<p>Inspired by the parts-based representation mechanism in human neural cognition, Non-negative Matrix Factorization (NMF) serves as a fundamental neural network paradigm for feature extraction across information retrieval and computer vision domains. However, since the learning rules of the NMF algorithm only converge to local minima of its objective function, it results in slow convergence and instability. Although significant improvements have been proposed to address these problems, they introduce some other problems such as trivial solutions and high computational cost. Studies have shown that interconnected neurons in the human brain form a neural network, i.e., a dynamical system governed by ordinary differential equations (ODEs), which establishes a nonlinear mapping from external inputs to their associated attractors. In this paper, we propose a novel NMF-based neural model by leveraging this insight. Specifically, we adopt <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$sin^2(\cdot )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mi>i</mi> <msup> <mi>n</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as the activation function of the dynamical system, enabling the global attractor property to guarantee the convergence of the neural model. By imposing a constraint of unique ODE solution on the original NMF cost function, a global attractor is embedded into the existing NMF framework, allowing the proposed model to converge to the global minimum of the dynamic system. In this model, 1) Enhanced nonlinearity strengthens part-based learning performance; 2) The learning rules are non-increasing and stable, converging to global attractors with fewer iterations, greatly boosting performance in image analysis; 3) Its dynamic, multi-layer mechanism better captures the intrinsic structures of samples. The convergence of the algorithm is also analyzed in this paper. Extensive experiments are conducted to demonstrate the effectiveness of the proposed model. Compared with some classic NMF models and the most recently developed NMF related models, test results on four different datasets show that the proposed method can obtain state-of-the-art performance in image clustering with accuracy improvements: 1.31% on ORL, 1.16% on COIL20, 1.16% on Caltech101, and 1.15% on YouTube Faces.</p>

A Global Attractor Guided Learning of Parts-based Representation for Image Clustering

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2025年11月23日

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Jingdian Yang,
Jingye Cai

摘要

Inspired by the parts-based representation mechanism in human neural cognition, Non-negative Matrix Factorization (NMF) serves as a fundamental neural network paradigm for feature extraction across information retrieval and computer vision domains. However, since the learning rules of the NMF algorithm only converge to local minima of its objective function, it results in slow convergence and instability. Although significant improvements have been proposed to address these problems, they introduce some other problems such as trivial solutions and high computational cost. Studies have shown that interconnected neurons in the human brain form a neural network, i.e., a dynamical system governed by ordinary differential equations (ODEs), which establishes a nonlinear mapping from external inputs to their associated attractors. In this paper, we propose a novel NMF-based neural model by leveraging this insight. Specifically, we adopt $sin^2(\cdot )$ $s i n^{2} (\cdot)$ as the activation function of the dynamical system, enabling the global attractor property to guarantee the convergence of the neural model. By imposing a constraint of unique ODE solution on the original NMF cost function, a global attractor is embedded into the existing NMF framework, allowing the proposed model to converge to the global minimum of the dynamic system. In this model, 1) Enhanced nonlinearity strengthens part-based learning performance; 2) The learning rules are non-increasing and stable, converging to global attractors with fewer iterations, greatly boosting performance in image analysis; 3) Its dynamic, multi-layer mechanism better captures the intrinsic structures of samples. The convergence of the algorithm is also analyzed in this paper. Extensive experiments are conducted to demonstrate the effectiveness of the proposed model. Compared with some classic NMF models and the most recently developed NMF related models, test results on four different datasets show that the proposed method can obtain state-of-the-art performance in image clustering with accuracy improvements: 1.31% on ORL, 1.16% on COIL20, 1.16% on Caltech101, and 1.15% on YouTube Faces.