Matrix Factorization (MF)� Image Compression� Dimension Reduction� Feature Extraction (clustering)

X= + noise

m

n r

m

r

n

Memory: mn Memory: (m+n)r

P: Pattern Matrix C: Coefficient MatrixD: Data Matrix

Image Compression

Pansy Flower image, collected fromhttp://www.ats.ucla.edu/stat/r/code/pansy.jpg

This image is 600×465 pixels

Low Rank Reconstruction

Rank-1 approximation Rank-5 approximation

Low Rank Reconstruction

Rank-50 approximation Rank-100 approximation Original image

Drosophila Image Analysis

NMF vs. MF

Matrix Completion

Customers

0 2 ? 0 3 ?

1 ? 1 0 ? 1

? 3 4 ? ? 2

1 1 ? 1 ? 6

? ? 1 1 0 1

2 2 ? ? ? ?

Item

s (W

ines

)

Quantity /

Rating