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

Background: Logistic Discriminant method was applied to differentiate malignant from benign in a group of patients with proved breast lesions on the basis of ultrasonic parameters. Materials and Methods: Our database include 273 patients ultrasonographic pictures consisting of 14 quantitative variables. The measured variables were ultrasound propagation velocity, acoustic impedence and attenuation coefficient at 10 MHz in breast lesions at 20, 25, 30 and 35 oc temperature, physicsl density and age. This database was randomly divided into the estimation of 201 and validation of 72 samples. The estimation samples were used to build the logistic Discriminant model, and validation samples were used to validate the performance. Finally, important criteria such as sensitivity, specificity, accuracy and area under the receiver operating characteristic curve (ROC) were evaluated. Results: Our results showed that the logistic Discriminant method was able to classify correctly 67 out of 72 cases presented in the validation sample. The results indicate a remarkable diagnostic accuracy of 93%. Conclusion: A logistic Discriminantor approach is capable of predicting the probability of malignancy of breast cancer. Features extracted from ultrasonic measurement on ultrasound imaging is used in this approach. Iran