Metric learning has been widely used in face and kinship verification and a number of such algorithms have been proposed over the past decade. However, most existing metric learning methods only learn one Mahalanobis distance metric from a single feature representation for each face image and cannot deal with multiple feature representations directly. In many face verification applications, we ...

The purpose of this paper is to introduce a new distance metric learning algorithm for ordinal regression. Ordinal regression addresses the problem predicting classes which there natural ordering, but real distances between are unknown. Since walks fine line standard and classification, it common pitfall either apply regression-like numerical treatment variables or underrate information applyin...

Using a metric feature space for pattern recognition, data mining, and machine learning greatly simplifies the mathematics because distances are preserved under rotation and translation in feature space. A metric space also provides a “ruler”, or absolute measure of how different two feature vectors are. In the computer vision community color can easily be misstreated as a metric distance. This...

In this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. Our results generalize the corresponding results obtained by Y. J. Cho, R. Saadati, Shenghua Wang (Y. J. Cho, R. Saadati, Shenghua Wang, Common fixed point  heorems on generalized distance in ordere...

In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

In many machine learning and pattern recognition tasks, there is always a need for appropriate metric functions to measure pairwise distance or similarity between data, where a metric function is a function that defines a distance or similarity between each pair of elements of a set. In this thesis, we propose Triangular Similarity Metric Learning (TSML) for automatically specifying a metric fr...

Efficient learning of an appropriate distance metric is an increasingly important problem in machine learning. However, current methods are limited by scalability issues or are unsuited to use with general similarity/dissimilarity constraints. In this paper, we propose an efficient metric learning method based on the max-margin framework with pairwise constraints that has a strong generalizatio...

In this paper, we address the metric learning problem utilizing a margin-based approach. Our metric learning problem is formulated as a quadratic semi-definite programming problem (QSDP) with local neighborhood constraints, which is based on the Support Vector Machine (SVM) framework. The local neighborhood constraints ensure that examples of the same class are separated from examples of differ...

We propose to learn multiple local Mahalanobis distance metrics to perform knearest neighbor (kNN) classification of temporal sequences. Temporal sequences are first aligned by dynamic time warping (DTW); given the alignment path, similarity between two sequences is measured by the DTW distance, which is computed as the accumulated distance between matched temporal point pairs along the alignme...