A novel extension of Generalized Low-Rank Approximation of Matrices based on multiple-pairs of transformations

TL;DR

This paper introduces an extended multilinear dimensionality reduction method that enhances the search space of existing approaches like GLRAM, preserving spatial relations and reducing overfitting in higher-order data.

Contribution

It proposes a generalized form of GLRAM with a larger search space, improving flexibility and performance while maintaining advantages of multilinear methods.

Findings

Experimental results confirm improved quality of the proposed method.

The approach can be easily applied to other multilinear methods like MPCA and MLDA.

The new method preserves spatial relations and reduces overfitting in higher-order data.

Abstract

Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means that for higher order data like matrices or more generally tensors, data should be fold to the vector format. So, in this approach, the spatial relations of features are not considered and also the probability of over-fitting is increased. Due to these issues, in recent years some methods like Generalized low-rank approximation of matrices (GLRAM) and Multilinear PCA (MPCA) are proposed which deal with the data in their own format. So, in these methods, the spatial relationships of features are preserved and the probability of overfitting could be fallen. Also, their time and space complexities are less than vector-based ones. However, because of the fewer parameters, the search space in a multilinear approach is much smaller than the search space of the vector-based approach. To overcome this drawback of multilinear methods like GLRAM, we proposed a new method which is a general form of GLRAM and by preserving the merits of it have a larger search space. Experimental results confirm the quality of the proposed method. Also, applying this approach to the other multilinear dimensionality reduction methods like MPCA and MLDA is straightforward.