A Procedure for Selecting Key Core Elements in Tensor Decomposition

Abstract

Tensors are sophisticated objects characterized by numerous indices, capable of collecting vast amounts of data while preserving the underlying patterns of the phenomena being studied. They are utilized in various fields for diverse purposes, including exploratory analysis. Typically, a tensor is decomposed into loading matrices and a smaller dimensional core tensor.
Many algorithms exist for decomposing this type of object, and one of the more challenging questions for users and researchers is determining the optimal number of loadings to use for each mode. The trade-off between interpretability and information loss is a problem that remains insufficiently explored. Traditional tools, such as scree plots and information criteria, are often employed to find solutions.
This talk will provide an overview of various strategies for selecting the best combination of loadings to effectively reduce the dimensionality of datasets, revealing underlying patterns and relationships that may not be immediately apparent in the original high-dimensional data.