Expected Mutual Information profiling

emi_out.txt

Line #      Hits         Time  Per Hit   % Time  Line Contents
==============================================================
   627                                           def expected_mutual_information(contingency, n_samples):
   628                                               """Calculate the expected mutual information for two labelings."""
   629        25           82      3.3      0.0      R, C = contingency.shape
   630        25           53      2.1      0.0      N = n_samples
   631        25         1059     42.4      0.0      a = np.sum(contingency, axis=1, dtype='int')
   632        25          932     37.3      0.0      b = np.sum(contingency, axis=0, dtype='int')
   633        25           58      2.3      0.0      emi = 0
   634      1839         4005      2.2      0.0      for i in range(R):
   635    165963       346569      2.1      1.0          for j in range(C):
   636    164149      1155150      7.0      3.4              start = int(max(a[i] + b[j] - N, 1))
   637    164149       804241      4.9      2.4              end = int(min(a[i], b[j]) + 1)
   638    331098       882214      2.7      2.6              for nij in range(start, end):
   639    166949       464229      2.8      1.4                  term1 = nij / float(N)
   640    166949      2607495     15.6      7.7                  term2 = np.log(float(N * nij) / (a[i] * b[j]))
   641                                                           # a! / (a - n)!
   642    166949      3473142     20.8     10.3                  term3a = np.multiply.reduce(range(a[i] - nij + 1, a[i] + 1))
   643                                                           # b! / (b - n)!
   644    166949      3190928     19.1      9.4                  term3b = np.multiply.reduce(range(b[j] - nij + 1, b[j] + 1))
   645                                                           # (N - a)! / N!
   646    166949      2952123     17.7      8.7                  t = np.multiply.reduce(range(N - a[i] + 1, N + 1))
   647    166949       578205      3.5      1.7                  if t == 0:
   648                                                               continue
   649    166949      1683693     10.1      5.0                  term3c = 1. / t
   650                                                           # (N - b)! / (N - a - b - n)!
   651    166949       902521      5.4      2.7                  num3d = N - b[j] + 1
   652    166949      1057582      6.3      3.1                  den3d = N - a[i] - b[j] + nij + 1
   653    166949       386928      2.3      1.1                  if num3d > den3d:
   654     16173       256298     15.8      0.8                      term3d = np.multiply.reduce(range(den3d, num3d))
   655                                                           else:
   656    150776      2519192     16.7      7.5                      term3d = np.multiply.reduce(range(num3d, den3d))
   657    150776       585305      3.9      1.7                      term3d = 1. / term3d
   658                                                           # 1 / n!
   659    166949      8339780     50.0     24.7                  term3e = 1. / factorial(nij)
   660                                                           # Add the product of all terms
   661    166949       405512      2.4      1.2                  emi += (term1 * term2 * term3a * term3b
   662    166949      1176503      7.0      3.5                          * term3c * term3d * term3e)
   663        25           49      2.0      0.0      return emi

To reproduce the preceding plot, install line profiler in IPython as explained in the profiling scikit-learn documentation:

%run examples/cluster/plot_adjusted_for_chance_measures.py
%lprun -f metrics.cluster.supervised.expected_mutual_information uniform_labelings_scores(metrics.ami_score, 100, np.linspace(2, n_samples, 5).astype(np.int))