Rank Selection

Authors: Federico Raimondo, Kaustubh Patil

License: BSD 3 clause

from opnmf.selection import rank_permute
from opnmf.logging import configure_logging
import matplotlib.pyplot as plt
import seaborn as sns

set up logging

configure_logging('INFO')

Out:

2021-11-09 12:43:58,319 - opnmf - INFO - ===== Lib Versions =====
2021-11-09 12:43:58,320 - opnmf - INFO - numpy: 1.19.5
2021-11-09 12:43:58,320 - opnmf - INFO - scipy: 1.7.2
2021-11-09 12:43:58,320 - opnmf - INFO - sklearn: 0.24.2
2021-11-09 12:43:58,320 - opnmf - INFO - opnmf: 0.0.2
2021-11-09 12:43:58,320 - opnmf - INFO - ========================

Load IRIS dataset

iris = sns.load_dataset("iris")
features = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']
X = iris[features].values.T

Find rank. In this example we are bounded by the number of features (4)

min_components = 1
max_components = 4

result = rank_permute(X, min_components, max_components)

good_ranks, tested_ranks, errors, random_errors, estimators = result

Out:

2021-11-09 12:43:58,621 - opnmf - INFO - Choosing ranks between: [1 2 3 4]
2021-11-09 12:43:58,621 - opnmf - INFO - Fitting estimators with random permutations
2021-11-09 12:43:58,622 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,623 - opnmf - INFO - iter=0 diff=0.8927963651857725, obj=44.363702933673245
2021-11-09 12:43:58,623 - opnmf - INFO - Converged in 1 iterations
2021-11-09 12:43:58,624 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,624 - opnmf - INFO - iter=0 diff=0.896281151850484, obj=42.971387351469374
2021-11-09 12:43:58,630 - opnmf - INFO - iter=100 diff=0.0029398337326028696, obj=35.58698152468964
2021-11-09 12:43:58,639 - opnmf - INFO - iter=200 diff=0.0003171431400759283, obj=35.34949974559752
2021-11-09 12:43:58,651 - opnmf - INFO - iter=300 diff=7.754099142109854e-05, obj=35.3324779903705
2021-11-09 12:43:58,663 - opnmf - INFO - iter=400 diff=2.6689515567926128e-05, obj=35.32899436386406
2021-11-09 12:43:58,674 - opnmf - INFO - iter=500 diff=1.0405334018094638e-05, obj=35.327894246573294
2021-11-09 12:43:58,675 - opnmf - INFO - Converged in 505 iterations
2021-11-09 12:43:58,675 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,681 - opnmf - INFO - iter=0 diff=0.8976623999686378, obj=41.422010470080295
2021-11-09 12:43:58,692 - opnmf - INFO - iter=100 diff=0.00020818656953698473, obj=26.049208627681804
2021-11-09 12:43:58,705 - opnmf - INFO - iter=200 diff=0.0002942189486071896, obj=26.07355340627813
2021-11-09 12:43:58,717 - opnmf - INFO - iter=300 diff=0.0008200712631473474, obj=26.159067929016707
2021-11-09 12:43:58,729 - opnmf - INFO - iter=400 diff=0.003440842157905699, obj=25.64931103119671
2021-11-09 12:43:58,739 - opnmf - INFO - iter=500 diff=0.0003553420328116165, obj=24.829016614150092
2021-11-09 12:43:58,745 - opnmf - INFO - iter=600 diff=7.545713389746581e-05, obj=24.78217795511598
2021-11-09 12:43:58,751 - opnmf - INFO - iter=700 diff=3.272849734215369e-05, obj=24.77257011545198
2021-11-09 12:43:58,757 - opnmf - INFO - iter=800 diff=3.125373328278115e-05, obj=24.768648068527778
2021-11-09 12:43:58,763 - opnmf - INFO - iter=900 diff=3.4051969781166636e-05, obj=24.766887780475304
2021-11-09 12:43:58,769 - opnmf - INFO - iter=1000 diff=3.12703354574981e-05, obj=24.766592481555435
2021-11-09 12:43:58,775 - opnmf - INFO - iter=1100 diff=2.4374523870220313e-05, obj=24.767123845457586
2021-11-09 12:43:58,781 - opnmf - INFO - iter=1200 diff=1.7108387598397127e-05, obj=24.76784667080174
2021-11-09 12:43:58,787 - opnmf - INFO - iter=1300 diff=1.1436047636091781e-05, obj=24.76843498824242
2021-11-09 12:43:58,789 - opnmf - INFO - Converged in 1333 iterations
2021-11-09 12:43:58,789 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,790 - opnmf - INFO - iter=0 diff=0.8988431866437399, obj=39.620744072126556
2021-11-09 12:43:58,797 - opnmf - INFO - iter=100 diff=0.0002442011795665008, obj=1.8404900175132692
2021-11-09 12:43:58,803 - opnmf - INFO - iter=200 diff=5.289042500263592e-05, obj=0.8567803188985617
2021-11-09 12:43:58,809 - opnmf - INFO - iter=300 diff=2.2223185551858824e-05, obj=0.554913988960818
2021-11-09 12:43:58,815 - opnmf - INFO - iter=400 diff=1.2122146928567085e-05, obj=0.40950251068929355
2021-11-09 12:43:58,818 - opnmf - INFO - Converged in 439 iterations
2021-11-09 12:43:58,818 - opnmf - INFO - Fitting estimators with original data
2021-11-09 12:43:58,818 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,819 - opnmf - INFO - iter=0 diff=0.8979166119932411, obj=18.19299122423655
2021-11-09 12:43:58,819 - opnmf - INFO - Converged in 1 iterations
2021-11-09 12:43:58,819 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,820 - opnmf - INFO - iter=0 diff=0.9005345540236736, obj=17.592898608366433
2021-11-09 12:43:58,825 - opnmf - INFO - iter=100 diff=0.00478233404661628, obj=12.374361231854795
2021-11-09 12:43:58,831 - opnmf - INFO - iter=200 diff=0.0017090250985304766, obj=9.236112536836712
2021-11-09 12:43:58,837 - opnmf - INFO - iter=300 diff=0.00046703490549873124, obj=8.27411422719614
2021-11-09 12:43:58,842 - opnmf - INFO - iter=400 diff=0.00015084168501771364, obj=8.021475182985363
2021-11-09 12:43:58,848 - opnmf - INFO - iter=500 diff=5.3279572748430676e-05, obj=7.9417509947257425
2021-11-09 12:43:58,854 - opnmf - INFO - iter=600 diff=1.9508155278100318e-05, obj=7.9138893105962325
2021-11-09 12:43:58,858 - opnmf - INFO - Converged in 668 iterations
2021-11-09 12:43:58,858 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,859 - opnmf - INFO - iter=0 diff=0.9008854436852691, obj=17.589994890219803
2021-11-09 12:43:58,865 - opnmf - INFO - iter=100 diff=0.0064903519204170465, obj=12.28189236097726
2021-11-09 12:43:58,871 - opnmf - INFO - iter=200 diff=0.002908357343582906, obj=7.4284284947145345
2021-11-09 12:43:58,877 - opnmf - INFO - iter=300 diff=0.0008369396656013369, obj=4.692345362790706
2021-11-09 12:43:58,883 - opnmf - INFO - iter=400 diff=0.0003334059584117292, obj=3.746048776589676
2021-11-09 12:43:58,889 - opnmf - INFO - iter=500 diff=0.00016958404516659347, obj=3.386655667852878
2021-11-09 12:43:58,895 - opnmf - INFO - iter=600 diff=0.00010053594640468685, obj=3.224643627824672
2021-11-09 12:43:58,901 - opnmf - INFO - iter=700 diff=6.587474562984935e-05, obj=3.140665500006889
2021-11-09 12:43:58,907 - opnmf - INFO - iter=800 diff=4.62605747189034e-05, obj=3.0923386173788283
2021-11-09 12:43:58,913 - opnmf - INFO - iter=900 diff=3.416646735864023e-05, obj=3.06225625646368
2021-11-09 12:43:58,919 - opnmf - INFO - iter=1000 diff=2.6215926734490887e-05, obj=3.0423680638944566
2021-11-09 12:43:58,925 - opnmf - INFO - iter=1100 diff=2.0724385737880826e-05, obj=3.0285824848281915
2021-11-09 12:43:58,931 - opnmf - INFO - iter=1200 diff=1.6779513269241325e-05, obj=3.0186571197072416
2021-11-09 12:43:58,937 - opnmf - INFO - iter=1300 diff=1.3853983874180934e-05, obj=3.011285535705445
2021-11-09 12:43:58,943 - opnmf - INFO - iter=1400 diff=1.162648450490813e-05, obj=3.0056673153828544
2021-11-09 12:43:58,949 - opnmf - INFO - Converged in 1494 iterations
2021-11-09 12:43:58,949 - opnmf - INFO - Initializing using nndsvd
2021-11-09 12:43:58,950 - opnmf - INFO - iter=0 diff=0.9009726594607053, obj=17.57956702209738
2021-11-09 12:43:58,956 - opnmf - INFO - iter=100 diff=0.004736622724118771, obj=11.56302516543663
2021-11-09 12:43:58,962 - opnmf - INFO - iter=200 diff=0.0026013503303404665, obj=7.444752313840761
2021-11-09 12:43:58,968 - opnmf - INFO - iter=300 diff=0.0008629189126871971, obj=4.139826452234608
2021-11-09 12:43:58,974 - opnmf - INFO - iter=400 diff=0.00034684015663284087, obj=2.5709506761378065
2021-11-09 12:43:58,981 - opnmf - INFO - iter=500 diff=0.00017414127196778285, obj=1.8021428845057597
2021-11-09 12:43:58,987 - opnmf - INFO - iter=600 diff=0.00010195858124491413, obj=1.3696389513039644
2021-11-09 12:43:58,993 - opnmf - INFO - iter=700 diff=6.617752710359966e-05, obj=1.0980898895403604
2021-11-09 12:43:58,999 - opnmf - INFO - iter=800 diff=4.615562611244949e-05, obj=0.9135682660008758
2021-11-09 12:43:59,005 - opnmf - INFO - iter=900 diff=3.392284162986168e-05, obj=0.7807271391302761
2021-11-09 12:43:59,011 - opnmf - INFO - iter=1000 diff=2.594008726195127e-05, obj=0.6808413393286741
2021-11-09 12:43:59,018 - opnmf - INFO - iter=1100 diff=2.045866049870759e-05, obj=0.6031603926541299
2021-11-09 12:43:59,024 - opnmf - INFO - iter=1200 diff=1.6539575385095064e-05, obj=0.5411070811307576
2021-11-09 12:43:59,030 - opnmf - INFO - iter=1300 diff=1.3644125708542285e-05, obj=0.49044638273711505
2021-11-09 12:43:59,036 - opnmf - INFO - iter=1400 diff=1.1446172057168089e-05, obj=0.4483349544164567
2021-11-09 12:43:59,041 - opnmf - INFO - Converged in 1484 iterations

Plot the results

plt.figure()
plt.title('Rank selection on IRIS dataset')
plt.plot(tested_ranks, random_errors, label='permuted')
plt.plot(tested_ranks, errors, label='original')

good_errors = errors[good_ranks - min_components]

plt.plot(good_ranks, good_errors, label='selected', marker='o', c='r',
         ls='None')

plt.xticks(tested_ranks)
plt.xlabel('# Components')
plt.ylabel('Error')
plt.legend()
plt.show()