Trace Norm Regularized Tensor Classification and Its Online Learning Approaches

TL;DR

This paper introduces a novel tensor classification algorithm using trace norm regularization, employing advanced optimization techniques and extending to online learning, with demonstrated efficiency in experiments.

Contribution

It develops a tensor classification method based on trace norm regularization, utilizing Douglas-Rachford splitting and ADM, and extends it to online learning for real-time applications.

Findings

Efficient tensor classification achieved with proposed algorithms.

Successful extension to online learning with real-time data handling.

Experimental results confirm the effectiveness of the methods.

Abstract

In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification, the tensor classification is formulated as a convex optimization problem which can be solved by using the off-the-shelf accelerated proximal gradient (APG) method. However, there are no analytic solutions as the matrix case for the updating of the weight tensors via the proximal gradient. To tackle this problem, the Douglas-Rachford splitting technique and the alternating direction method of multipliers (ADM) used in tensor completion are adapted to update the weight tensors. Further more, due to the demand of real applications, we also propose its online learning approaches. Experiments demonstrate the efficiency of the methods.