Robust Orthogonal NMF with Label Propagation for Image Clustering

TL;DR

This work tackles image clustering under noise by introducing RONMF, a robust orthogonal NMF framework that combines a non-convex reconstruction loss $\|X - U Z^\top A^\top\|_{2,\phi}$ with graph Laplacian regularization $\lambda \mathrm{Tr}(A^\top L A)$ and label propagation via $\mu \mathrm{Tr}((A - Y)^\top S (A - Y))$, while enforcing $U^\top U = I$ and nonnegativity. The optimization is carried out with an ADMM scheme that yields closed-form updates for subproblems involving $U,A,Z,E,\Lambda$, and a split variable $E$ to handle the non-convex loss. The model unifies non-convex loss, orthogonality, graph- and label-based regularization to enhance robustness against noise, and extensive experiments on eight datasets demonstrate state-of-the-art performance and strong anti-noise capabilities. The results suggest that combining structured non-convex penalties with semi-supervised regularization and orthogonal feature selection yields meaningful gains for scalable, robust image clustering, with available code enabling reproducibility.

Abstract

Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are unable to effectively leverage limited supervised information. To overcome these drawbacks, we propose a unified non-convex framework with label propagation called robust orthogonal nonnegative matrix factorization (RONMF). This method not only considers the graph Laplacian and label propagation as regularization terms but also introduces a more effective non-convex structure to measure the reconstruction error and imposes orthogonal constraints on the basis matrix to reduce the noise corruption, thereby achieving higher robustness. To solve RONMF, we develop an alternating direction method of multipliers (ADMM)-based optimization algorithm. In particular, all subproblems have closed-form solutions, which ensures its efficiency. Experimental evaluations on eight public image datasets demonstrate that the proposed RONMF outperforms state-of-the-art NMF methods across various standard metrics and shows excellent robustness. The code will be available at https://github.com/slinda-liu.

Figures (8)

• Figure 1: ACC performance of our proposed RONMF (including RONMF-M, RONMF-S, and RONMF-E) and competitors on MNIST.
• Figure 2: All metrics for different clustering numbers $k$ on Type-I and Type-II datasets, where the horizontal axis denotes $k$, and the vertical axis denotes the value of indicators.
• Figure 3: All metrics for different clustering numbers $k$ on Type-III and Type-IV datasets, where the horizontal axis denotes $k$, and the vertical axis denotes the value of indicators.
• Figure 4: Performance of all methods on YALE, COIL20, and USPS with 10%, 30%, 50%, and 70% noise.
• Figure 5: Effects of parameters $p$ and $\lambda$ on the ACC, F1, PUR, and NMI results.