Adaptive Tensor Decomposition for High-Dimensional Sparse Data

Abstract

High-dimensional sparse data poses significant challenges for traditional tensor decomposition techniques. These methods often suffer from instability, poor generalization, and difficulty in capturing the underlying structure of the data due to the curse of dimensionality and the irregular sparsity patterns. This work introduces an adaptive tensor decomposition algorithm designed to overcome these limitations. The algorithm employs a reinforcement learning (RL) agent to dynamically adjust the tensor order and decomposition method – specifically, Canonical Polyadic (CP) and Tucker tensor decompositions – based on real-time feedback from the data. Key metrics considered during the learning process include reconstruction error, rank deficiency, and sparsity pattern analysis. The adaptive nature of the algorithm allows it to effectively handle high-dimensional and sparse datasets, leading to more stable and accurate decompositions compared to static methods. The core contribution lies in the synergistic combination of tensor decomposition with adaptive learning, offering a robust solution for analyzing complex, high-dimensional sparse datasets where the underlying structure is inherently irregular.