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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 Simplex Volume Maximization for CUR [1]
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8
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9 SIVMCUR: class for SiVM-CUR
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10
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11 [1] C. Thurau, K. Kersting, and C. Bauckhage. Yes We Can - Simplex Volume
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12 Maximization for Descriptive Web-Scale Matrix Factorization. In Proc. Int.
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13 Conf. on Information and Knowledge Management. ACM. 2010.
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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 import scipy
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19 from sivm import SIVM
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20 from cur import CUR
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21
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22 __all__ = ["SIVM_CUR"]
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23
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24 class SIVM_CUR(CUR):
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25 '''
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26 SIVM_CUR(data, num_bases=4, dist_measure='l2')
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27
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28 Simplex Volume based CUR Decomposition. Factorize a data matrix into three
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29 matrices s.t. F = | data - USV| is minimal. Unlike CUR, SIVMCUR selects the
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30 rows and columns using SIVM, i.e. it tries to maximize the volume of the
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31 enclosed simplex.
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32
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33 Parameters
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34 ----------
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35 data : array_like [data_dimension x num_samples]
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36 the input data
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37 rrank: int, optional
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38 Number of rows to sample from data.
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39 4 (default)crank
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40 crank: int, optional
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41 Number of columns to sample from data.
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42 4 (default)
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43 dist_measure: string, optional
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44 The distance measure for finding the next best candidate that
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45 maximizes the simplex volume ['l2','l1','cosine','sparse_graph_l2']
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46 'l2' (default)
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47
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48 Attributes
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49 ----------
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50 U,S,V : submatrices s.t. data = USV
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51
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52 Example
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53 -------
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54 >>> import numpy as np
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55 >>> data = np.array([[1.0, 0.0, 2.0], [0.0, 1.0, 1.0]])
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56 >>> sivmcur_mdl = SIVM_CUR(data, show_progress=False, rrank=1, crank=2)
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57 >>> sivmcur_mdl.factorize()
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58 '''
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59
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60 def __init__(self, data, k=-1, rrank=0, crank=0, dist_measure='l2', init='origin'):
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61 CUR.__init__(self, data, k=k, rrank=rrank, crank=rrank)
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62 self._dist_measure = dist_measure
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63 self.init = init
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64
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65 def sample(self, A, c):
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66 # for optimizing the volume of the submatrix, set init to 'origin' (otherwise the volume of
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67 # the ordinary simplex would be optimized)
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68 sivm_mdl = SIVM(A, num_bases=c, dist_measure=self._dist_measure,
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69 init=self.init)
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70 sivm_mdl.factorize(show_progress=False, compute_w=True, niter=1,
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71 compute_h=False, compute_err=False)
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72
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73 return sivm_mdl.select
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74
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75
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76 def factorize(self):
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77 """ Factorize s.t. CUR = data
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78
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79 Updated Values
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80 --------------
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81 .C : updated values for C.
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82 .U : updated values for U.
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83 .R : updated values for R.
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84 """
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85 # sample row and column indices that maximize the volume of the submatrix
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86 self._rid = self.sample(self.data.transpose(), self._rrank)
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87 self._cid = self.sample(self.data, self._crank)
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88
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89 self._rcnt = np.ones(len(self._rid))
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90 self._ccnt = np.ones(len(self._cid))
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91
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92 self.computeUCR()
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93
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94
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95 if __name__ == "__main__":
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96 import doctest
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97 doctest.testmod()
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