mi@0: #!/usr/bin/python
mi@0: #
mi@0: # Copyright (C) Christian Thurau, 2010. 
mi@0: # Licensed under the GNU General Public License (GPL). 
mi@0: # http://www.gnu.org/licenses/gpl.txt
mi@0: """  
mi@0: PyMF Semi Non-negative Matrix Factorization.
mi@0: 
mi@0:     SNMF(NMF) : Class for semi non-negative matrix factorization
mi@0:     
mi@0: [1] Ding, C., Li, T. and Jordan, M.. Convex and Semi-Nonnegative Matrix Factorizations.
mi@0: IEEE Trans. on Pattern Analysis and Machine Intelligence 32(1), 45-55. 
mi@0: """
mi@0: 
mi@0: 
mi@0: 
mi@0: import numpy as np
mi@0: 
mi@0: from nmf import NMF
mi@0: 
mi@0: __all__ = ["SNMF"]
mi@0: 
mi@0: class SNMF(NMF):
mi@0:     """      
mi@0:     SNMF(data, num_bases=4)
mi@0:     
mi@0:     Semi Non-negative Matrix Factorization. Factorize a data matrix into two 
mi@0:     matrices s.t. F = | data - W*H | is minimal.
mi@0:     
mi@0:     Parameters
mi@0:     ----------
mi@0:     data : array_like, shape (_data_dimension, _num_samples)
mi@0:         the input data
mi@0:     num_bases: int, optional
mi@0:         Number of bases to compute (column rank of W and row rank of H).
mi@0:         4 (default)       
mi@0:     
mi@0:     Attributes
mi@0:     ----------
mi@0:     W : "data_dimension x num_bases" matrix of basis vectors
mi@0:     H : "num bases x num_samples" matrix of coefficients
mi@0:     ferr : frobenius norm (after calling .factorize())
mi@0:         
mi@0:     Example
mi@0:     -------
mi@0:     Applying Semi-NMF to some rather stupid data set:
mi@0:     
mi@0:     >>> import numpy as np
mi@0:     >>> data = np.array([[1.0, 0.0, 2.0], [0.0, 1.0, 1.0]])
mi@0:     >>> snmf_mdl = SNMF(data, num_bases=2)
mi@0:     >>> snmf_mdl.factorize(niter=10)
mi@0:     
mi@0:     The basis vectors are now stored in snmf_mdl.W, the coefficients in snmf_mdl.H. 
mi@0:     To compute coefficients for an existing set of basis vectors simply    copy W 
mi@0:     to snmf_mdl.W, and set compute_w to False:
mi@0:     
mi@0:     >>> data = np.array([[1.5], [1.2]])
mi@0:     >>> W = np.array([[1.0, 0.0], [0.0, 1.0]])
mi@0:     >>> snmf_mdl = SNMF(data, num_bases=2)
mi@0:     >>> snmf_mdl.W = W
mi@0:     >>> snmf_mdl.factorize(niter=1, compute_w=False)
mi@0:     
mi@0:     The result is a set of coefficients snmf_mdl.H, s.t. data = W * snmf_mdl.H. 
mi@0:     """
mi@0: 
mi@0: 
mi@0:     def update_w(self):
mi@0:         W1 = np.dot(self.data[:,:], self.H.T)
mi@0:         W2 = np.dot(self.H, self.H.T)    
mi@0:         self.W = np.dot(W1, np.linalg.inv(W2))
mi@0:         
mi@0:     def update_h(self):
mi@0:         def separate_positive(m):
mi@0:             return (np.abs(m) + m)/2.0 
mi@0:         
mi@0:         def separate_negative(m):
mi@0:             return (np.abs(m) - m)/2.0
mi@0:             
mi@0:         XW = np.dot(self.data[:,:].T, self.W)                
mi@0: 
mi@0:         WW = np.dot(self.W.T, self.W)
mi@0:         WW_pos = separate_positive(WW)
mi@0:         WW_neg = separate_negative(WW)
mi@0:         
mi@0:         XW_pos = separate_positive(XW)
mi@0:         H1 = (XW_pos + np.dot(self.H.T, WW_neg)).T
mi@0:         
mi@0:         XW_neg = separate_negative(XW)
mi@0:         H2 = (XW_neg + np.dot(self.H.T,WW_pos)).T + 10**-9
mi@0:         
mi@0:         self.H *= np.sqrt(H1/H2)    
mi@0:     
mi@0: if __name__ == "__main__":
mi@0:     import doctest  
mi@0:     doctest.testmod()