}) = m \\left[1 + g(\\mu^{'},\\sigma^{'})\\right]$, we have: $f(\\mu^{'},\\sigma^{'}) \\geq m$, and according to eq(3), $LB = \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\\sqrt{\\min f(\\mu^{'},\\sigma^{'})}$, we can see that:" + ] + }, + { + "cell_type": "markdown", + "id": "06f789ce", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " LB ={}& \n", + " \\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\\sqrt{m} \\quad \\text{ if } \\rho_{ij} \\leq 0\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "810ab4ae", + "metadata": {}, + "source": [ + "**NOTE:** Please note that a stronger LB for $\\rho_{ij} \\leq 0$ is $2\\frac{(-\\rho_{ij})\\sigma_{i,m}}{\\sigma^{'}}$; see eq(19) above. **However,** this has $\\sigma^{'}$ which is unknown. we would like to find LB that is only based on known parameters. Therefore, we are okay with the LB proposed in the paper." + ] + }, + { + "cell_type": "markdown", + "id": "a8b816ff", + "metadata": {}, + "source": [ + "### Derving Equation (2): Continued\n", + "**Is the LB calculated for the case $\\rho_{ij} \\gt 0$ a global minimum?**" + ] + }, + { + "cell_type": "markdown", + "id": "fc7711bb", + "metadata": {}, + "source": [ + "We need to show that the LB discovered for $\\rho_{ij} \\gt 0$ is actually a global minimum. In other words, we need to show that the inequation below holds true for all $\\rho_{ij} \\gt 0$:" + ] + }, + { + "cell_type": "markdown", + "id": "cc4dc1b6", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " f(\\mu^{'},\\sigma^{'}) \\geq{}&\n", + " f(\\mu_{c}^{'},\\sigma_{c}^{'})\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "81e012b9", + "metadata": {}, + "source": [ + "where, $\\mu_{c}^{'}$ (eq(11)) and $\\sigma_{c}^{'}$ (eq(12)) are the values of the critical point." + ] + }, + { + "cell_type": "markdown", + "id": "372a014e", + "metadata": {}, + "source": [ + "We replace left-hand side $f(\\mu^{'},\\sigma^{'})$ with its equivalent term (16), and we replace $f(\\mu_{c}^{'},\\sigma_{c}^{'})$ with eq(13), i.e. $m(1 - \\rho_{ij}^{2})$. Therefore:" + ] + }, + { + "cell_type": "markdown", + "id": "e10ed8a8", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " m \\left[1 + g(\\mu^{'},\\sigma^{'})\\right] \\geq{}& m(1 - \\rho_{ij}^{2})\n", + " \\\\\n", + " 1 + g(\\mu^{'},\\sigma^{'}) \\geq{}& 1 - \\rho_{ij}^{2}\n", + " \\\\\n", + " g(\\mu^{'},\\sigma^{'}) + \\rho_{ij}^{2} \\geq{}& 0 \\quad (20)\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "7988c834", + "metadata": {}, + "source": [ + "Therefore, we need to show that inequation (20) is satisfied for all $\\mu^{'}$ and $\\sigma^{'}$ when $\\rho_{i,j} \\geq 0$.
\n", + "We now subtitute eq(18) for $g(.)$. Thus:" + ] + }, + { + "cell_type": "markdown", + "id": "ea2a5a7e", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + " \\frac{\n", + " \\sigma_{i,m}^{2}\n", + " }{\n", + " \\sigma^{'2}\n", + " }\n", + " +\n", + " 2\\frac{-\\rho_{ij}\\sigma_{i,m}}{\\sigma^{'}}\n", + " +\n", + " \\left[\n", + " \\left(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}}\\right)\n", + " -\n", + " \\left(\\frac{\n", + " \\mu_{j,m} - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\\right)\n", + " \\right]^{2}\n", + " + \n", + " \\rho_{ij}^{2} \n", + " \\geq{}& 0\n", + " \\\\\n", + " \\left[\n", + " \\left(\\frac{\n", + " \\sigma_{i,m}\n", + " }{\n", + " \\sigma^{'}\n", + " }\\right)^{2}\n", + " +\n", + " \\rho_{ij}^{2} \n", + " -\n", + " 2\\left(\\frac{\\sigma_{i,m}}{\\sigma^{'}}\\right)\\rho_{ij}\n", + " \\right]\n", + " + \n", + " \\left[\n", + " \\left(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}}\\right)\n", + " -\n", + " \\left(\\frac{\n", + " \\mu_{j,m} - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\\right)\n", + " \\right]^{2}\n", + " \\geq{}& \n", + " 0\n", + " \\\\\n", + " \\left(\\frac{\n", + " \\sigma_{i,m}\n", + " }{\n", + " \\sigma^{'}\n", + " }\n", + " -\n", + " \\rho_{ij}\n", + " \\right)^{2} \n", + " + \n", + " \\left[\n", + " \\left(\\frac{\\mu_{i,m}-\\mu^{'}}{\\sigma^{'}}\\right)\n", + " -\n", + " \\left(\\frac{\n", + " \\mu_{j,m} - \\mu_{j,m+k}\n", + " }{\n", + " \\sigma_{j,m}\n", + " }\\right)\n", + " \\right]^{2}\n", + " \\geq{}& \n", + " 0\n", + "\\end{align}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "fe8f12ec", + "metadata": {}, + "source": [ + "The above inequation is always satisfied. Therefore, the critical point gives global minimum." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ebf2b75e", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/Tutorial_VALMOD.ipynb b/docs/Tutorial_VALMOD.ipynb new file mode 100644 index 000000000..f5c58265d --- /dev/null +++ b/docs/Tutorial_VALMOD.ipynb @@ -0,0 +1,992 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c7a27406", + "metadata": {}, + "source": [ + "In this tutorial, we would like to implement VALMOD algorithm proposed in paper [VALMOD](https://arxiv.org/pdf/2008.13447.pdf), and reproduce its results as closely as possible.\n", + "\n", + "The **VAriable Length MOtif Discovery (VALMOD)** algorithm takes time series `T` and a range of subsequence length `[min_m, max_m]`, and find motifs and discords." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "0adbe18a", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import stumpy\n", + "from stumpy import stump, core, config\n", + "import pandas as pd\n", + "import numpy as np\n", + "import numba\n", + "from numba import njit, prange\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "import time\n", + "\n", + "plt.style.use('https://raw.githubusercontent.com/TDAmeritrade/stumpy/main/docs/stumpy.mplstyle')" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "44d283f8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.7444217828807693, 2, -1, 2],\n", + " [1.5382980393045818, 4, -1, 4],\n", + " [0.19836142937718138, 5, 0, 5],\n", + " [0.44958674269840077, 7, 0, 7],\n", + " [1.5382980393045818, 1, 1, 7],\n", + " [0.19836142937718138, 2, 2, 7],\n", + " [0.9901822253111079, 2, 2, -1],\n", + " [0.44958674269840077, 3, 3, -1]], dtype=object)" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stump(np.random.rand(10), 3)" + ] + }, + { + "cell_type": "markdown", + "id": "e9d48c97", + "metadata": {}, + "source": [ + "# 1- Introduction" + ] + }, + { + "cell_type": "markdown", + "id": "b0423978", + "metadata": {}, + "source": [ + "**Notation:** $T_{i,m} = T[i:i+m]$ is a subsequence of `T` that starts at index `i` and has length `m`. " + ] + }, + { + "cell_type": "markdown", + "id": "4a4af7fd", + "metadata": {}, + "source": [ + "## Motif discovery" + ] + }, + { + "cell_type": "markdown", + "id": "78ac5b0f", + "metadata": {}, + "source": [ + "For a given motif pair $\\{T_{idx,m},T_{nn\\_idx,n}\\}$, Motif set $S^{m}_{r}$ is a set of subsequences of length `m` that has `distance < r` to either $T_{idx,m}$ or $T_{nn\\_idx,n}$. And, the cardinality of set is called the frequency of the motif set.\n", + "\n", + "We would like to find set $S^{*} = \\bigcup\\limits_{m=min\\_m}^{max\\_m}{S^{m}_{r}}$, and $S^{m}_{r} \\cap S^{m'}_{r'} = \\emptyset$. In other words, we want to find motif sets for different length `m` and we want to make sure there is no \"common\" (see note below) subsequence between any two motif sets. \n", + "\n", + "**NOTE:** The subsequences in motif set of length m and m' are indeed different because they have different length. However, by the constraint $S^{m}_{r} \\cap S^{m'}_{r'} = \\emptyset$, the authors meant to avoid considering two subsequences (of different length) that start from the same index. For instance, if $T_{200,m}$ is in one set and $T_{200,m'}$ in another set, the authors consider the intersection of their corresponding set to be non-empty because both of these two subsequences start from the same index." + ] + }, + { + "cell_type": "markdown", + "id": "7fc09927", + "metadata": {}, + "source": [ + "## Discord Discovery" + ] + }, + { + "cell_type": "markdown", + "id": "0f4ee615", + "metadata": {}, + "source": [ + "First, we need to provide a few definitions...\n", + "\n", + "**$n^{th}$ best match**: For the subsequence $T_{i,m}$, its $n^{th}$ best match is simply the $n^{th}$ smallest distance in the distance profile.
\n", + "\n", + "**$n^{th}$ discord**: a subsequence $T_{i,m}$ is the $n^{th}$ discord if it has the largest value to its $n^{th}$ best match compared to the distances between any other subsequences and their ($n^{th}$) best match.
\n", + "\n", + "**NOTE**:
\n", + "Why should we care about $n^{th}$ discord (n>1)? We provide a simple example below:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "37fdbb26", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "T = np.random.uniform(-100,100,size=3000)\n", + "m = 200\n", + "i, j = 100, 1500\n", + "\n", + "T[i:i+m] = 0\n", + "T[j:j+m] = 0\n", + "\n", + "plt.plot(T)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cb3a3940", + "metadata": {}, + "source": [ + "Here, the subsequences at index `i` and `j` can be considered an anomaly. However, the 1NN distance is 0 for them. Therefore, we may need to investigate other neighbors rather than just 1NN. In discord discovery, it is called twin-freak problem (see [Tutorial](https://cci.drexel.edu/bigdata/bigdata2017/files/Tutorial4.pdf)). It happens when the (same) anomally occurs more than once. In our example above, the anomaly occurs twice. Therefore, we should be able to detect it if we consider 2nd nearest neighbor. \n", + "\n", + "For further details, see Fig. 2 of the paper." + ] + }, + { + "cell_type": "markdown", + "id": "45eeecf5", + "metadata": {}, + "source": [ + "**Variable-length Top-k $n^{th}$ Discord Discovery:**
\n", + "Given a time series `T`, a subsequence length-range `[min_m, max_m]`,`K`, and `N`, we want to find **top-k $n^{th}$ discord** for each `k` in $\\{1,...,K\\}$, for each `n` in $\\{1,...,N\\}$, and for all `m` in $\\{min\\_m,...,max\\_m\\}$." + ] + }, + { + "cell_type": "markdown", + "id": "e503fb0a", + "metadata": {}, + "source": [ + "# 2-Lower Bound of Distance Profile" + ] + }, + { + "cell_type": "markdown", + "id": "8538f0e3", + "metadata": {}, + "source": [ + "Lower Bound (LB) for $d_{j,i}^{(m+k)} = d(T_{j,m+k}, T_{i,m+k})$ can be calculated as follows:" + ] + }, + { + "cell_type": "markdown", + "id": "a7f08024", + "metadata": {}, + "source": [ + "**Non-normalized distance (p-norm):**" + ] + }, + { + "cell_type": "markdown", + "id": "297e8f9e", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "LB_{j,i}^{(m+k)} ={}& \n", + "d_{j,i}^{(m)} \\quad (1)\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "7ff2e666", + "metadata": {}, + "source": [ + "**Normalized distance(see eq(2) of the paper):**" + ] + }, + { + "cell_type": "markdown", + "id": "0f192dfa", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "LB_{j,i}^{(m+k)} ={}& \n", + "\\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + "\\sqrt{\n", + "m\\left(\n", + "1 - \\left(\\max(\\rho^{(m)}_{j,i},0)\\right)^{2}\n", + "\\right)\n", + "} \\quad (2)\n", + "\\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "a6b6a92f", + "metadata": {}, + "source": [ + "And, the pearson correlation, $\\rho^{(m)}_{j,i}$, can be calculated as follows: " + ] + }, + { + "cell_type": "markdown", + "id": "06f74a00", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "\\rho^{(m)}_{j,i} ={}& \n", + "\\frac{\\sum \\limits_{t=0}^{m-1}{T[i+t]T[j+t]} - m\\mu_{i,m}\\mu_{j,m}}{m\\sigma_{i,m}\\sigma_{j,m}} \\quad (2a)\n", + "\\end{align} \n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1e23d962", + "metadata": {}, + "source": [ + "Alternatively, $\\rho^{(m)}_{j,i}$ and $d^{(m)}_{j,i}$ are related to each other according to the following formula:" + ] + }, + { + "cell_type": "markdown", + "id": "bd2e70a1", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "d^{(m)}_{j,i} ={}& \n", + "\\sqrt{\n", + "2m \\left(\n", + "1-\\rho^{(m)}_{j,i}\n", + "\\right)\n", + "} \\quad {(2b)}\n", + "\\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1dd3b3a4", + "metadata": {}, + "source": [ + "# 3- Core Idea" + ] + }, + { + "cell_type": "markdown", + "id": "9b0ebd60", + "metadata": {}, + "source": [ + "The core idea of VALMOD can be explained as follows:" + ] + }, + { + "cell_type": "markdown", + "id": "d3c23204", + "metadata": {}, + "source": [ + "## 3-1: Ranked Lower Bound (LB) of Distance Profile \n", + "Ranked LB of distance profile refers to the values of the LB of a distance profile sorted in the ascending order. It is important to note that such ranking is preserved for all subsequence length range `(min_m+1, max_m)` having assumed that they are all being calculated based on the $\\rho_{j,i}$ values for length `min_m`.\n", + "\n", + "In other words,
\n", + "**IF:**" + ] + }, + { + "cell_type": "markdown", + "id": "33bc22e8", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "LB^{(m+k_{1})}_{j,i} \\leq{}& \n", + "LB^{(m+k_{1})}_{j,i^{'}}\n", + "\\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "02b333a3", + "metadata": {}, + "source": [ + "**THEN:**" + ] + }, + { + "cell_type": "markdown", + "id": "3fc03958", + "metadata": {}, + "source": [ + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{\n", + "\\sigma_{j,m+k_{1}}}\n", + "{\\sigma_{j,m+k_{2}}\n", + "}\n", + "LB^{(m+k_{1})}_{j,i} \n", + "\\leq{}&\n", + "\\frac{\n", + "\\sigma_{j,m+k_{1}}}\n", + "{\\sigma_{j,m+k_{2}}\n", + "}\n", + "LB^{(m+k_{1})}_{j,i'}\n", + "\\\\\n", + "\\frac{\n", + "\\sigma_{j,m+k_{1}}}\n", + "{\\sigma_{j,m+k_{2}}\n", + "}\n", + "\\left[\n", + "\\frac{\\sigma_{j,m}}{\\sigma_{j,m+k_{1}}}\n", + "\\sqrt{\n", + "m\\left(\n", + "1 - \\max(\\rho^{(m)}_{j,i},0)^{2}\n", + "\\right)\n", + "}\n", + "\\right]\n", + "\\leq{}&\n", + "\\frac{\n", + "\\sigma_{j,m+k_{1}}}\n", + "{\\sigma_{j,m+k_{2}}\n", + "}\n", + "\\left[\n", + "\\frac{\\sigma_{j,m}}{\\sigma_{j,m+k_{1}}}\n", + "\\sqrt{\n", + "m\\left(\n", + "1 - \\max(\\rho^{(m)}_{j,i'},0)^{2}\n", + "\\right)\n", + "}\n", + "\\right]\n", + "\\\\\n", + "LB^{(m+k_{2})}_{j,i} \\leq{}& \n", + "LB^{(m+k_{2})}_{j,i'}\n", + "\\\\\n", + "\\end{align}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "8f1df704", + "metadata": {}, + "source": [ + "## 3-2: Accelerating Matrix Profile calculation\n", + "Storing all \"ranked LB\" for all indices requires a significant amount of memory. Instead, we can just store the `top-p` smallest values of the ranked $LB^{(m+k)}_{j}$ and their corresponding indices. The parameter `p` is set by the user (e.g. see Table 2 on page 28). As we will see in the next section, we can use this meta information to skip some unnecessary calculation of distances for length larger than `min_m`." + ] + }, + { + "cell_type": "markdown", + "id": "833c4f6b", + "metadata": {}, + "source": [ + "# 4-VALMOD algorithm\n", + "The VALMOD algorithm (see Algorithm1 and Algorithm2 on page 13) discovers variable-length matrix profile and the matrix profile indices. In this section, we implement the functions by taking a bottom-up approach. So, we first implement the functions that are being called by VALMOD algorithm, and then we implement VALMOD algorithm." + ] + }, + { + "cell_type": "markdown", + "id": "f6cbecbd", + "metadata": {}, + "source": [ + "## 4-1- ComputeMatrixProfile (see algorith3 on page 15)\n", + "This algorithm scans all pairs of subsequences. However, instead of returning the matrix profile and its indices, the algorithm returns the `top-p` smallest value of each distance profile and their corresponding indices.\n", + "\n", + "In the paper, the authors used the LB formula to convert distances to LB. So, as they scan pairs of subsequences, they calculate LB for each pair of subsequences. The authors used max_heap data structure to store `top-p` smallest LB values for each distance profile. " + ] + }, + { + "cell_type": "markdown", + "id": "eb51f0f6", + "metadata": {}, + "source": [ + "**NOTE (1): Our implementation is slightly different than what proposed in the Algorithm3 of the paper**\n", + "We can skip line19 of Algorithm 3 provided in the paper. We do NOT need to calculate $LB^{(m+k)}_{j,i}$ for each $d^{(m)}_{j,i}$. As we prove below, the ranked distance profile, $DP^{(m)}_{j}$, is in the same order as its corresponding ranked Lower Bound, $LB^{(m+k)}_{j}$. Therefore, we can simply return the `top-p` smallest value of distance profile and then calculate their corresponding LB value all at once." + ] + }, + { + "cell_type": "markdown", + "id": "3a1ba5e4", + "metadata": {}, + "source": [ + "**IF:**\n", + "\n", + "$$\n", + "\\begin{align}\n", + "d^{(m)}_{j,i} \n", + "\\geq{}&{}\n", + "d^{(m)}_{j,i'}\n", + "\\\\\n", + "\\end{align}\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "f7f22edc", + "metadata": {}, + "source": [ + "**THEN:**\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\rho^{(m)}_{j,i} \n", + "\\leq&{}\n", + "\\rho^{(m)}_{j,i'}\n", + "\\\\\n", + "\\max(\\rho^{(m)}_{j,i}, 0) \n", + "\\leq&{}\n", + "\\max(\\rho^{(m)}_{j,i'},0)\n", + "\\\\\n", + "\\left(\\max(\\rho^{(m)}_{j,i}, 0)\\right)^{2}\n", + "\\leq&{}\n", + "\\left(\\max(\\rho^{(m)}_{j,i'},0)\\right)^{2}\n", + "\\\\\n", + "1 - \\left(\\max(\\rho^{(m)}_{j,i}, 0)\\right)^{2}\n", + "\\geq&{}\n", + "1 - \\left(\\max(\\rho^{(m)}_{j,i'},0)\\right)^{2}\n", + "\\\\\n", + "\\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + "\\sqrt{m\n", + "\\left[\n", + "1 - \\left(\\max(\\rho^{(m)}_{j,i}, 0)\\right)^{2}\n", + "\\right]\n", + "}\n", + "\\geq&{}\n", + "\\frac{\\sigma_{j,m}}{\\sigma_{j,m+k}}\n", + "\\sqrt{m\n", + "\\left[\n", + "1 - \\left(\\max(\\rho^{(m)}_{j,i'}, 0)\\right)^{2}\n", + "\\right]\n", + "}\n", + "\\\\\n", + "LB^{(m)}_{j,i} \\geq{}& \n", + "LB^{(m)}_{j,i'}\n", + "\\\\\n", + "\\end{align}\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "ec7b8819", + "metadata": {}, + "source": [ + "This proves that the ranked distance profile and its ranked lower bound have the same order." + ] + }, + { + "cell_type": "markdown", + "id": "3db70f03", + "metadata": {}, + "source": [ + "**NOTE (2):** \n", + "
\n", + "In STUMPY, parameter `p` is used to denote the kind of p-norm distance. To this end, from this point onwards, we use `k` to denote the number of elements that should be stored for each distance profile." + ] + }, + { + "cell_type": "markdown", + "id": "4711a892", + "metadata": {}, + "source": [ + "First, let us implement the naive version of VALMOD, that is we do not take advantage of previously-calculated top-k profiles, and we just iteratively call `stump`." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "4a17e969", + "metadata": {}, + "outputs": [], + "source": [ + "def naive_VALMOD(T, m_min, m_max):\n", + " # out_P is the scaled version of matrix profile value. \n", + " n = len(T) - m_min + 1\n", + " out_P = np.full(n, np.inf, dtype=np.float64)\n", + " out_I = np.full(n, -1, dtype=np.int64)\n", + " out_M = np.full(n, -1, dtype=np.int64)\n", + " \n", + " for m in range(m_min, m_max + 1):\n", + " mp = stump(T, m)\n", + " P = mp[:,0].astype(np.float64)\n", + " I = mp[:,1].astype(np.int64)\n", + " \n", + " P[:] = P / np.sqrt(m)\n", + " \n", + " l = len(P)\n", + " mask = P < out_P[:l]\n", + " out_P[:l][mask] = P[mask]\n", + " out_I[:l][mask] = I[mask]\n", + " out_M[:l][mask] = m\n", + " \n", + " out = np.empty((n, 3), dtype=object)\n", + " out[:, 0] = out_P\n", + " out[:, 1] = out_I\n", + " out[:, 2] = out_M\n", + " \n", + " return out" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "62a300d8", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "a010e37e", + "metadata": {}, + "outputs": [], + "source": [ + "def _VALMOD_stump(T, m, k):\n", + " \"\"\"\n", + " Computes the top-1 matrix profile and matrix profile indice, and also computes the lower bound component\n", + " and their coresponding indices.\n", + " \n", + " Parameters\n", + " ----------\n", + " T : numpy.ndarray\n", + " The time series or sequence for which to compute the matrix profile\n", + " \n", + " m : int\n", + " Window size\n", + " \n", + " k : int\n", + " Number of nearest neighbors to consider in constructing the profiles and lower bounds.\n", + " \n", + " Returns\n", + " -------\n", + " out 1: np.ndarray\n", + " A 1D array containing the exact matix profile values\n", + " \n", + " out 2: np.ndarray\n", + " A 1D array containing the exact matix profile indices\n", + " \n", + " out 3: np.ndarray\n", + " A 2D array, with k columns, containing the core component of lowerbound values,\n", + " \n", + " out 4 : np.ndarray\n", + " A 2D array, with k columns, containing the indices that correspond to the lowerbound values\n", + " \"\"\"\n", + " mp = stump(T, m, k=k)\n", + " P = mp[:, :k].astype(np.float64)\n", + " I = mp[:, k:2*k].astype(np.int64)\n", + " is_mp_valid = np.full(len(T) - m + 1, 0, dtype=bool)\n", + " \n", + " # In VALMOD paper, LB has the following component:\n", + " # np.sqrt(m * (1 - np.square(ρ_clip))). Here, we\n", + " # show it by `LB_σr`\n", + "\n", + " ρ = 1.0 - np.square(P) / (2 * m)\n", + " # clipping ρ\n", + " ρ[:] = np.clip(ρ, a_min=0.0, a_max=1.0)\n", + " _, σ = core.compute_mean_std(T, m)\n", + " LB_σr = σ.reshape(-1,1) * np.sqrt(m * (1.0 - np.square(ρ))) \n", + " is_mp_valid[:] = True\n", + " \n", + " return P[:, 0], I[:, 0], LB_σr, I, is_mp_valid\n", + " \n", + "\n", + "def _VALMOD_stump_partial(T, m, k, LB_σr, LB_I):\n", + " \"\"\"\n", + " Compute partial matrix profile for subsequence length `m`, \n", + " with help of lowerbound. \n", + " \n", + " Parameters\n", + " ----------\n", + " T : numpy.ndarray\n", + " The time series or sequence for which to compute the matrix profile\n", + " \n", + " m : int\n", + " Window size\n", + " \n", + " k : int\n", + " The number of nearest neighbor to consider for constructing lowerbound \n", + " profiles\n", + " \n", + " LB_ar : np.ndarray\n", + " The array that contains the main component of lowerbound values\n", + " \n", + " LB_I : np.ndarray\n", + " The array that corresponds to the indices of lower bound values\n", + " \n", + " Returns\n", + " -------\n", + " P : np.ndarray\n", + " A 1D array containing the exact matix profile values\n", + " \n", + " I : np.ndarray\n", + " A 1D array containing the exact matix profile indices\n", + " \n", + " LB_σr : np.ndarray\n", + " A 2D array, with k columns, containing the core component of lowerbound values,\n", + " \n", + " LB_I : np.ndarray\n", + " A 2D array, with k columns, containing the indices that correspond to the lowerbound values\n", + " \"\"\"\n", + " n = len(T) - m + 1\n", + " P = np.full(n, np.inf,dtype=np.float64)\n", + " I = np.full(n, -1,dtype=np.int64)\n", + " is_mp_valid = np.full(n, 0, dtype=bool)\n", + " \n", + " # may add support for `T_B` (AB-join)\n", + " Q, μ_Q, σ_Q, Q_subseq_isconstant = core.preprocess(T, m)\n", + " T, M_T, Σ_T, T_subseq_isconstant = core.preprocess(T, m)\n", + " \n", + " σ_Q_inv = 1.0 / σ_Q # add code to handle `σ_Q==0` cases\n", + " LB = σ_Q_inv.reshape(-1, 1) * LB_σr[:len(σ_Q_inv)]\n", + " \n", + " global_min_maxLB = np.inf\n", + " excl_zone = int(np.ceil(m / config.STUMPY_EXCL_ZONE_DENOM))\n", + " for i in range(n):\n", + " excl_zone_start = max(i - excl_zone, 0)\n", + " excl_zone_stop = min(i + excl_zone + 1, n)\n", + " excl_zone_range = range(excl_zone_start, excl_zone_stop)\n", + " \n", + " min_dist = np.inf\n", + " idx = -1\n", + " for enum, j in enumerate(LB_I[i]):\n", + " if j >= n or j in excl_zone_range:\n", + " continue\n", + " \n", + " QT = np.dot(T[i:i+m], T[j:j+m])\n", + " d_square = core._calculate_squared_distance(\n", + " m,\n", + " QT,\n", + " μ_Q[i],\n", + " σ_Q[i],\n", + " M_T[j],\n", + " Σ_T[j],\n", + " Q_subseq_isconstant[i],\n", + " T_subseq_isconstant[j],\n", + " )\n", + " d = np.sqrt(d_square)\n", + " if d < min_dist:\n", + " min_dist = d\n", + " idx = j\n", + " \n", + " maxLB = LB[i, -1]\n", + " if min_dist < maxLB:\n", + " P[i] = min_dist\n", + " I[i] = idx\n", + " is_mp_valid[i] = True\n", + " else:\n", + " global_min_maxLB = min(global_min_maxLB, maxLB)\n", + " is_mp_valid[i] = False\n", + " \n", + " global_min_dist = np.min(P)\n", + " if global_min_dist <= global_min_maxLB:\n", + " return P, I, LB_σr, LB_I, is_mp_valid\n", + " \n", + " if np.sum(~is_mp_valid) < (n * np.log2(k) / np.log2(n)):\n", + " for idx in np.flatnonzero(~is_mp_valid):\n", + " if global_min_dist <= maxLB_profile[idx]:\n", + " continue \n", + " \n", + " QT = core.sliding_dot_product(T[idx:idx+m], T)\n", + " D = core._mass(\n", + " T[idx:idx+m], \n", + " T, \n", + " QT, \n", + " μ_Q[idx], \n", + " σ_Q[idx], \n", + " M_T, \n", + " Σ_T, \n", + " Q_subseq_isconstant[idx], \n", + " T_subseq_isconstant\n", + " )\n", + " core.apply_exclusion_zone(D, idx, m, np.inf)\n", + "\n", + " arg = np.argmin(D)\n", + " if D[arg] < np.inf:\n", + " P[idx] = D[arg]\n", + " I[idx] = arg\n", + " global_min_dist = min(global_min_dist, P[idx])\n", + " \n", + " args_topk = np.argsort(D, kind='mergesort')[:k]\n", + " LB_I[idx] = args_topk\n", + "\n", + " ρ = 1.0 - np.square(D[args_topk]) / (2 * m)\n", + " ρ[:] = np.clip(ρ, a_min=0.0, a_max=1.0)\n", + " LB_σr[idx] = σ_Q[idx] * np.sqrt(m * (1 - np.square(ρ)))\n", + " is_mp_valid[idx] = True\n", + "\n", + " else:\n", + " mp = stump(T, m, k=k)\n", + " P = mp[:, :k].astype(np.float64)\n", + " I = mp[:, k:2*k].astype(np.int64)\n", + "\n", + " ρ = 1.0 - np.square(P) / (2 * m)\n", + " ρ[:] = np.clip(ρ, a_min=0.0, a_max=1.0)\n", + " _, σ = core.compute_mean_std(T, m)\n", + " LB_σr = σ.reshape(-1,1) * np.sqrt(m * (1 - np.square(ρ)))\n", + " LB_I = I\n", + " is_mp_valid[:] = True\n", + "\n", + " return P[:,0], I[:,0], LB_σr, LB_I, is_mp_valid" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "be7b439d", + "metadata": {}, + "outputs": [], + "source": [ + "def _update_PIM(P, P_new, I, I_new, M, m_new):\n", + " \"\"\"\n", + " Update P (profile values), I (profile indices), M (length of subsequences), in place, \n", + " by using the new values `P_new`, `I_new`, `m_new`\n", + " \n", + " Parameters\n", + " ----------\n", + " P : np.ndarray\n", + " The matrix profile value containing the scaled distance between a subsequence to the nearest neighbor\n", + " \n", + " P_new : np.ndarray\n", + " The matrix profile value containing the scaled distance between a subsequence to the nearest neighbor, \n", + " computed for a subsequence length that is longer than the one used for `P`\n", + " \n", + " I : np.ndarray\n", + " The matrix profile indices containing the nearest neighbor index of each subsequence\n", + " \n", + " I_new : np.ndarray\n", + " The matrix profile indices containing the nearest neighbor index of each subsequence, computed \n", + " for a subsequence length that is longer than the one used for `I`. These indices correspond to \n", + " the matrix profile `P_new`\n", + " \n", + " M : np.ndarray\n", + " For a subequence at index `i`, `M[i]` is the lenght of subsequence for which the lowest distance \n", + " between `i` and its nearest neighbor is discovered.\n", + " \n", + " m_new : int\n", + " The new subsequence length that is used for computing P_new, I_new\n", + " \n", + " Returns \n", + " -------\n", + " None\n", + " \"\"\"\n", + " n = len(P_new)\n", + " mask = P_new < P[:n]\n", + " P[:n][mask] = P_new[mask]\n", + " I[:n][mask] = I_new[mask]\n", + " M[:n][mask] = m_new" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "94eceff1", + "metadata": {}, + "outputs": [], + "source": [ + "def print_verbose(msg, verbose=False):\n", + " if verbose:\n", + " print(msg)\n", + "\n", + "\n", + "def VALMOD(T, m_min, m_max, k):\n", + " \"\"\"\n", + " This function finds the matrix profile of T_A while considering different length of subsequences in \n", + " range `[m_min, m_max]` inclusive. To be able to compare distances across different subsequence length, \n", + " each distance is scaled by a factor of `1 / sqrt(m)`. \n", + " \n", + " Parameters\n", + " T : np.ndarray\n", + " The timeseries of interest\n", + " \n", + " m_min : int\n", + " The smallest window size\n", + " \n", + " m_max : int\n", + " The largest window size\n", + " \n", + " k : int\n", + " The number of nearest neighbors to capture for speeding up the computaion.\n", + " \n", + " Return\n", + " ------\n", + " PIM : np.ndarray\n", + " A 2D array, with exactly three columns, representing the ensembled matrix profile. The first column \n", + " contains the ensembled matrix profile value. The second column contains their corresponding nearest\n", + " neighbor index, and the third (last) column contains the corresponding subsequence length. Hence, \n", + " for instance, when `dist = PIM[i, 0]`, `j = PIM[i, 1]`, and `m = PIM[i, 2]`, then `dist` is a (scaled) \n", + " distance between subsequence `S_i` and subsequence `S_j`, each with length `m`. `dist` is the lowest \n", + " scaled distance between `S_i` and all of its neighbors considering all values of `m`.\n", + " \"\"\"\n", + " n = len(T) - m_min + 1\n", + " out_P = np.full(n, np.inf, dtype=np.float64)\n", + " out_I = np.full(n, -1, dtype=np.int64)\n", + " out_M = np.full(n, -1, dtype=np.int64)\n", + " \n", + " # out_P, out_I, out_M = _update_PIM(out_P, P_TopK[:,0] / np.sqrt(m), out_I, I_TopK[:, 0], out_M, m)\n", + " LB_σr = None\n", + " is_exact = np.full(n, 1, dtype=bool)\n", + " for m in range(m_min, m_max + 1):\n", + " if LB_σr is None: # only runs for the first iteration, i,e, lowest `m` \n", + " idx = 1232\n", + " P, I, LB_σr, LB_I, is_mp_valid = _VALMOD_stump(T, m, k)\n", + " else:\n", + " P, I, LB_σr, LB_I, is_mp_valid = _VALMOD_stump_partial(T, m, k, LB_σr, LB_I)\n", + " \n", + " l = len(is_mp_valid) # which is: len(T) - m + 1 \n", + " is_exact[:l] = is_exact[:l] & is_mp_valid\n", + " \n", + " _update_PIM(out_P, P/np.sqrt(m), out_I, I, out_M, m)\n", + " \n", + " out = np.empty((n, 3), dtype=object)\n", + " out[:, 0] = out_P\n", + " out[:, 1] = out_I\n", + " out[:, 2] = out_M\n", + " \n", + " return out, is_exact" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "d0800ab7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computing time: 5.127043724060059\n", + "Computing time: 34.47108221054077\n" + ] + } + ], + "source": [ + "# Input\n", + "seed = 0\n", + "np.random.seed(seed)\n", + "T = np.random.rand(10000)\n", + "m_min = 50\n", + "m_max = 60\n", + "\n", + "#####################\n", + "\n", + "# naive valmod: a simple for-loop, computing full mp for each `m`\n", + "t_start = time.time()\n", + "mp_ref = naive_VALMOD(T, m_min, m_max)\n", + "t_stop = time.time()\n", + "print(\"The computing time: \", t_stop - t_start)\n", + "\n", + "#####################\n", + "\n", + "# valmod\n", + "t_start = time.time()\n", + "mp_comp, is_exact = VALMOD(T, m_min, m_max, k=20) # k=20 is provided by user\n", + "t_stop = time.time()\n", + "print(\"Computing time: \", t_stop - t_start)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "b3f9d40b", + "metadata": {}, + "outputs": [], + "source": [ + "np.testing.assert_almost_equal(mp_ref[is_exact, 0], mp_comp[is_exact,0])" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "8aabf529", + "metadata": {}, + "outputs": [ + { + "ename": "AssertionError", + "evalue": "\nArrays are not almost equal to 7 decimals\n\nMismatched elements: 5771 / 9915 (58.2%)\nMax absolute difference: 0.0592546542833442\nMax relative difference: 0.06382009396320394\n x: array([0.9452865772913406, 0.9344991685815902, 0.9092612749994912, ...,\n 0.9612889703718848, 0.9425392112609088, 0.9439425333188787],\n dtype=object)\n y: array([0.9678644071613989, 0.9574466161924685, 0.9319605844727593, ...,\n 0.9612889703718848, 0.9425392112609088, 0.9478057237030245],\n dtype=object)", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[53], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtesting\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43massert_almost_equal\u001b[49m\u001b[43m(\u001b[49m\u001b[43mmp_ref\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m~\u001b[39;49m\u001b[43mis_exact\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmp_comp\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m~\u001b[39;49m\u001b[43mis_exact\u001b[49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n", + " \u001b[0;31m[... skipping hidden 2 frame]\u001b[0m\n", + "File \u001b[0;32m~/miniconda3/envs/stumpypy39/lib/python3.10/site-packages/numpy/testing/_private/utils.py:844\u001b[0m, in \u001b[0;36massert_array_compare\u001b[0;34m(comparison, x, y, err_msg, verbose, header, precision, equal_nan, equal_inf)\u001b[0m\n\u001b[1;32m 840\u001b[0m err_msg \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;130;01m\\n\u001b[39;00m\u001b[38;5;124m'\u001b[39m\u001b[38;5;241m.\u001b[39mjoin(remarks)\n\u001b[1;32m 841\u001b[0m msg \u001b[38;5;241m=\u001b[39m build_err_msg([ox, oy], err_msg,\n\u001b[1;32m 842\u001b[0m verbose\u001b[38;5;241m=\u001b[39mverbose, header\u001b[38;5;241m=\u001b[39mheader,\n\u001b[1;32m 843\u001b[0m names\u001b[38;5;241m=\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mx\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124my\u001b[39m\u001b[38;5;124m'\u001b[39m), precision\u001b[38;5;241m=\u001b[39mprecision)\n\u001b[0;32m--> 844\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mAssertionError\u001b[39;00m(msg)\n\u001b[1;32m 845\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m:\n\u001b[1;32m 846\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtraceback\u001b[39;00m\n", + "\u001b[0;31mAssertionError\u001b[0m: \nArrays are not almost equal to 7 decimals\n\nMismatched elements: 5771 / 9915 (58.2%)\nMax absolute difference: 0.0592546542833442\nMax relative difference: 0.06382009396320394\n x: array([0.9452865772913406, 0.9344991685815902, 0.9092612749994912, ...,\n 0.9612889703718848, 0.9425392112609088, 0.9439425333188787],\n dtype=object)\n y: array([0.9678644071613989, 0.9574466161924685, 0.9319605844727593, ...,\n 0.9612889703718848, 0.9425392112609088, 0.9478057237030245],\n dtype=object)" + ] + } + ], + "source": [ + "np.testing.assert_almost_equal(mp_ref[~is_exact, 0], mp_comp[~is_exact,0])" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "9557a1ad", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(30,3))\n", + "plt.plot(mp_ref[:,0], c='k', label='naive')\n", + "plt.plot(mp_comp[:,0], c='r', label='valmod')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}