Discriminant analysis is a way for classification of one object or a group to one or more separate groups that are known or unknown. in scientific researches we often use linear or quadratic functions for classification. But in this paper, we suggest a nonlinear discrimination method that uses two nonparametric.regression methods, namely multivariate adaptive regression splines and adaptive additive model in a simulation study, we investigate the application way of proposed methods and comparing them with the ordinary nonlinear discrimination methods via their means of error rates.

Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA  is to find mode-specific projections that optimally separate tensor data from different classes. However, to solve this task, standard MDA methods use alternating optimization heuristics involving the computation of a succession of tensor-matrix products. Such approaches are most of the time difficult to solve and not natural, highligthing the difficulty to formulate this problem in fully tensor form. In this paper, we propose to solve multilinear discriminant analysis (MDA) by using the concept of transform domain (TD) recently proposed in [15]. We show here that moving MDA to this specific transform domain make its resolution easier and more natural. More precisely, each frontal face of the transformed tensor is processed independently to build a separate optimization sub-problems easier to solve. Next, the obtained solutions are converted into projective tensors by inverse transform. By considering a large number of experiments, we show the effectiveness of our approach with respect to existing MDA methods.

This paper is concerned with the discrimination between two stationary AR(1) plus noise processes in the time domain approach. The distribution of the discriminant function, when the differences between two stationary processes is concentrated in their variances rather than their means, leads to a linear combination of one degree of freedom chisquare random variables. The coefficents are calculated numerically. An analytic method is given by other investigations for ARMA processes, and an extension is given here for AR(1) plus noise processes which have two errors rather than one. The weights and cumulants of the discriminant function are compared using a numerical method

The use of mixture models for clustering and classification has burgeoned into an important subfield of multivariate analysis. These approaches have been around for a half-century or so, with significant activity in the area over the past decade. The primary focus of this paper is to review work in model-based clustering, classification, and discriminant analysis, with particular attention being paid to two techniques that can be implemented using respective R packages. Parameter estimation and model selection are also discussed. The paper concludes with a summary, discussion, and some thoughts on future work.