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Implementation of CP-APR algorithm #27

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6f7a55f
Implementation of CP-APR algorithm
theosotr Nov 25, 2016
dd76b32
cp-apr: edited inner loop exit condition; reversed Khatri-Rao factor …
brianholland Nov 29, 2016
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2 changes: 1 addition & 1 deletion sktensor/__init__.py
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Original file line number Diff line number Diff line change
Expand Up @@ -9,6 +9,6 @@
from .ktensor import ktensor

# import algorithms
from .cp import als as cp_als
from .cp import als as cp_als, apr as cp_apr
from .tucker import hooi as tucker_hooi
from .tucker import hooi as tucker_hosvd
70 changes: 69 additions & 1 deletion sktensor/cp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@
from numpy import array, dot, ones, sqrt
from scipy.linalg import pinv
from numpy.random import rand
from .core import nvecs, norm
from .core import nvecs, norm, khatrirao
from .ktensor import ktensor

_log = logging.getLogger('CP')
Expand All @@ -38,6 +38,7 @@

__all__ = [
'als',
'apr',
'opt',
'wopt'
]
Expand Down Expand Up @@ -171,6 +172,73 @@ def als(X, rank, **kwargs):
return P, fit, itr, array(exectimes)


def apr(X, r, M=None, outer_iter=100, inner_iter=10, t=1e-4, k=0.01,
k_tol=1e-10, e=1e-10):
"""
Alternating Poisson Regression algorithm to compute the CP decomposition.

Parameters
----------
X : tensor
The tensor to be decomposed.
r : Number of R components.
M : Initial guess for tensor decomposed components.
outer_iter : Number of maximum outer iterations.
inner_iter : Number of maximum inner iterations.
t : Convergence tolerance of KKT conditions.
k : Inadmissible zero avoidance adjustment.
k_tol : Tolerance of identifying a potentional inadmissible zero.
e : Minimum divisor to prevent divide-by-zero.

Returns
-------
M : ktensor
Rank ``rank`` factorization of X. ``M.U[i]`` corresponds to the factor
matrix for the i-th mode. ``M.lambda[i]`` corresponds to the weight
of the i-th mode.
i : int
Number of iterations that were needed until convergence
exectimes : ndarray of floats
Time needed for each single iteration
References
----------
.. [1] EC Chi, TG Kolda.
On Tensors, Sparsity, and Nonnegative Factorizations.
SIAM Journal on Matrix Analysis and Applications, (2012).
"""
N = len(X.shape)
if M is None:
M = ktensor([np.random.rand(X.shape[i], r) for i in range(N)])
phi = np.empty([N, ], dtype=object)

exectimes = []
for i in range(outer_iter):
tic = time.clock()
is_converged = True
for n in range(N):
S = np.zeros((X.shape[n], r))
if i > 0:
S[(phi[n] > 1) & (M.U[n] < k_tol)] = k
b = np.dot((M.U[n] + S), np.diag(M.lmbda))
pi = khatrirao(tuple(
[M.U[i] for i in range(n) + range(n + 1, N)]),
reverse=True).transpose()
for j in range(inner_iter):
phi[n] = np.dot(X.unfold(n) / np.maximum(np.dot(b, pi), e),
pi.transpose())
if np.amax(np.abs(np.ravel(np.minimum(b, 1-phi[n])))) < t:
break

is_converged = False
b *= phi[n]
M.lmbda = np.dot(np.ones(b.shape[0]).transpose(), b)
M.U[n] = np.dot(b, np.linalg.inv(np.diag(M.lmbda)))
exectimes.append(time.clock() - tic)
if is_converged:
break
return M, i, exectimes


def opt(X, rank, **kwargs):
ainit = kwargs.pop('init', _DEF_INIT)
maxiter = kwargs.pop('maxIter', _DEF_MAXITER)
Expand Down