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Dimensionality Reduction for Histogram Features Based on Supervised Nonnegative Matrix Factorization
Mitsuru AMBAI Nugraha P. UTAMA Yuichi YOSHIDA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E94D
No.10
pp.18701879 Publication Date: 2011/10/01
Online ISSN: 17451361
DOI: 10.1587/transinf.E94.D.1870
Print ISSN: 09168532 Type of Manuscript: Special Section PAPER (Special Section on InformationBased Induction Sciences and Machine Learning) Category: Keyword: dimensionality reduction, nonnegative matrix factorization, histogrambased features,
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Summary:
Histogrambased image features such as HoG, SIFT and histogram of visual words are generally represented as highdimensional, nonnegative vectors. We propose a supervised method of reducing the dimensionality of histogrambased features by using nonnegative 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 cannotlinks and mustlinks in pairs of training data. A multiplicative update rule for minimizing the newlydefined 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 lowdimensional 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.

