LogDet Divergence-Based Metric Learning With Triplet Constraints and Its Applications

Abstract

How to select and weigh features has always been a difficult problem in many image processing and pattern recognition applications. A data-dependent distance measure can address this problem to a certain extent, and therefore an accurate and efficient metric learning becomes necessary. In this paper, we propose a LogDet divergence-based metric learning with triplet constraints (LDMLT) approach, which can learn Mahalanobis distance metric accurately and efficiently. First of all, we demonstrate the good properties of triplet constraints and apply it in LogDet divergence-based metric learning model. Then, to deal with high-dimensional data, we apply a compressed representation method to learn, store, and evaluate Mahalanobis matrix efficiently. Besides, a dynamic triplets building strategy is proposed to build a feedback from the obtained Mahalanobis matrix to the triplet constraints, which can further improve the LDMLT algorithm. Furthermore, the proposed method is applied to various applications, including pattern recognition, facial expression recognition, and image retrieval. The results demonstrate the improved performance of the proposed approach.

Learning a Mahalanobis Distance-Based Dynamic Time Warping Measure for Multivariate Time Series Classification

“…References [25] and [38] pointed out that triplet constraints can be derived from pairwise constraints, but not vice versa. In our previous work [37], we have demonstrated that triplet constraints are weaker than the pairwise constraints theoretically. Thus, triplet constraint is the weakest one as well as the most natural constraint of these three constraints.…”

“…If two instances belongs to the same category, the pair is labeled as similarity and their target Mahalanobis distance should be smaller than a desired superior limit; if not, the pair will be labeled as dissimilarity and their target Mahalanobis distance should be larger than a desired lower limit. Although pairwise labels are weaker than class labels [35], some of the constraints are needless [37]. The pairwise label still has some limitations in practical applications.…”

“…It means that the scale of the Mahalanobis distance has no effect on the performance of classification or clustering of MTS. All these advantages make Mahalanobis distance a good local distance metric [22] for MTS comparison. However, how to learn a Mahalanobis metric from the training samples is a complex process.…”

Online Similarity Learning for Big Data with Overfitting

“…Similarity measurement is a fundamental problem in machine learning and computer vision domain [6], [24], [25], [26], [27], [28], [29], [30]. In comparison with traditional fixed metrics, e.g., euclidean and Mahalanobis distance, metric learning [1], [2], [3], [4] is the task of learning a distance function over objects.…”

“…Liu et al [40] propose an interesting work to handle the similarity metric learning with low-rank constraint for high dimensional data, where the number of training samples n is much smaller than the feature dimension d, i.e., n < < d. Mei et al [27] propose a logdet divergencebased metric learning model. In [38], [39], Shalit et al design an embedded manifold of low rank matrix for online metric learning model, and in [37], a Riemannian method is proposed to pursue a low rank positive semidefinite matrix.…”