High dimensional data sets can be represented in terms of 2-D arrays, i.e. matrices, using a preprocessing method called "unfolding". However, this property provides great convenience and flexibility in using conventional linear algebraic structures in data analysis of any dimension. To this end, matrix decomposition is considered as an essential way of data decomposition. Thus, decomposing matrices effectively plays an important role in data processing.

This work focuses on matrix decomposition using Enhance Multivariance Products Representation (EMPR). EMPR is a high dimensional data decomposition method and enables to represent an N-D array as a finite sum. The finite sum contains N support vectors and determining these vectors are crucial since they affect the representation quality of EMPR directly. In this paper, a new method based on the gradient descent (GD) for optimizing these support vectors is proposed. GD is one of the essential machine learning (ML) algorithms for determining the global minimum of a convex cost function. To improve the efficacy of GD, its variants called Batch GD (BGD) and Stochastic GD (SGD) are employed to the corresponding convex optimization problem and the obtained results are compared. The numerical experiments are conducted on some ill-conditioned matrices and real application data such as greyscale, colour and hyperspectral images.