py_nnma Package¶
py_nnma
Package¶
Routines for nonnegative matrix approximation (nnma)
nnma
Module¶
py_nnma: python modules for nonnegative matrix approximation (NNMA)
- 2009 Uwe Schmitt, uschmitt@mineway.de
NNMA minimizes dist(Y, A X)
- where: Y >= 0, m x n
A >= 0, m x k X >= 0, n x k
k < min(m,n)
- dist(A,B) can be || A - B ||_fro
- or KL(A,B)
This moudule provides the following functions:
NMF, NMFKL, SNMF, RRI, ALS, GDCLS, GDCLS_L1, FNMAI, FNMAI_SPARSE, NNSC and FastHALS
The common parameters when calling such a function are:
input:
- Y – the matrix for decomposition, maybe dense
- from numpy or sparse from scipy.sparse package
k – number of componnets to estimate
Astart Xstart – matrices to start iterations. Maybe None
for using random start matrices.eps – termination swell value
maxcount – max number of iterations to be performed
- verbose – if False: produce no output durint interations
- if integer: give all ‘verbose’ itetations some output about current state of iterations
output:
A, X – result matrices of algorithm
obj – value of objective function of last iteration
count – number of iterations done
- converged – flag: indicates if iterations stoped within
- max number of iterations
The following extra parameters exist depending on algorithm:
RRI : damping parameter ‘psi’ (default: 1e-12)
SNMF : sparsity parameter ‘sparse_par’ (default: 0)
- ALS : regularization parameter ‘regul’ for stabilizing iterations
- (default value 0). needed if objective value jitters.
GCDLS : ‘regul’ for l2-smoothness of X (default 0)
GDCLS_L1 : ‘regul’ for l1-smoothness of X (default 0)
- FNMAI : ‘stabil’ for stabilizing algorithm (default value 1e-12)
- ‘alpha’ for stepsize (default value 0.1) ‘tau’ for number of inner iterations (default value 2)
- FNMAI_SPARSE : as FNMAI plus
- ‘regul’ for l1-smoothness of X (default 0)
- NNSC : ‘alpha’ for stepsize of gradient update of A
- ‘sparse_par’ for sparsity
Copyright (c) 2009 Uwe Schmitt, uschmitt@mineway.de
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright
- notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above
- copyright notice, this list of conditions and the following
- disclaimer in the documentation and/or other materials provided
- with the distribution. Neither the name of the <ORGANIZATION>
- nor the names of its contributors may be used to endorse or
- promote products derived from this software without specific
- prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
This module is based on:
Daniel D. Lee and H. Sebastian Seung:
“Algorithms for non-negative matrix factorization”, in Advances in Neural Information Processing 13 (Proc. NIPS*2000) MIT Press, 2001.
- “Learning the parts of objects by non-negative matrix
factorization”,
Nature, vol. 401, no. 6755, pp. 788-791, 1999.
Cichocki and A-H. Phan:
- “Fast local algorithms for large scale Nonnegative Matrix and
Tensor Factorizations”,
IEICE Transaction on Fundamentals, in print March 2009.
- Hoyer
- “Non-negative Matrix Factorization with sparseness
constraints”,
Journal of Machine Learning Research, vol. 5, pp. 1457-1469, 2004.
Dongmin Kim, Suvrit Sra,Inderjit S. Dhillon:
“Fast Newton-type Methods for the Least Squares Nonnegative Matrix Approximation Problem” SIAM Data Mining (SDM), Apr. 2007
Ngoc-Diep Ho:
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
A_inexact_lsq_update
(Y, YT, A, X, **param)[source]¶ ALS fixed point update
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
A_mult_update
(Y, YT, A, X, **param)[source]¶ Lee and Sung multiplicative update
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
A_mult_update_kl_div
(Y, YT, A, X, **param)[source]¶ update A for minimization of KL(Y || A X)
-
class
PyMca5.PyMcaMath.mva.py_nnma.nnma.
AlgorunnerTemplate
[source]¶ Bases:
object
-
dist
(Y, A, X)¶ frobenius distance between Y and A X
-
frob_dist
(Y, A, X)¶ frobenius distance between Y and A X
-
init_factors
(Y, k, A=None, X=None)¶ generate start matrices U, V
-
kl_divergence
(Y, A, X)¶ kullbach leibler divergence D(Y | A X)
-
param_update
= None¶
-
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
FNMAI_A_update
(Y, YT, A, X, **param)[source]¶ FNMAI (Kim et al) update for A
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
FNMAI_X_update
(Y, YT, A, X, **param)[source]¶ FNMAI (Kim et al) update for V
-
class
PyMca5.PyMcaMath.mva.py_nnma.nnma.
FactorizedNNMA
(update_A, update_X, param_update=None)[source]¶ Bases:
PyMca5.PyMcaMath.mva.py_nnma.nnma.AlgorunnerTemplate
-
update
(Y, YT, A, X, **param)¶
-
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
GradA
(Y, YT, A, X, **param)[source]¶ dPhi(Y, A, X) / dA with Phi(Y, A, X) = || Y - A X ||_fro
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
GradX
(Y, YT, A, X, **param)[source]¶ dPhi(Y, A, X) / dX with Phi(Y, A, X) = || Y - A X ||_fro
-
class
PyMca5.PyMcaMath.mva.py_nnma.nnma.
RRI_
[source]¶ Bases:
PyMca5.PyMcaMath.mva.py_nnma.nnma.AlgorunnerTemplate
Runtime optimisations from Cichocki applied to Damped rank one residual iteration from Ngoc-Diep Ho.
-
update
(Y, YT, A, X, **param)¶
-
-
class
PyMca5.PyMcaMath.mva.py_nnma.nnma.
SNMF_
[source]¶ Bases:
PyMca5.PyMcaMath.mva.py_nnma.nnma.AlgorunnerTemplate
W. Liu, N. Zheng, and X. Lu.: “Non-negative matrix factorization for visual coding”. In Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP2003), 2003
-
dist
(Y, A, X)¶ kullbach leibler divergence D(Y | A X)
-
update
(Y, YT, A, X, **param)¶
-
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
X_inexact_lsq_update
(Y, YT, A, X, **param)[source]¶ ALS fixed point update
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
X_inexact_lsq_update_l1regul
(Y, YT, A, X, **param)[source]¶ ALS fixed point update with L1 regularization for X
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
X_mult_update
(Y, YT, A, X, **param)[source]¶ Lee and Sung multiplicative update
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
X_mult_update_kl_div
(Y, YT, A, X, **param)[source]¶ update V for minimization of KL(Y || A X)
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
X_mult_update_nnsc
(Y, YT, A, X, **param)[source]¶ Lee and Sung multiplicative update
-
PyMca5.PyMcaMath.mva.py_nnma.nnma.
is_sparse
(A)¶