Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...

Wepropose the reduced twin support vector regressor (RTSVR) that uses the notion of rectangular kernels to obtain significant improvements in execution time over the twin support vector regressor (TSVR), thus facilitating its application to larger sized datasets. & 2011 Elsevier B.V. All rights reserved.

Feature selection methods are efficient in modern computer vision applications to reduce the computational cost and the chance of over-fitting. Recently, a novel selectable factor extraction (SFE[3]) framework is proposed to simultaneously perform feature selection and extraction, and is theoretically and practically proved to be effective for high-dimensional data. Although it is advantageous ...

The purpose of this article is to explain how to conduct a multinomial logistic regression (MLR) to increase its usage among social work researchers. A challenge for social work researchers carrying out practice-based research is to incorporate statistical analyses that are comprehensible to clinicians. Another challenge is that categorical variables, as opposed to continuous, commonly occur in...

In recent years much attention has been given to models for two-way contingency tables that can be formulated in terms of reduced rank of a matrix with probabilities. A well-known reduced rank model is the independence model, where the rank is one. For rank higher than one distinct classes of reduced rank models are possible. Each has the independence model as the special case for rank one. A f...

The performance of reduced-rank linear filtering is studied for the suppression of multiple-access interference. A reduced-rank filter resides in a lower dimensional space, relative to the full-rank filter, which enables faster convergence and tracking. We evaluate the large system output signal-to-interference plus noise ratio (SINR) as a function of filter rank for the multistage Wiener filte...

A reduced-rank framework with set-membership filtering (SMF) techniques is presented for adaptive beamforming problems encountered in radar systems. We develop and analyze stochastic gradient (SG) and recursive least squares (RLS)-type adaptive algorithms, which achieve an enhanced convergence and tracking performance with low computational cost as compared to existing techniques. Simulations s...

This paper provides a unified view of, and a further insight into, a class of optimal reduced-rank estimators and filters. An alternating power (AP) method for computing the optimal reduced-rank estimators and filters is derived and analyzed. The AP method is a generalization of the conventional power method for subspace computation, which is shown to be globally and exponentially convergent un...