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1 """
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2 C-NMF method for segmentation, modified from here:
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3
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4 Nieto, O., Jehan, T., Convex Non-negative Matrix Factorization For Automatic
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mi@0
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5 Music Structure Identification. Proc. of the 38th IEEE International Conference
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6 on Acoustics, Speech, and Signal Processing (ICASSP). Vancouver, Canada, 2013.
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7 """
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8
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9 __author__ = "Oriol Nieto"
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10 __copyright__ = "Copyright 2014, Music and Audio Research Lab (MARL)"
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11 __license__ = "GPL"
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12 __version__ = "1.0"
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13 __email__ = "oriol@nyu.edu"
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14
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15 import numpy as np
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16 import pymf
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17
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18 # Local stuff
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19 from utils import SegUtil
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20
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21 # Algorithm params
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22 h = 8 # Size of median filter for features in C-NMF
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23 R = 15 # Size of the median filter for the activation matrix C-NMF
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24 rank = 4 # Rank of decomposition for the boundaries
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25 rank_labels = 6 # Rank of decomposition for the labels
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26 R_labels = 6 # Size of the median filter for the labels
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27
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28 def cnmf(S, rank, niter=500):
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29 """(Convex) Non-Negative Matrix Factorization.
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30
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31 Parameters
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32 ----------
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33 S: np.array(p, N)
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34 Features matrix. p row features and N column observations.
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35 rank: int
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36 Rank of decomposition
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37 niter: int
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38 Number of iterations to be used
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39
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40 Returns
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41 -------
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42 F: np.array
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43 Cluster matrix (decomposed matrix)
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44 G: np.array
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45 Activation matrix (decomposed matrix)
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46 (s.t. S ~= F * G)
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47 """
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48 nmf_mdl = pymf.CNMF(S, num_bases=rank)
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49 nmf_mdl.factorize(niter=niter)
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50 F = np.asarray(nmf_mdl.W)
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51 G = np.asarray(nmf_mdl.H)
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52 return F, G
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53
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54
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55 def most_frequent(x):
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56 """Returns the most frequent value in x."""
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57 return np.argmax(np.bincount(x))
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58
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59
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60 def compute_labels(X, rank, R, bound_idxs, niter=300):
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61 """Computes the labels using the bounds."""
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62
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63 X = X.T
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64 try:
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65 F, G = cnmf(X, rank, niter=niter)
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66 except:
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67 return [1]
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68
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69 label_frames = filter_activation_matrix(G.T, R)
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70 label_frames = np.asarray(label_frames, dtype=int)
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71
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72 # Get labels from the label frames
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73 labels = []
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74 bound_inters = zip(bound_idxs[:-1], bound_idxs[1:])
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75 for bound_inter in bound_inters:
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76 if bound_inter[1] - bound_inter[0] <= 0:
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77 labels.append(np.max(label_frames) + 1)
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78 else:
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79 labels.append(most_frequent(
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80 label_frames[bound_inter[0]:bound_inter[1]]))
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81
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82 return labels
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83
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84
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85 def filter_activation_matrix(G, R):
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86 """Filters the activation matrix G, and returns a flattened copy."""
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87 idx = np.argmax(G, axis=1)
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88 max_idx = np.arange(G.shape[0])
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89 max_idx = (max_idx, idx.flatten())
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90 G[:, :] = 0
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91 G[max_idx] = idx + 1
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92 G = np.sum(G, axis=1)
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93 G = SegUtil.median_filter(G[:, np.newaxis], R)
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94 return G.flatten()
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95
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96
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97 def segmentation(X, rank=4, R=15, h=8, niter=300):
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98 """
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99 Gets the segmentation (boundaries and labels) from the factorization
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100 matrices.
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101
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102 Parameters
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103 ----------
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104 X: np.array()
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105 Features matrix (e.g. chromagram)
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106 rank: int
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107 Rank of decomposition
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108 R: int
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109 Size of the median filter for activation matrix
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110 niter: int
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111 Number of iterations for k-means
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112 bound_idxs : list
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113 Use previously found boundaries (None to detect them)
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114
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115 Returns
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116 -------
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117 bounds_idx: np.array
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118 Bound indeces found
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119 labels: np.array
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120 Indeces of the labels representing the similarity between segments.
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121 """
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122
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123 # Filter
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124 X = SegUtil.median_filter(X, M=h)
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125 X = X.T
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126
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127 # Find non filtered boundaries
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128 bound_idxs = None
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129 while True:
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130 if bound_idxs is None:
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131 try:
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132 F, G = cnmf(X, rank, niter=niter)
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133 except:
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134 return np.empty(0), [1]
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135
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136 # Filter G
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137 G = filter_activation_matrix(G.T, R)
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138 if bound_idxs is None:
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139 bound_idxs = np.where(np.diff(G) != 0)[0] + 1
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140
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141 if len(np.unique(bound_idxs)) <= 2:
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142 rank += 1
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143 bound_idxs = None
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144 else:
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145 break
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146
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147 return G, bound_idxs
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