Initialization enhancer for non-negative matrix factorization

Initialization enhancer for non-negative matrix factorization

Zhonglong Zheng, Jie Yang, Yitan Zhu

Engineering Applications of Artificial Intelligence 20 (2007) 101–110

Presenter Chia-Cheng Chen 1

Introduction

Non-negative matrix factorization algorithm

Initializing NMF with different techniques

Experimental results

Conclusion

Outline

2

Background(1/2)

3

Background(2/2)

4

NMF has been applied to many areas such as dimensionality reduction, image classification, image compression.

However, particular emphasis has to be placed on the initialization of NMF because of its local convergence, although it is usually ignored in many documents.

Introduction

5

Non-negative matrix factorization (NMF) algorithm

where

Dimensionality reduction is achieved when r < N

Non-negative matrix factorization algorithm(1/4)

6

Euclidean distance

◦Update rule

Non-negative matrix factorization algorithm(2/4)

7

KL divergence

Update rule

Non-negative matrix factorization algorithm(3/4)

8

SJTU-face-database◦ 400 images ◦ Size: 64x64

Non-negative matrix factorization algorithm(4/4)

9

Three techniques

◦ PCA-based initialization

◦Clustering-based initialization

◦Gabor-based initialization

Initializing NMF with different techniques(1/5)

10

PCA-based initialization

m x N matrix X

Use SVD compute the eigenvectors and eigenvalues

Initializing NMF with different techniques(2/4)

11

PCA-based initialization

Initializing NMF with different techniques(3/5)

12

Clustering-based initialization (Fuzzy c-means) Membership matrix

Objective function

Update rule

Initializing NMF with different techniques(4/5)

13

Gabor-based initialization Gabor kernals

where

Gabor feature

Initializing NMF with different techniques(5/5)

14

Experimental results

15

Experimental results

16

Non-negative matrix factorization is a useful tool in the analysis of a diverse range of data.

Researchers often take random initialization into account when utilizing NMF.

In fact, random initialization may make the experiments unrepeatable because of its local minima property, although neural networks are not.

Conclusion

17