Feature-Graph-Guided Adaptive Sparse NMF with Anchor Dual Graphs Under the Logarithmic Framework for Data Clustering

Abstract

Graph-based nonnegative matrix factorization (GNMF) has been widely used for dimensionality reduction and data clustering because it can preserve the intrinsic geometric structure of data. However, many existing GNMF-based methods still rely on full sample similarity graphs, resulting in high computational costs; moreover, their sparsity constraints usually treat all features uniformly, making it difficult to distinguish structurally important features from redundant or noisy ones. To address these issues, this paper proposes a feature-graph-guided adaptive Log-L2,1 sparse NMF with anchor dual graphs under a logarithmic framework. Specifically, anchor-based representations are simultaneously constructed in the sample and feature spaces to approximate the corresponding full-scale graphs. The sample anchor graph preserves the local manifold structure among samples, whereas the feature anchor graph plays a dual role: it preserves structural relationships among features and provides degree information for generating the adaptive weights gi of the row-wise Log-L2,1 penalty imposed on the basis matrix U. Consequently, structurally well-connected features receive weaker sparsity penalties, while weakly connected and potentially redundant features are more strongly suppressed. In addition, a logarithmic reconstruction framework is introduced to reduce the influence of large residuals caused by noise and outliers. These mechanisms jointly integrate sample structure preservation, feature structure preservation, and feature-aware sparse learning within a unified graph-NMF model. To optimize the model, multiplicative update rules are derived, while the nonnegativity of the factor matrices is inherently preserved throughout the iterations. Extensive evaluations on several benchmark datasets demonstrate the effectiveness and robustness of the proposed method.