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.
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