Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition

• URL: http://arxiv.org/abs/2606.03654v1
• Date: Tue, 02 Jun 2026 13:44:28 GMT
• Title: Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition
• Abstract summary: We propose a graph regularized non-negative reduced biquaternion matrix factorization model for color image recognition.<n>The proposed model incorporates a graph Laplacian regularizer into the reduced biquaternion coefficient matrix, encouraging nearby samples to have similar representations in the learned feature space.<n> Experimental results demonstrate that the proposed GNRBMF model achieves competitive or superior recognition performance in some tested settings.
• Score: 1.9079293459113584
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-negative reduced biquaternion matrix factorization (NRBMF) uses the product of reduced biquaternion (RB) matrices to incorporate the non-negativity constraints of color image pixels into the factorization process. However, NRBMF mainly focuses on reconstruction accuracy and does not exploit the local geometric structure of image data, which may limit the discriminative ability of the learned low-dimensional features. To address this issue, we propose a graph regularized non-negative reduced biquaternion matrix factorization (GNRBMF) model for color image recognition. The proposed model incorporates a graph Laplacian regularizer into the reduced biquaternion coefficient matrix, encouraging nearby samples in the original space to have similar representations in the learned feature space. Meanwhile, GNRBMF retains the non-negativity-preserving property of NRBMF in the reduced biquaternion domain. To solve the optimization problem, a component-wise alternating projected gradient algorithm is derived, and its convergence properties are analyzed. Experimental results demonstrate that the proposed GNRBMF model achieves competitive or superior recognition performance in some tested settings.

Related papers

• Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization [5.524295668575852]
  We propose persistent nonnegative matrix factorization (pNMF) that produces a sequence of persistence-aligned embeddings rather than a single one.<n>We analyze the structural properties of the embeddings along the scale parameter and establish bounds on their increments between consecutive scales.<n>The resulting model defines a nontrivial solution path across scales, rather than a single factorization, which poses new computational challenges.
  arXiv  Detail & Related papers  (2026-02-26T02:23:50Z)
• Dynamic PET Image Reconstruction via Non-negative INR Factorization [2.6408529601818422]
  We introduce an unsupervised learning approach, Non-negative Implicit Neural Representation Factorization (textttNINRF), based on low rank matrix factorization of unknown images.<n>Experiments on dynamic PET reconstruction with Poisson noise demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2025-03-11T04:13:30Z)
• Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition [27.149638378672755]
  We introduce a concept of the non-negative RB matrix and then use the multiplication properties of RB to propose a non-negative RB matrix factorization model.<n>We validate the effectiveness and superiority of the proposed NRBMF model in color face recognition.
  arXiv  Detail & Related papers  (2024-08-10T15:25:42Z)
• Orthogonal Nonnegative Matrix Factorization with Sparsity Constraints [0.0]
  This article presents a novel approach to solving the sparsity-constrained Orthogonal Nonnegative Matrix Factorization (SCONMF) problem.<n>By reformulating SCONMF as a capacity-constrained facility-location problem, the proposed method naturally integrates non-negativity, orthogonality, and sparsity constraints.<n>Specifically, our approach integrates control-barrier function (CBF) based framework used for dynamic optimal control design problems with maximum-entropy-principle-based framework used for facility location problems to enforce these constraints while ensuring robust factorization.
  arXiv  Detail & Related papers  (2022-10-06T04:30:59Z)
• Quaternion Optimized Model with Sparse Regularization for Color Image Recovery [10.137095668835439]
  This paper is inspired by an appreciation of the fact that different signal types, including audio formats and images, possess structures that are inherently sparse in respect of their respective bases. Since color images can be processed as a whole in the quaternion domain, we depicted the sparsity of the color image in the quaternion discrete cosine transform (QDCT) domain. To achieve a more superior low-rank approximation, the quatenrion-based truncated nuclear norm (QTNN) is employed in the proposed model.
  arXiv  Detail & Related papers  (2022-04-19T03:07:12Z)
• 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)
• Entropy Minimizing Matrix Factorization [102.26446204624885]
  Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization.
  arXiv  Detail & Related papers  (2021-03-24T21:08:43Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• Semiparametric Nonlinear Bipartite Graph Representation Learning with Provable Guarantees [106.91654068632882]
  We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution. We show that the proposed objective is strongly convex in a neighborhood around the ground truth, so that a gradient descent-based method achieves linear convergence rate. Our estimator is robust to any model misspecification within the exponential family, which is validated in extensive experiments.
  arXiv  Detail & Related papers  (2020-03-02T16:40:36Z)
• Kullback-Leibler Divergence-Based Fuzzy $C$-Means Clustering Incorporating Morphological Reconstruction and Wavelet Frames for Image Segmentation [152.609322951917]
  We come up with a Kullback-Leibler (KL) divergence-based Fuzzy C-Means (FCM) algorithm by incorporating a tight wavelet frame transform and a morphological reconstruction operation. The proposed algorithm works well and comes with better segmentation performance than other comparative algorithms.
  arXiv  Detail & Related papers  (2020-02-21T05:19:10Z)
• Residual-Sparse Fuzzy $C$-Means Clustering Incorporating Morphological Reconstruction and Wavelet frames [146.63177174491082]
  Fuzzy $C$-Means (FCM) algorithm incorporates a morphological reconstruction operation and a tight wavelet frame transform. We present an improved FCM algorithm by imposing an $ell_0$ regularization term on the residual between the feature set and its ideal value. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.
  arXiv  Detail & Related papers  (2020-02-14T10:00:03Z)

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.