We show that the widely used Kendall tau correlation coefficient, and the related Mallows kernel, are positive definite kernels for permutations. They offer computationally attractive alternatives to more complex kernels on the symmetric group to learn from rankings, or learn to rank. We show how to extend these kernels to partial rankings, multivariate rankings and uncertain rankings. Examples...

Ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (CV index), distance between fuzzy set...

Our goal is to learn a Mahalanobis distance by minimizing a loss defined on the weighted sum of the precision at different ranks. Our core motivation is that minimizing a weighted rank loss is a natural criterion for many problems in computer vision such as person re-identification. We propose a novel metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). We th...

Face recognition systems typically have a rather short operating distance with standoff (distance between the camera and the subject) limited to 1∼2 meters. When these systems are used to capture face images at a larger distance (5∼10 m), the resulting images contain only a small number of pixels on the face region, resulting in a degradation in face recognition performance. To address this pro...

A proper distance metric is fundamental in many computer vision and pattern recognition applications such as classification, image retrieval, face recognition and so on. However, it is usually not clear what metric is appropriate for specific applications, therefore it becomes more reliable to learn a task oriented metric. Over the years, many metric learning approaches have been reported in li...

We compare the two duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes, in a form that never appeared in the literature. The identities which we derive are very easy to handle, and allow us to re-establish in a very c...

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.

The results of this paper are concerned with the multi-covering radius, a generalization of covering radius, of Rank Distance (RD) codes. This leads to greater understanding of RD codes and their distance properties. Results on multi-covering radii of RD codes under various constructions are given by varying the parameters. Some bounds are established. A relationship between multi-covering radi...

This paper focuses on applications of fuzzy segmentation in region indexing and image retrieval. First, our algorithm of fuzzy segmentation is shortly explained. Some features characterizing a fuzzy region are then defined, and a distance between fuzzy regions is proposed. This distance can be used to rank regions on color and/or shape features or to perform a partial request from a image, requ...

Ranking of a company's financial information is one of the most important tools for identifying strengths and weaknesses and identifying opportunities and threats outside the company. In this study, it is attempted to examine the financial statements of companies to rank and explain the transparency of financial information of 198 companies during 2009-2017 using artificial intelligence and neu...