Logistic Component Analysis for Fast Distance Metric Learning

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Abstract
Discriminating feature extraction is important to achieve high recognition rate in a classification problem. Fisher's linear discriminant analysis (LDA) is one of the well-known discriminating feature extraction methods and is closely related to the Mahalanobis distance metric learning. Neighborhood component analysis (NCA) is one of the Mahalanobis distance metric learning methods based on stochastic nearest neighbor assignment. The objective function of NCA can be expressed as a within-class coherency by a simple formula, and NCA extracts discriminating features by minimizing the objective function. Unfortunately, the computational cost of NCA significantly increases as the number of input data increases. For reducing the computational cost, we propose a fast distance metric learning method by taking the between-class distinguish ability into account of nearest mean classification. According to the experimental results using standard repository datasets, the computational time of our method is evaluated as 27 times shorter than that of NCA while keeping or improving the accuracy.

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