Robust ℓp-Norm Two-Dimensional Discriminative Clustering for Image Data

For image data, matrix-based clustering methods are gaining popularity because they can directly process two-dimensional (2D) data structures without vectorization. However, most existing approaches rely on squared Frobenius norms in their objective functions, making them sensitive to outliers and noise commonly encountered in real-world images. To overcome this limitation, we propose a novel robust ℓp-norm two-dimensional discriminative clustering method (R2DDC) specifically designed for image clustering. R2DDC utilizes the ℓp-norm to simultaneously minimize within-cluster distances and maximize between-cluster distances at the matrix level, thus preserving the inherent 2D spatial information of images while providing enhanced robustness against pixel-level outliers and noise. An efficient iterative optimization algorithm is designed to solve the proposed objective function. Extensive experiments on contaminated face image datasets demonstrate that R2DDC consistently surpasses conventional clustering approaches, highlighting its effectiveness for robust image analysis.