Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation

TL;DR

This paper introduces three robust manifold nonnegative Tucker factorization algorithms that effectively handle outliers and rotational ambiguity in tensor data, improving data representation accuracy.

Contribution

The paper proposes novel robust NTF algorithms incorporating outlier-aware weights and manifold regularization to enhance tensor data analysis.

Findings

Improved accuracy and NMI on real-world image datasets.

Effective handling of outliers through novel weighting functions.

Overcoming rotational ambiguity with manifold regularization.

Abstract

Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation which often suffers from grossly corruptions or outliers and the neglect of manifold structures of data. In particular, NTF suffers from rotational ambiguity, whose solutions with and without rotation transformations are equally in the sense of yielding the maximum likelihood. In this paper, we propose three Robust Manifold NTF algorithms to handle outliers by incorporating structural knowledge about the outliers. They first applies a half-quadratic optimization algorithm to transform the problem into a general weighted NTF where the weights are influenced by the outliers. Then, we introduce the correntropy induced metric, Huber function and Cauchy function for weights respectively, to handle the outliers. Finally, we introduce a manifold regularization to overcome the rotational ambiguity of NTF. We have compared the proposed method with a number of representative references covering major branches of NTF on a variety of real-world image databases. Experimental results illustrate the effectiveness of the proposed method under two evaluation metrics (accuracy and nmi).