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In this paper we consider the problem of learning nearest-prototype classifiers in any finite distance space; that is, in any finite set equipped with a distance function. An important advantage of a distance space over a metric space is that the triangle inequality need not be satisfied, which makes our results potentially very useful in practice. We consider a family of binary classifiers for learning nearest-prototype classification on distance spaces, building on the concept of large-width learning which we introduced and studied in earlier works. Nearest-prototype is a more general version of the ubiquitous nearest-neighbor classifier: a prototype may or may not be a sample point. One advantage in the approach taken in this paper is that the error bounds depend on a ‘width’ parameter, which can be sample-dependent and thereby yield a tighter bound. [ABSTRACT FROM AUTHOR]

Abstract: Image-to-class (I2C) distance is a novel measure for image classification and has successfully handled datasets with large intra-class variances. However, due to the lack of a training phase, the performance of this distance is easily affected by irrelevant local features that may hurt the classification accuracy. Besides, the success of this I2C distance relies heavily on the large number of local features in the training set, which requires expensive computation cost for classifying test images. On the other hand, if there are small number of local features in the training set, it may result in poor performance. In this paper, we propose a distance learning method to improve the classification accuracy of this I2C distance as well as two strategies for accelerating its NN search. We first propose a large margin optimization framework to learn the I2C distance function, which is modeled as a weighted combination of the distance from every local feature in an image to its nearest-neighbor (NN) in a candidate class. We learn these weights associated with local features in the training set by constraining the optimization such that the I2C distance from image to its belonging class should be less than that to any other class. We evaluate the proposed method on several publicly available image datasets and show that the performance of I2C distance for classification can significantly be improved by learning a weighted I2C distance function. To improve the computation cost, we also propose two methods based on spatial division and hubness score to accelerate the NN search, which is able to largely reduce the on-line testing time while still preserving or even achieving a better classification accuracy. [Copyright &y& Elsevier]

The problem of nearest-neighbor condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds have been proved on the amount of reduction achieved. In this paper, we present one of the first theoretical results for practical nearest-neighbor condensation algorithms. We propose two condensation algorithms, called RSS and VSS, along with provable upper-bounds on the size of their selected subsets. Additionally, we shed light on the selection size of two well known condensation algorithms, called MSS and FCNN, and compare them to the new algorithms. [ABSTRACT FROM AUTHOR]