A Fast and Easy Regression Technique for k-NN Classification Without Using Negative Pairs

TL;DR

This paper introduces a fast, efficient regression-based method for learning a dissimilarity function for k-NN classification that avoids negative pairs, achieving comparable or better accuracy with significantly reduced training time.

Contribution

It presents a novel regression approach that learns a transformation for labeled data only, simplifying and speeding up metric learning for k-NN classification.

Findings

Achieves comparable or better accuracy than state-of-the-art metric learning methods.

Training is over two orders of magnitude faster on large datasets.

The method reduces hubness in data, improving classification performance.

Abstract

This paper proposes an inexpensive way to learn an effective dissimilarity function to be used for $k$-nearest neighbor ($k$-NN) classification. Unlike Mahalanobis metric learning methods that map both query (unlabeled) objects and labeled objects to new coordinates by a single transformation, our method learns a transformation of labeled objects to new points in the feature space whereas query objects are kept in their original coordinates. This method has several advantages over existing distance metric learning methods: (i) In experiments with large document and image datasets, it achieves $k$-NN classification accuracy better than or at least comparable to the state-of-the-art metric learning methods. (ii) The transformation can be learned efficiently by solving a standard ridge regression problem. For document and image datasets, training is often more than two orders of magnitude faster than the fastest metric learning methods tested. This speed-up is also due to the fact that the proposed method eliminates the optimization over "negative" object pairs, i.e., objects whose class labels are different. (iii) The formulation has a theoretical justification in terms of reducing hubness in data.