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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta content="width=device-width, initial-scale=1.0" name="viewport">
<title>Prabhat K Mishra</title>
<meta content="" name="description">
<meta content="" name="keywords">
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<style>
body {
font-family: Arial, sans-serif;
}
table {
width: 100%;
border-collapse: collapse;
}
th, td {
border: 1px solid #999;
padding: 10px;
text-align: left;
vertical-align: top;
}
th {
background-color: #f2f2f2;
}
tr:nth-child(even) td {
background-color: #f9f9f9;
}
tr:nth-child(odd) td {
background-color: #ffffff;
}
caption {
caption-side: top;
font-size: 1.3em;
font-weight: bold;
padding: 10px;
}
</style>
</head>
<body>
<!-- ======= Header ======= -->
<header id="header" class="fixed-top d-flex align-items-center">
<div class="container-fluid">
<div class="row justify-content-center align-items-center">
<div class="col-xl-11 d-flex align-items-center justify-content-between">
<!-- <h1 class="logo"><a href="index.html">Prabhat K Mishra</a></h1> -->
<!-- Uncomment below if you prefer to use an image logo -->
<!-- <a href="index.html" class="logo"><img src="assets/img/lab_logo.png" alt="" class="img-fluid"></a> -->
<nav id="navbar" class="navbar">
<ul>
<li><a class="nav-link scrollto active" href="./index.html">Home</a></li>
<!-- <li class="dropdown"><a class="nav-link scrollto "><span>Prabhat K Mishra</span> <i class="bi bi-chevron-down"></i></a> -->
<li><a class="nav-link scrollto active" href="./people.html">People</a></li>
<!-- <li><a class="nav-link scrollto " href="./research.html">Research</a></li> -->
<li class="dropdown"><a class="nav-link scrollto "><span>Research</span> <i class="bi bi-chevron-down"></i></a>
<ul>
<li><a class="nav-link scrollto " href="./research_projects.html">Projects</a></li>
<li><a class="nav-link scrollto " href="./publications.html">Publications</a></li>
</ul>
</li>
<li><a class="nav-link scrollto active" href="./resources.html">Facilities</a></li>
<li class="dropdown"><a class="nav-link scrollto "><span>Training</span> <i class="bi bi-chevron-down"></i></a>
<ul>
<li><a class="nav-link scrollto " href="./robot_autonomy.html">AI/ML for Robot autonomy</a></li>
<li><a class="nav-link scrollto " href="./cps.html">AI for Cyber Physical Systems</a></li>
<li><a class="nav-link scrollto " href="./la.html">Linear Algebra for AI/ML</a></li>
<li><a class="nav-link scrollto " href="./projects.html">Student Projects</a></li>
</ul>
<!-- <li><a class="nav-link scrollto active" href="./News.html">News</a></li> -->
<li><a class="nav-link scrollto" href="#footer">Contact</a></li>
</ul>
<i class="bi bi-list mobile-nav-toggle"></i>
</nav>
<!-- .navbar -->
</div>
</div>
</div>
</header><!-- End Header -->
<main id="main">
<section class="breadcrumbs">
<div class="container">
<div class="d-flex justify-content-between align-items-center">
<!-- <h2>Projects</h2>
<ol>
<li><a href="index.html">Home</a></li>
<li><a href="">Research</a></li>
<li>Projects</li>
</ol> -->
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<section id="la">
<div class="container" data-aos="fade-up">
<header class="section-header">
<h3>Linear Algebra for AI/ML</h3>
</header>
<h1>Objective</h1>
<p>Linear algebra, optimization techniques and statistical methods together form essential tools for
most of the algorithms in artificial intelligence and machine learning. In this course, we propose
to build some background in these mathematical foundations and prepare students to take on
advanced study or research in the field of AI and ML. The objective of this course is to be
familiarize the students with the important concepts and computational techniques in linear
algebra for AI and ML models.</p>
<h1>Modus Operandi</h1>
<ul>
<li>Class-room activities: 10%</li>
<ul>
<li>Participate in class-room discussions and ask quality questions</li>
<li>Five minutes teaching: Pick any small topic that is taught in the class before your schedule and teach it for five minutes.</li>
<li>Attendance</li>
</ul>
<li>Course project: 20%</li>
<ul>
<li>Refer to <a href = "./projects.html">guidelines</a>.</li>
</ul>
<li>Mid-sem: 30%</li>
<li>End-sem: 40%</li>
</ul>
<h1>Syllabus</h1>
<ul>
<li>Basics of vector space, norms, distance and linear functions</li>
<li>System of linear equations and the approaches to solve them</li>
<li>Eigenvalue and eigenvector of matrices and matrix decomposition</li>
<li>Low rank matrix approximation and structured low rank approximation</li>
<li>Convex optimization with gradient descent and accelerated gradient descent</li>
<li>Missing value and matrix completion methods</li>
</ul>
<table>
<caption>Lecture-wise Breakup</caption>
<thead>
<tr>
<th>Module</th>
<th>Topics</th>
<th>Hr (36)</th>
</tr>
</thead>
<tbody>
<tr>
<td>Introduction Module</td>
<td>Motivation, Connection to Machine Learning and Deep Learning, Case studies: Random walk on Graph, PageRank algorithm, Image deburring</td>
<td>3</td>
</tr>
<tr>
<td>Vector spaces</td>
<td>Vector spaces, Linear independence, Linear span, Basis and dimension, Inner product, Norm and distance</td>
<td>3</td>
</tr>
<tr>
<td>System of Linear Equations</td>
<td>Linear functions, System of linear equations (square, underdetermined and overdetermined)</td>
<td>3</td>
</tr>
<tr>
<td>Matrix Decomposition</td>
<td>QR decomposition, Existence and uniqueness of solutions, Inverse and pseudo inverse of matrices</td>
<td>3</td>
</tr>
<tr>
<td>Least square</td>
<td>Least squares solution, Constrained least squares</td>
<td>6</td>
</tr>
<tr>
<td>Eigenvalue and Eigenvector of Matrices</td>
<td>Eigenvalue and Eigenvector decomposition of square matrices, Spectral theorem for symmetric matrices, Power method for dominant eigenvector computation, Inverse power method, Inverse eigenvalue problem, SVD</td>
<td>9</td>
</tr>
<tr>
<td>Low rank matrix approximation</td>
<td>Low rank approximation and structured low rank approximation, Solution using SVD, Hankel structured low rank approximation</td>
<td>3</td>
</tr>
<tr>
<td>Introduction to Convex optimization</td>
<td>Convex optimality conditions: differentiable and non-differentiable cases, Gradient descent, Projected gradient methods, Accelerated gradient methods, alternating minimization</td>
<td>3</td>
</tr>
<tr>
<td>Matrix completion</td>
<td>Missing data and matrix completion problem, Matrix completion problem using nuclear norm</td>
<td>3</td>
</tr>
</tbody>
</table>
<h1>Resources</h1>
<ol>
<li>Introduction to Applied Linear Algebra: Vectors, Matrices and Least Squares, Stephan
Boyd, Lieven Vandenberghe, Cambridge University Press, 2018.</li>
<li>Linear Algebra and Learning from Data, Gilbert Strang, Wellesley Cambridge Press,
2019.</li>
<li>Statistical Learning with Sparsity: the LASSO and generalizations, Trevor Hastie, Robert
Tibshirani, Martin Wainwright, CRC Press 2017.</li>
</ol>
</div>
</section>
<section id="la">
<div class="container" data-aos="fade-up">
<header class="section-header">
<h3>Acknowledgement</h3>
</header>
<p>
This wonderful course was designed by <a href = "https://scholar.google.com/citations?user=tnzbgNwAAAAJ&hl=en">Prof. Swanand Khare</a>.
</p>
</div>
</section>
<!-- End Robot Autonomy -->
</main><!-- End #main -->
<!-- ======= Footer ======= -->
<footer id="footer">
<div class="footer-top">
<div class="container">
<div class="row">
<div class="col-lg-3 col-md-6 footer-info">
<!-- <h3>Prabhat K Mishra</h3> -->
<!-- <a href="index.html" class="logo"><img src="assets/img/lab_logo.png" alt="" class="img-fluid"></a> -->
<p>We are focused on research at the intersection of control theory and Artificial Intelligence (AI). The real world applications of AI require safety guarantee and explainability of the AI module. In addition, several modules such as sensing and perception, planning and action need to interact to complete the feedback loop. Our main focus is in planning and decision making but we also consider sensing and actuation along with the effects of communication channels whenever required.
</p>
</div>
<div class="col-lg-3 col-md-6 footer-links">
<h4>Useful Links</h4>
<ul>
<li><i class="bi bi-chevron-right"></i> <a href="index.html">Home</a></li>
<li><i class="bi bi-chevron-right"></i> <a href="people.html">People</a></li>
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</ul>
</div>
<div class="col-lg-3 col-md-6 footer-contact">
<h4>Contact Us</h4>
<p>
CET 021, Takshashila building <br>
IIT Kharagpur, Kharagpur, 721302<br>
India <br>
<strong>Phone:</strong> +91 3222-214-530<br>
<strong>Email:</strong> pkmishra@ai.iitkgp.ac.in<br>
</p>
<div class="social-links">
<a href="https://scholar.google.co.in/citations?user=rXhwtr0AAAAJ&hl=en"><i class="ai ai-google-scholar"></i></a>
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<a href="https://www.webofscience.com/wos/author/record/I-4305-2012"><i class="ai ai-researcherid"></i></a>
<a href="https://www.researchgate.net/profile/Prabhat-Kumar-Mishra-3"><i class="ai ai-researchgate"></i></a>
<a href="https://www.scopus.com/authid/detail.uri?authorId=57188646050"><i class="ai ai-scopus"></i></a>
<a href="https://www.semanticscholar.org/author/Prabhat-Kumar-Mishra/16154017"><i class="ai ai-semantic-scholar"></i></a>
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