Ali Akbar Shams Baboli - MSc Student at Department of Electrical Engineering, University of Science and Technology, Tehran, Iran
Samad Araghi - BSc Student at Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Aref Shams Baboli - BSc Student at Department of Electrical and computer Engineering, Noshirvani University of Technology, Babol
Gholamali Rezai rad - Associate professor at Department of Electrical Engineering, University of Science and Technology

This paper is proposed a method to find the best dimension for Multilinear discriminant analysis (MDA). The main algorithm is the same as MDA. As we knew, MDA is using an iterative algorithm to maximize a tensor-based discriminant criterion. Because the number of possible subspace dimensions for any kind of tensor objects is extremely high, so testing all of them for finding the best one is not feasible. So this paper is presented a method to solve that problem. The main criterion of this algorithm is not similar to Sequential mode truncation (SMT) and full projection is used to initialize the iterative solution and find the best dimension for MDA. This paper is saving the extra times that we should spend to find the best dimension. So the execution time will be decreasing so much. It should be noted that MDA works with tensor objects so the structure of the objects has been never broken. Therefore the performance of this method is getting better. The advantage of this algorithm is avoiding the curse of dimensionality and having a better performance in the cases with small sample sizes. Finally, some experiments on ORL, FERET and CMU-PIE databases have been provided.

Multilinear discriminant analysis, subspace learning, Dimensionality reduction, full projection, tensor objects