The rank aggregation problem consists in finding a consensus ranking on a set of alternatives, based on the preferences of individual voters. These are expressed by permutations, whose distance can be measured in many ways. In this work we study a collection of distances, including the Kendall tau, Spearman footrule, Spearman rho, Cayley, Hamming, Ulam, and Minkowski distances, and compute the ...

This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension of a rank-metric code with given specified Ferrers diagram shape and rank distance. While the conjecture in its generality is wide open, several cases have ...

Error-correcting pairs were introduced independently by Pellikaan and Kötter as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise products of vectors, and are used for many well-known families of codes. In this paper, we define new types of vector products, extending the coordinatewise product, some of which preserve symbolic products of linearize...

Speech is the medium through which information can be conveyed from one person to another. Audible frequency range of human beings is between 20Hz to 20 kHz, significant frequency components has range up to 4 kHz. Rank Order Mean method has been proposed in this work which is used for ejection of impulse noise from the speech signal using Rank. To estimate the time occurrence of impulsive noise...

As the use of web is increasing more day by day, the web users get easily lost in the web’s rich hyper structure. The main aim of the owner of the website is to give the relevant information according their needs to the users. We explained the Web mining is used to categorize users and pages by analyzing user’s behavior, the content of pages and then describe Web Structure mining. This paper in...

In the traditional way of learning from examples of objects the classifiers are built in a feature space. However, alternative ways can be found by constructing decision rules on dissimilarity (distance) representations, instead. In such a recognition process a new object is described by its distances to (a subset of) the training samples. In this paper a number of methods to tackle this type o...

The random matrix uniformly distributed over the set of all mby-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-dista...

Mitochondrial cytochrome b (cytb) is among the most extensively sequenced genes to date across the vertebrates. Here, we employ nearly 2,000 cytb gene sequences from GenBank to calculate and compare levels of genetic distance between sister species, congeneric species, and confamilial genera within and across the major vertebrate taxonomic classes. The results of these analyses parallel and rei...

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed BOOSTMETRIC, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used t...

A classical problem in matrix analysis, total least squares estimation and model reduction theory is that of finding a best approxiniant of a given matrix by lower rank ones. It is common believe that behind every such least squares problem there is an algebraic Riccati equation. In this paper we consider the task of minimizing the distance function fA(X) = | |A —A'|| on varieties of fixed rank...