Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation

• URL: http://arxiv.org/abs/2211.03934v1
• Date: Tue, 8 Nov 2022 01:16:21 GMT
• Title: Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation
• Authors: Jianyu Wang, Linruize Tang, Jie Chen, Jingdong Chen
• Abstract summary: Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation. NTF suffers from rotational ambiguity, whose solutions with and without rotation transformations are equally in the sense of yielding the maximum likelihood. We propose three Robust Manifold NTF algorithms to handle outliers by incorporating structural knowledge about the outliers.
• Score: 44.845291873747335
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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).

Related papers

• Variance-Reducing Couplings for Random Features [57.73648780299374]
  Random features (RFs) are a popular technique to scale up kernel methods in machine learning. We find couplings to improve RFs defined on both Euclidean and discrete input spaces. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm.
  arXiv  Detail & Related papers  (2024-05-26T12:25:09Z)
• Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components [13.989390077752232]
  We solve the problem of common and unique feature extraction from noisy data. Despite the intricate nature of the problem, we provide a Taylor series characterization by solving the corresponding KarushKuhn-Tucker algorithm. Numerical experiments in video segmentation and anomaly detection highlight the superior feature extraction abilities of TCMF.
  arXiv  Detail & Related papers  (2024-03-21T14:41:12Z)
• Wasserstein Nonnegative Tensor Factorization with Manifold Regularization [14.845504084471527]
  We introduce Wasserstein manifold nonnegative tensor factorization (WMNTF) We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.
  arXiv  Detail & Related papers  (2024-01-03T17:20:27Z)
• Multi-View Clustering via Semi-non-negative Tensor Factorization [120.87318230985653]
  We develop a novel multi-view clustering based on semi-non-negative tensor factorization (Semi-NTF) Our model directly considers the between-view relationship and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point.
  arXiv  Detail & Related papers  (2023-03-29T14:54:19Z)
• Revisiting Rotation Averaging: Uncertainties and Robust Losses [51.64986160468128]
  We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar. We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging.
  arXiv  Detail & Related papers  (2023-03-09T11:51:20Z)
• Hard-label Manifolds: Unexpected Advantages of Query Efficiency for Finding On-manifold Adversarial Examples [67.23103682776049]
  Recent zeroth order hard-label attacks on image classification models have shown comparable performance to their first-order, gradient-level alternatives. It was recently shown in the gradient-level setting that regular adversarial examples leave the data manifold, while their on-manifold counterparts are in fact generalization errors. We propose an information-theoretic argument based on a noisy manifold distance oracle, which leaks manifold information through the adversary's gradient estimate.
  arXiv  Detail & Related papers  (2021-03-04T20:53:06Z)
• Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets [85.71360365315128]
  In many applications, we need algorithms which can align partially overlapping point sets are invariant to the corresponding corresponding RPM algorithm. We first show that the objective is a cubic bound function. We then utilize the convex envelopes of trilinear and bilinear monomial transformations to derive its lower bound. We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently.
  arXiv  Detail & Related papers  (2021-01-19T04:24:23Z)
• Online nonnegative CP-dictionary learning for Markovian data [8.490619842547739]
  We introduce a novel algorithm that learns a CANDECOMP/PARAFAC basis from a given stream of tensor-valued data under general constraints. We prove that our algorithm converges almost surely to the set of stationary points of the objective function under the hypothesis that the sequence of data tensors is generated by an underlying Markov chain.
  arXiv  Detail & Related papers  (2020-09-16T11:41:01Z)
• The Heavy-Tail Phenomenon in SGD [7.366405857677226]
  We show that depending on the structure of the Hessian of the loss at the minimum, the SGD iterates will converge to a emphheavy-tailed stationary distribution. We translate our results into insights about the behavior of SGD in deep learning.
  arXiv  Detail & Related papers  (2020-06-08T16:43:56Z)
• A Unified Framework for Coupled Tensor Completion [42.19293115131073]
  Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
  arXiv  Detail & Related papers  (2020-01-09T02:15:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.