NMF learns interpretable parts

Unsupervised Learning in Python

Benjamin Wilson

Director of Research at lateral.io

Example: NMF learns interpretable parts

Word-frequency array articles (tf-idf)
20,000 scientific articles (rows)
800 words (columns)

Articles word frequency array

Applying NMF to the articles

print(articles.shape)

(20000, 800)

from sklearn.decomposition import NMF
nmf = NMF(n_components=10)
nmf.fit(articles)

NMF(n_components=10)

print(nmf.components_.shape)

(10, 800)

NMF components are topics

nmf.components_

NMF components are topics

one row of nmf.components_ selected and a bar plot for each word where height represents the tfidf

NMF components are topics

box with top words and values: species 2.95, plant 1.05, plants 0.78, etc.

NMF components are topics

new box with top words from different row of nmf.components_: university 3.57, prof 1.19, college 0.88, etc

NMF components

For documents:
- NMF components represent topics
- NMF features combine topics into documents
For images, NMF components are parts of images

box with 3 stripes approximately equals 0.98 times box with one stripe plus 0.91 times box with a different stripe plus 0.95 times box with a different stripe

Grayscale images

"Grayscale" image = no colors, only shades of gray
Measure pixel brightness
Represent with value between 0 and 1 (0 is black)
Convert to 2D array

2 by 3 rectangle of pixels with varying degrees of white/black/gray

Grayscale image example

An 8x8 grayscale image of the moon, written as an array

pixelated illustration of the moon with arrow pointing to array of numbers with the same dimension holding numbers between 0 to 1

Grayscale images as flat arrays

Enumerate the entries
Row-by-row
From left to right, top to bottom

2 by 3 pixel box pointing to array with numbers

Grayscale images as flat arrays

Enumerate the entries
Row-by-row
From left to right, top to bottom

2 by 3 pixel box pointing to 2 by 3 array with numbers pointing to a 1 by 6 array of numbers

Encoding a collection of images

Collection of images of the same size
Encode as 2D array
Each row corresponds to an image
Each column corresponds to a pixel
... can apply NMF!

One row of nmf.components_ that represents the 2x3 pixel image

Visualizing samples

print(sample)

[ 0.   1.   0.5  1.   0.   1. ]

bitmap = sample.reshape((2, 3))
print(bitmap)

[[ 0.   1.   0.5]
 [ 1.   0.   1. ]]

from matplotlib import pyplot as plt
plt.imshow(bitmap, cmap='gray', interpolation='nearest')
plt.show()

Let's practice!

Unsupervised Learning in Python