Multilinear Subspace Learning: Dimensionality Reduction of Multidimensional Data

With the advances in data collection and storage capabilities, massive multidimensional data such as surveillance videos, DNA sequences, and biomedical images are being generated on a daily basis in applications including computer vision, bioinformatics, and biomedical engineering. These data are usually very high-dimensional, with a large amount of redundancy and only occupying a subspace of the input space. Therefore, dimensionality reduction is frequently employed to map high-dimensional data to a low-dimensional space while retaining as much information as possible. However, this is a challenging problem due to the large variability and complex pattern distribution of the input data, and the limited number of samples available for training. Linear subspace learning algorithms are traditional dimensionality reduction techniques that represent input data as vectors and solve for an optimal linear mapping to a lower dimensional space. Unfortunately, they often become inadequate when dealing with multidimensional data in high-dimensional space.

This talk will present multilinear subspace learning (MSL), a novel approach to dimensionality reduction of multidimensional data where the input data are represented in their natural multidimensional form as tensors. Multilinear projections will be introduced first for the direct mapping from high-dimensional tensorial representations to low-dimensional vectorial or tensorial representations. A unifying MSL framework will then be formulated for systematic treatment of the MSL problem and detailed analysis of existing MSL algorithms. Next, three MSL algorithms will be discussed and their applications on pattern recognition and data visualization will be demonstrated. The introduced MSL framework will be of great interest to researchers working on massive multidimensional data.