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1 #!/usr/bin/python
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2 #
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3 # Copyright (C) Christian Thurau, 2010.
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4 # Licensed under the GNU General Public License (GPL).
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5 # http://www.gnu.org/licenses/gpl.txt
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6 #$Id$
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7 """
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8 PyMF Non-negative Double Singular Value Decompositions.
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9
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10 NNDSVD: Class for Non-negative Double Singular Value Decompositions [1]
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11
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12 [1] C. Boutsidis and E. Gallopoulos (2008), SVD based initialization: A head
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13 start for nonnegative matrix factorization, Pattern Recognition, 41, 1350-1362
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14 """
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15
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16
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17 import numpy as np
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18
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19 from nmf import NMF
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20 from svd import SVD
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21
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22 __all__ = ["NNDSVD"]
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23
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24 class NNDSVD(NMF):
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25 """
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26 NNDSVD(data, num_bases=4)
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27
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28
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29 Non-negative Double Singular Value Decompositions. Factorize a data
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30 matrix into two matrices s.t. F = | data - W*H | = | is minimal. H, and
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31 W are restricted to non-negative data. NNDSVD is primarily used for
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32 initializing NMF.
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33
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34 Parameters
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35 ----------
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36 data : array_like, shape (_data_dimension, _num_samples)
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37 the input data
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38 num_bases: int, optional
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39 Number of bases to compute (column rank of W and row rank of H).
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40 4 (default)
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41
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42 Attributes
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43 ----------
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44 W : "data_dimension x num_bases" matrix of basis vectors
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45 H : "num bases x num_samples" matrix of coefficients
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46 ferr : frobenius norm (after calling .factorize())
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47
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48 Example
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49 -------
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50 Applying NNDSVD to some rather stupid data set:
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51
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52 >>> import numpy as np
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53 >>> data = np.array([[1.0, 0.0, 2.0], [0.0, 1.0, 1.0]])
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54 >>> nndsvd_mdl = NNDSVD(data, num_bases=2)
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55 >>> nndsvd_mdl.factorize()
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56
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57 The basis vectors are now stored in nndsvd_mdl.W, the coefficients in
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58 nndsvd_mdl.H. To initialize NMF with nndsvd_mdl.W, nndsvd_mdl.H
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59 simply copy W to nmf_mdl.W and H to nmf_mdl.H:
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60
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61 >>> data = np.array([[1.5], [1.2]])
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62 >>> W = np.array([[1.0, 0.0], [0.0, 1.0]])
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63 >>> nmf_mdl = NMF(data, num_bases=2)
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64 >>> nmf_mdl.W = nndsvd_mdl.W
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65 >>> nmf_mdl.H = nndsvd_mdl.H
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66 >>> nmf_mdl.factorize(niter=20)
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67
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68 The result is a set of (more optimal) coefficients nmf_mdl.H, nmf_mdl.W.
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69 """
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70 def init_w(self):
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71 self.W = np.zeros((self._data_dimension, self._num_bases))
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72
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73 def init_h(self):
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74 self.H = np.zeros((self._num_bases, self._num_samples))
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75
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76 def update_h(self):
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77 pass
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78
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79 def update_w(self):
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80 svd_mdl = SVD(self.data)
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81 svd_mdl.factorize()
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82
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83 U, S, V = svd_mdl.U, svd_mdl.S, svd_mdl.V
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84
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85 # The first left singular vector is nonnegative
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86 # (abs is only used as values could be all negative)
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87 self.W[:,0] = np.sqrt(S[0,0]) * np.abs(U[:,0])
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88
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89 #The first right singular vector is nonnegative
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90 self.H[0,:] = np.sqrt(S[0,0]) * np.abs(V[0,:].T)
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91
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92 for i in range(1,self._num_bases):
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93 # Form the rank one factor
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94 Tmp = np.dot(U[:,i:i+1]*S[i,i], V[i:i+1,:])
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95
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96 # zero out the negative elements
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97 Tmp = np.where(Tmp < 0, 0.0, Tmp)
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98
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99 # Apply 2nd SVD
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100 svd_mdl_2 = SVD(Tmp)
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101 svd_mdl_2.factorize()
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102 u, s, v = svd_mdl_2.U, svd_mdl_2.S, svd_mdl_2.V
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103
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104 # The first left singular vector is nonnegative
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105 self.W[:,i] = np.sqrt(s[0,0]) * np.abs(u[:,0])
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106
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107 #The first right singular vector is nonnegative
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108 self.H[i,:] = np.sqrt(s[0,0]) * np.abs(v[0,:].T)
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109
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110 def factorize(self, niter=1, show_progress=False,
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111 compute_w=True, compute_h=True, compute_err=True):
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112
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113 # enforce certain default values, otherwise it won't work
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114 NMF.factorize(self, niter=1, show_progress=show_progress,
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115 compute_w=True, compute_h=True, compute_err=compute_err)
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116
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117 if __name__ == "__main__":
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118 import doctest
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119 doctest.testmod()
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