Reduced-rank Method Research Articles

Reduced-rank STAP performance analysis

The space-time radar problem is well suited to the application of techniques that take advantage of the low-rank property of the space-time covariance matrix. It is shown that reduced-rank (RR) methods outperform full-rank space-time adaptive processing (STAP) when the space-time covariance matrix is estimated from a data set with limited support. The utility of RR methods is demonstrated by theoretical analysis, simulations and analysis of real data. It is shown that RR processing has two opposite effects on the performance: increased statistical stability which tends to improve performance, and introduction of a bias which lowers the signal-to-noise ratio (SNR). A method for evaluating the theoretical conditioned SNR for fixed RR transforms is also presented. It Is shown that while best performance is obtained using data-dependent transforms, the loss incurred by the application of fixed transforms (such as the discrete cosine transform) may be relatively small. The main advantage of fixed transforms is the availability of efficient computational procedures for their implementation. These findings suggest that RR methods could facilitate the development of practical, real-time STAP technology.

Reduced-Rank Models for Nutrition Knowledge Assessment

The dependence of multiple interrelated responses on a set of covariates can be efficiently and parsimoniously modeled using reduced-rank methods. Two forms of reduced-rank models are possible depending on assumptions about response error correlations. When the response outcomes are binary, a minimum distance estimator based on first-stage marginal probit regressions can be used to estimate the reduced-rank models. The alternative models and the estimation procedure are illustrated using a data set on the dietary fats and cholesterol knowledge of a sample of U.S. household meal planners.

Optimal Reduced Rank Modeling, Prediction, Monitoring and Control using Canonical Variate Analysis

Abstract Reduced rank methods such as partial least squares (PLS), principal component analysis (PCA), and canonical variate analysis (CVA), offer methods to determine economical models of relationships between process variables. It is shown that for multivariate regression, CVA is a maximum likelihood method for determining the rank of such a relationship. As a result CVA has optimal statistical properties in terms of prediction accuracy and testing hypotheses not shared by PLS and PCA. The extension of CVA to system identification of dynamical processes that gives optimal selection of the process state order is discussed. The use of CVA in process monitoring is developed for detecting process changes. Applications to chemical processes and particularly to a continuous stirred tank reactor for system identification, monitoring and control is discussed.