Low-Rank Linear Embedding for Robust Clustering

The performance of
k
-means clustering is often degenerate when dealing with high-dimensional and noisy scenarios. In this study, an end-to-end robust clustering method with low-rank linear embedding techniques (RCLR) is presented in conjunction with
k
-means. Sparse coefficients and a space projection matrix can be simultaneously learned. The global structures and local neighborhood properties are well captured in the learning procedures. Both the processes of clustering and dimensionality reduction are realized at the same time. The notions of clustering, dimensionality reduction, low-rank representation, and local property preservation are seamlessly integrated into a unified model. The limitation of error accumulation encountered in the previous two-stage clustering framework involving low-rank representation can be alleviated. This is the first attempt to introduce both the global and local geometrical structures into
k
-means directly, as well
${L_{2,1}}$
-norm is used as a basic metric instead of the conventional
$F$
-norm to further improve the robustness and interpretation of the model. The superiority of the proposed RCLR method is demonstrated by extensive experiments completed on various well-known benchmark datasets.