Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to the problem, but typically requires solving a semidefinite programming (SDP) problem, which is computationally expensive. Standard interior-point SDP solvers ...

Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is usually employed, with samples identified through computing the Euclidean feature distance. However, the global Euclidean distance cannot faithfully charact...

In the past few years, metric learning, semi-supervised learning, and manifold learning methods have aroused a great deal of interest in the machine learning community. Many machine learning and pattern recognition algorithms rely on a distance metric. Instead of choosing the metric manually, a promising approach is to learn the metric from data automatically. Besides some early work on metric ...

The scaling parameter α helps maintain a balance between supervised and unsupervised learning in semi-supervised Fuzzy c-Means (ssFCM). In this study, we investigated the effects of different α values, 0.1, 0.5, 1 and 10 in Pedrycz and Waletsky’s ssFCM with various amounts of labelled data, 10%, 20%, 30%, 40%, 50% and 60% and three distance metrics, Euclidean, Mahalanobis and kernel-based on th...

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

Conventional pairwise constrained metric learning methods usually restrict the distance between samples of a similar pair to be lower than a fixed upper bound, and the distance between samples of a dissimilar pair higher than a fixed lower bound. Such fixed bound based constraints, however, may not work well when the intraand inter-class variations are complex. In this paper, we propose a shrin...

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they ...

The success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data. It is often beneficial to learn such a metric from the input training data, instead of using a default one such as the Euclidean distance. In this work, we propose a boosting-based technique, termed BOOSTMETRIC, for learning a quadratic...

Metric learning algorithms can provide useful distance functions for a variety of domains, and recent work has shown good accuracy for problems where the learner can access all distance constraints at once. However, in many real applications, constraints are only available incrementally, thus necessitating methods that can perform online updates to the learned metric. Existing online algorithms...

During last decade, tremendous efforts have been devoted to the research of time series classification. Indeed, many previous works suggested that the simple nearest-neighbor classification is effective and difficult to beat. However, we usually need to determine the distance metric (e.g., Euclidean distance and Dynamic Time Warping) for different domains, and current evidence shows that there ...