# Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation

arXiv: https://arxiv.org/abs/2211.03934 · HTML: https://mlsanity.com/paper/2211.03934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Structured Low-Rank Matrix Factorization: Global Optimality, Algorithms, and Applications](https://mlsanity.com/paper/1708.07850/) (2017)
- [Alternating proximal gradient method for sparse nonnegative Tucker decomposition](https://mlsanity.com/paper/1302.2559/) (2013)
- [Truncated Cauchy Non-negative Matrix Factorization](https://mlsanity.com/paper/1906.00495/) (2019)
- [Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization](https://mlsanity.com/paper/1504.01777/) (2015)
- [Generalized Separable Nonnegative Matrix Factorization](https://mlsanity.com/paper/1905.12995/) (2019)
- [HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction](https://mlsanity.com/paper/2101.06827/) (2021)
- [Deep NMF Topic Modeling](https://mlsanity.com/paper/2102.12998/) (2021)
- [Orthogonal Nonnegative Tucker Decomposition](https://mlsanity.com/paper/1910.09979/) (2019)

## Abstract (arXiv)

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).