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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 """
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7 PyMF Non-negative Matrix Factorization.
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8
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9 NMFALS: Class for Non-negative Matrix Factorization using non negative
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10 least squares optimization (requires scipy.optimize)
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11
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12 [1] Lee, D. D. and Seung, H. S. (1999), Learning the Parts of Objects by Non-negative
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13 Matrix Factorization, Nature 401(6755), 788-799.
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14 """
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15
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16
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17
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18 import scipy.optimize
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19 from nmf import NMF
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20
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21 __all__ = ["NMFNNLS"]
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22
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23 class NMFNNLS(NMF):
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24 """
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25 NMFNNLS(data, num_bases=4)
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26
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27
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28 Non-negative Matrix Factorization. Factorize a data matrix into two matrices
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29 s.t. F = | data - W*H | = | is minimal. H, and W are restricted to non-negative
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30 data. Uses the Lawsons and Hanson's algorithm for non negative constrained
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31 least squares (-> also see scipy.optimize.nnls)
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32
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33 Parameters
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34 ----------
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35 data : array_like, shape (_data_dimension, _num_samples)
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36 the input data
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37 num_bases: int, optional
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38 Number of bases to compute (column rank of W and row rank of H).
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39 4 (default)
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40
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41 Attributes
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42 ----------
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43 W : "data_dimension x num_bases" matrix of basis vectors
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44 H : "num bases x num_samples" matrix of coefficients
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45 ferr : frobenius norm (after calling .factorize())
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46
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47 Example
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48 -------
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49 Applying NMF to some rather stupid data set:
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50
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51 >>> import numpy as np
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52 >>> data = np.array([[1.0, 0.0, 2.0], [0.0, 1.0, 1.0]])
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53 >>> nmf_mdl = NMFALS(data, num_bases=2)
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54 >>> nmf_mdl.factorize(niter=10)
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55
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56 The basis vectors are now stored in nmf_mdl.W, the coefficients in nmf_mdl.H.
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57 To compute coefficients for an existing set of basis vectors simply copy W
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58 to nmf_mdl.W, and set compute_w to False:
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59
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60 >>> data = np.array([[1.5], [1.2]])
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61 >>> W = np.array([[1.0, 0.0], [0.0, 1.0]])
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62 >>> nmf_mdl = NMFALS(data, num_bases=2)
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63 >>> nmf_mdl.W = W
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64 >>> nmf_mdl.factorize(niter=1, compute_w=False)
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65
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66 The result is a set of coefficients nmf_mdl.H, s.t. data = W * nmf_mdl.H.
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67 """
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68
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69 def update_h(self):
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70 def updatesingleH(i):
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71 self.H[:,i] = scipy.optimize.nnls(self.W, self.data[:,i])[0]
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72
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73 map(updatesingleH, xrange(self._num_samples))
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74
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75
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76 def update_w(self):
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77 def updatesingleW(i):
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78 self.W[i,:] = scipy.optimize.nnls(self.H.T, self.data[i,:].T)[0]
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79
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80 map(updatesingleW, xrange(self._data_dimension))
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