In real tasks, it is usually the case that a better classification performance can be obtained when a good distance metric is used; therefore, distance metric learning has attracted significant attention in the past few years. Typical studies of distance metric learning concern about how to construct an appropriate distance metric that is able to separate training data points from different cla...

Most distance metric learning (DML) approaches focus on learning a Mahalanobis metric for measuring distances between examples. However, for particular feature representations, e.g., histogram features like BOW and SPM, Mahalanobis metric could not model the correlations between these features well. In this work, we define a nonMahalanobis distance for histogram features, via Expected Hitting T...

In this work, we propose a scalable and fast algorithm to learn a Mahalanobis distance metric. The key issue in this task is to learn an optimal Mahalanobis matrix in this distance metric. It has been shown in the statistical learning theory [?] that increasing the margin between different classes helps to reduce the generalization error. Hence, our algorithm formulates the Mahalanobis matrix a...

It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. A weak point of ITML-based methods is that the distance threshold for similarity/dissimilarity constraints must be determined manually and it is sensitive to generalization performance, although the ITML-based methods enjoy an advantage that the Bregman projection framewor...

Distance metric plays an important role in machine learning which is crucial to the performance of a range of algorithms. Metric learning, which refers to learning a proper distance metric for a particular task, has attracted much attention in machine learning. In particular, multi-task learning deals with the scenario where there are multiple related metric learning tasks. By jointly training ...

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a number of methods have been proposed to efficiently learn it. However, the nature ...

In this paper we study the problem of learning a low-rank (sparse) distance matrix. We propose a novel metric learning model which can simultaneously conduct dimension reduction and learn a distance matrix. The sparse representation involves a mixed-norm regularization which is non-convex. We then show that it can be equivalently formulated as a convex saddle (min-max) problem. From this saddle...

The contributions of this work are threefold. First, various metric learning techniques are analyzed and systematically studied under a unified framework to highlight the criticality of data-dependent distance metric in machine learning. The metric learning algorithms are categorized as naive, semi-naive, complete and high-level metric learning, under a common distance measurement framework. Se...

Anomaly detection methods can be very useful in identifying unusual or interesting patterns in data. A recently proposed conditional anomaly detection framework extends anomaly detection to the problem of identifying anomalous patterns on a subset of attributes in the data. The anomaly always depends (is conditioned) on the value of remaining attributes. The work presented in this paper focuses...