UoI-NMF for robust parts-based decomposition of noisy data

This example will demonstrate parts-based decomposition with UoI-NMF on the swimmer dataset. The swimmer dataset is the canonical example of separable data.

Swimmer dataset

import matplotlib
import matplotlib.pyplot as plt
import numpy as np

from sklearn.preprocessing import minmax_scale
from sklearn.manifold import TSNE

from pyuoi.decomposition import UoI_NMF
from pyuoi.datasets import load_swimmer


matplotlib.rcParams['figure.figsize'] = [4, 4]
np.random.seed(10)

swimmers = load_swimmer()
swimmers = minmax_scale(swimmers, axis=1)

Original Swimmer samples

fig, ax = plt.subplots(4, 4, subplot_kw={'xticks': [], 'yticks': []})
indices = np.random.randint(16, size=16) + np.arange(0, 256, 16)
ax = ax.flatten()
for i in range(len(indices)):
    ax[i].imshow(swimmers[indices[i]].reshape(32, 32).T,
                 aspect='auto', cmap='gray')

Swimmer samples corrupted with Absolute Gaussian noise

Corrupt the images with with absolute Gaussian noise with std = 0.25.

reps = 1
n_swim = swimmers.shape[0]
corrupted = np.zeros((n_swim * reps, swimmers.shape[1]))
for r in range(reps):
    noise = np.abs(np.random.normal(scale=0.25, size=swimmers.shape))
    corrupted[r * n_swim:(r + 1) * n_swim] = swimmers + noise

fig, ax = plt.subplots(4, 4, subplot_kw={'xticks': [], 'yticks': []})
ax = ax.flatten()
for i in range(len(indices)):
    ax[i].imshow(corrupted[indices[i]].reshape(32, 32).T,
                 aspect='auto', cmap='gray')

Run UoI NMF on corrupted Swimmer data

Twenty bootstraps should be enough. min_pts should be half of the number of bootstraps.

nboot = 20
min_pts = nboot / 2
ranks = [16]

shape = corrupted.shape

uoi_nmf = UoI_NMF(n_boots=nboot, ranks=ranks, db_min_samples=min_pts,
                  nmf_max_iter=800)

transformed = uoi_nmf.fit_transform(corrupted)
recovered = transformed @ uoi_nmf.components_

NMF Swimmer bases

order = np.argsort(np.sum(uoi_nmf.components_, axis=1))

fig, ax = plt.subplots(4, 4, subplot_kw={'xticks': [], 'yticks': []})
ax = ax.flatten()
for i in range(uoi_nmf.components_.shape[0]):
    ax[i].imshow(uoi_nmf.components_[order[i]].reshape(32, 32).T,
                 aspect='auto', cmap='gray')

Recovered Swimmers

fig, ax = plt.subplots(4, 4, subplot_kw={'xticks': [], 'yticks': []})
ax = ax.flatten()
for i in range(len(indices)):
    ax[i].imshow(recovered[indices[i]].reshape(32, 32).T,
                 aspect='auto', cmap='gray')

Plot them all together so we can see how well we recovered the original swimmer data.

fig, ax = plt.subplots(3, 16, figsize=(27, 5),
                       subplot_kw={'xticks': [], 'yticks': []})
indices = np.random.randint(16, size=16) + np.arange(0, 256, 16)
ax = ax.flatten()

# plot Original
ax[0].set_ylabel('Original', rotation=0, fontsize=25, labelpad=40)
ax[0].yaxis.set_label_coords(-1.0, 0.5)
for i in range(len(indices)):
    ax[i].imshow(swimmers[indices[i]].reshape(32, 32).T,
                 aspect='auto', cmap='gray')

# plot Corrupted
ax[16].set_ylabel('Corrupted', rotation=0, fontsize=25, labelpad=40)
ax[16].yaxis.set_label_coords(-1.1, 0.5)
for i in range(len(indices)):
    ax[16 + i].imshow(corrupted[indices[i]].reshape(32, 32).T,
                      aspect='auto', cmap='gray')

# plot Recovered
ax[32].set_ylabel('Recovered', rotation=0, fontsize=25, labelpad=40)
ax[32].yaxis.set_label_coords(-1.1, 0.5)
for i in range(len(indices)):
    ax[32 + i].imshow(recovered[indices[i]].reshape(32, 32).T,
                      aspect='auto', cmap='gray')

To see what DBSCAN is doing, let’s look at the bases samples.

plt.figure()
embedding = TSNE(n_components=2).fit_transform(uoi_nmf.bases_samples_)
sc = plt.scatter(embedding[:, 0], embedding[:, 1],
                 c=uoi_nmf.bases_samples_labels_, s=80, cmap="nipy_spectral")
sc.set_facecolor('none')
plt.show()

Out:

/home/docs/checkouts/readthedocs.org/user_builds/pyuoi/envs/latest/lib/python3.7/site-packages/sklearn/manifold/_t_sne.py:783: FutureWarning: The default initialization in TSNE will change from 'random' to 'pca' in 1.2.
  FutureWarning,
/home/docs/checkouts/readthedocs.org/user_builds/pyuoi/envs/latest/lib/python3.7/site-packages/sklearn/manifold/_t_sne.py:793: FutureWarning: The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.
  FutureWarning,