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 K-means clustering (unary-convex matrix factorization).
mi@0: """
mi@0: 
mi@0: 
mi@0: import numpy as np
mi@0: import random
mi@0: 
mi@0: import dist
mi@0: from nmf import NMF
mi@0: 
mi@0: __all__ = ["Kmeans"]
mi@0: 
mi@0: class Kmeans(NMF):
mi@0:     """      
mi@0:     Kmeans(data, num_bases=4)
mi@0:     
mi@0:     K-means clustering. Factorize a data matrix into two matrices s.t.
mi@0:     F = | data - W*H | is minimal. H is restricted to unary vectors, W
mi@0:     is simply the mean over the corresponding samples in "data".
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 K-means 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:     >>> kmeans_mdl = Kmeans(data, num_bases=2)
mi@0:     >>> kmeans_mdl.factorize(niter=10)
mi@0:     
mi@0:     The basis vectors are now stored in kmeans_mdl.W, the coefficients in kmeans_mdl.H. 
mi@0:     To compute coefficients for an existing set of basis vectors simply    copy W 
mi@0:     to kmeans_mdl.W, and set compute_w to False:
mi@0:     
mi@0:     >>> data = np.array([[1.5], [1.2]])
mi@0:     >>> W = [[1.0, 0.0], [0.0, 1.0]]
mi@0:     >>> kmeans_mdl = Kmeans(data, num_bases=2)
mi@0:     >>> kmeans_mdl.W = W
mi@0:     >>> kmeans_mdl.factorize(niter=1, compute_w=False)
mi@0:     
mi@0:     The result is a set of coefficients kmeans_mdl.H, s.t. data = W * kmeans_mdl.H.
mi@0:     """        
mi@0:     def init_h(self):
mi@0:         # W has to be present for H to be initialized  
mi@0:         self.H = np.zeros((self._num_bases, self._num_samples))
mi@0:         self.update_h()
mi@0:          
mi@0:     def init_w(self):
mi@0:         # set W to some random data samples
mi@0:         sel = random.sample(xrange(self._num_samples), self._num_bases)
mi@0:         
mi@0:         # sort indices, otherwise h5py won't work
mi@0:         self.W = self.data[:, np.sort(sel)]        
mi@0:        
mi@0:         
mi@0:     def update_h(self):                    
mi@0:         # and assign samples to the best matching centers
mi@0:         self.assigned = dist.vq(self.W, self.data)
mi@0:         self.H = np.zeros(self.H.shape)
mi@0:         self.H[self.assigned, range(self._num_samples)] = 1.0
mi@0:                 
mi@0:                     
mi@0:     def update_w(self):            
mi@0:         for i in range(self._num_bases):
mi@0:             idx = np.where(self.assigned==i)[0]
mi@0:             n = len(idx)        
mi@0:             if n > 1:
mi@0:                 self.W[:,i] = np.sum(self.data[:,idx], axis=1)/n