Dimensionality Reduction for Histogram Features Based on Supervised Non-negative Matrix Factorization

Mitsuru AMBAI  Nugraha P. UTAMA  Yuichi YOSHIDA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E94-D   No.10   pp.1870-1879
Publication Date: 2011/10/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Information-Based Induction Sciences and Machine Learning)
Category: 
Keyword: 
dimensionality reduction,  non-negative matrix factorization,  histogram-based features,  

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Summary: 
Histogram-based image features such as HoG, SIFT and histogram of visual words are generally represented as high-dimensional, non-negative vectors. We propose a supervised method of reducing the dimensionality of histogram-based features by using non-negative matrix factorization (NMF). We define a cost function for supervised NMF that consists of two terms. The first term is the generalized divergence term between an input matrix and a product of factorized matrices. The second term is the penalty term that reflects prior knowledge on a training set by assigning predefined constants to cannot-links and must-links in pairs of training data. A multiplicative update rule for minimizing the newly-defined cost function is also proposed. We tested our method on a task of scene classification using histograms of visual words. The experimental results revealed that each of the low-dimensional basis vectors obtained from the proposed method only appeared in a single specific category in most cases. This interesting characteristic not only makes it easy to interpret the meaning of each basis but also improves the power of classification.