Non-Negative Matrix Factorization with Scale Data Structure Preservation

• URL: http://arxiv.org/abs/2209.10881v1
• Date: Thu, 22 Sep 2022 09:32:18 GMT
• Title: Non-Negative Matrix Factorization with Scale Data Structure Preservation
• Authors: Rachid Hedjam, Abdelhamid Abdesselam, Abderrahmane Rahiche, Mohamed Cheriet
• Abstract summary: The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. The idea is to add, to the NMF cost function, a penalty term to impose a scale relationship between the pairwise similarity matrices of the original and transformed data points. The proposed clustering algorithm is compared to some existing NMF-based algorithms and to some manifold learning-based algorithms when applied to some real-life datasets.
• Score: 23.31865419578237
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve the structure of data during matrix factorization. The idea is to add, to the NMF cost function, a penalty term to impose a scale relationship between the pairwise similarity matrices of the original and transformed data points. The solution of the new model involves deriving a new parametrized update scheme for the coefficient matrix, which makes it possible to improve the quality of reduced data when used for clustering and classification. The proposed clustering algorithm is compared to some existing NMF-based algorithms and to some manifold learning-based algorithms when applied to some real-life datasets. The obtained results show the effectiveness of the proposed algorithm.

Related papers

• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Input Guided Multiple Deconstruction Single Reconstruction neural network models for Matrix Factorization [0.0]
  This paper develops two models based on the concept of Non-negative Matrix Factorization (NMF) They aim to deal with high-dimensional data by discovering its low rank approximation by determining a unique pair of factor matrices. The superiority of low dimensional embedding over that of the original data justifying the need for dimension reduction has been established.
  arXiv  Detail & Related papers  (2024-05-22T08:41:32Z)
• Accelerated structured matrix factorization [0.0]
  Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors.
  arXiv  Detail & Related papers  (2022-12-13T11:35:01Z)
• Supervised Class-pairwise NMF for Data Representation and Classification [2.7320863258816512]
  Non-negative Matrix factorization (NMF) based methods add new terms to the cost function to adapt the model to specific tasks. NMF method adopts unsupervised approaches to estimate the factorizing matrices.
  arXiv  Detail & Related papers  (2022-09-28T04:33:03Z)
• Comparative Study of Inference Methods for Interpolative Decomposition [4.913248451323163]
  We propose a probabilistic model with automatic relevance determination (ARD) for learning interpolative decomposition (ID) We evaluate the model on a variety of real-world datasets including CCLE $EC50$, CCLE $IC50$, Gene Body Methylation, and Promoter Methylation datasets with different sizes, and dimensions.
  arXiv  Detail & Related papers  (2022-06-29T11:37:05Z)
• Adversarially-Trained Nonnegative Matrix Factorization [77.34726150561087]
  We consider an adversarially-trained version of the nonnegative matrix factorization. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices.
  arXiv  Detail & Related papers  (2021-04-10T13:13:17Z)
• Feature Weighted Non-negative Matrix Factorization [92.45013716097753]
  We propose the Feature weighted Non-negative Matrix Factorization (FNMF) in this paper. FNMF learns the weights of features adaptively according to their importances. It can be solved efficiently with the suggested optimization algorithm.
  arXiv  Detail & Related papers  (2021-03-24T21:17:17Z)
• Self-supervised Symmetric Nonnegative Matrix Factorization [82.59905231819685]
  Symmetric nonnegative factor matrix (SNMF) has demonstrated to be a powerful method for data clustering. Inspired by ensemble clustering that aims to seek better clustering results, we propose self-supervised SNMF (S$3$NMF) We take advantage of the sensitivity to code characteristic of SNMF, without relying on any additional information.
  arXiv  Detail & Related papers  (2021-03-02T12:47:40Z)
• Nonnegative Matrix Factorization with Toeplitz Penalty [0.0]
  Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. We propose a new NMF algorithm that makes use of non-data dependent auxiliary constraints.
  arXiv  Detail & Related papers  (2020-12-07T13:49:23Z)
• Model Fusion with Kullback--Leibler Divergence [58.20269014662046]
  We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors.
  arXiv  Detail & Related papers  (2020-07-13T03:27:45Z)
• Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering [50.43424130281065]
  We propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step.
  arXiv  Detail & Related papers  (2020-05-19T05:54:14Z)

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.