#!/usr/bin/python
#
# Copyright (C) Christian Thurau, 2010.
# Licensed under the GNU General Public License (GPL).
# http://www.gnu.org/licenses/gpl.txt
"""
PyMF Non-negative Matrix Factorization.
NMFALS: Class for Non-negative Matrix Factorization using alternating least
squares optimization (requires cvxopt)
[1] Lee, D. D. and Seung, H. S. (1999), Learning the Parts of Objects by Non-negative
Matrix Factorization, Nature 401(6755), 788-799.
"""
import numpy as np
from cvxopt import solvers, base
from .nmf import NMF
__all__ = ["NMFALS"]
class NMFALS(NMF):
"""
NMF(data, num_bases=4)
Non-negative Matrix Factorization. Factorize a data matrix into two matrices
s.t. F = | data - W*H | = | is minimal. H, and W are restricted to non-negative
data. Uses the an alternating least squares procedure (quite slow for larger
data sets)
Parameters
----------
data : array_like, shape (_data_dimension, _num_samples)
the input data
num_bases: int, optional
Number of bases to compute (column rank of W and row rank of H).
4 (default)
Attributes
----------
W : "data_dimension x num_bases" matrix of basis vectors
H : "num bases x num_samples" matrix of coefficients
ferr : frobenius norm (after calling .factorize())
Example
-------
Applying NMF to some rather stupid data set:
>>> import numpy as np
>>> data = np.array([[1.0, 0.0, 2.0], [0.0, 1.0, 1.0]])
>>> nmf_mdl = NMFALS(data, num_bases=2)
>>> nmf_mdl.factorize(niter=10)
The basis vectors are now stored in nmf_mdl.W, the coefficients in nmf_mdl.H.
To compute coefficients for an existing set of basis vectors simply copy W
to nmf_mdl.W, and set compute_w to False:
>>> data = np.array([[1.5], [1.2]])
>>> W = np.array([[1.0, 0.0], [0.0, 1.0]])
>>> nmf_mdl = NMFALS(data, num_bases=2)
>>> nmf_mdl.W = W
>>> nmf_mdl.factorize(niter=1, compute_w=False)
The result is a set of coefficients nmf_mdl.H, s.t. data = W * nmf_mdl.H.
"""
def update_h(self):
def updatesingleH(i):
# optimize alpha using qp solver from cvxopt
FA = base.matrix(np.float64(np.dot(-self.W.T, self.data[:,i])))
al = solvers.qp(HA, FA, INQa, INQb)
self.H[:,i] = np.array(al['x']).reshape((1,-1))
# float64 required for cvxopt
HA = base.matrix(np.float64(np.dot(self.W.T, self.W)))
INQa = base.matrix(-np.eye(self._num_bases))
INQb = base.matrix(0.0, (self._num_bases,1))
map(updatesingleH, range(self._num_samples))
def update_w(self):
def updatesingleW(i):
# optimize alpha using qp solver from cvxopt
FA = base.matrix(np.float64(np.dot(-self.H, self.data[i,:].T)))
al = solvers.qp(HA, FA, INQa, INQb)
self.W[i,:] = np.array(al['x']).reshape((1,-1))
# float64 required for cvxopt
HA = base.matrix(np.float64(np.dot(self.H, self.H.T)))
INQa = base.matrix(-np.eye(self._num_bases))
INQb = base.matrix(0.0, (self._num_bases,1))
map(updatesingleW, range(self._data_dimension))
