An ordered sparse subspace clustering algorithm based on p‐Norm

• Published in: Expert systems Vol. 38; no. 7
• Main Authors: Chen, Liping, Guo, Gongde, Wang, Hui
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.11.2021
• Subjects: Algorithms; block‐diagonal transform; Clustering; Datasets; Feature extraction; Handwriting recognition; Histograms; Image segmentation; image sequence clustering; Noise; Object recognition; Random noise; Robustness; Rotation; sparse subspace clustering; Subspace methods; Subspaces; wavelet‐HOG
• ISSN: 0266-4720; 1468-0394; 1468-0394
• DOI: 10.1111/exsy.12368

Images in video may include both Gaussian noise and geometric rotation. Thus, it is challenging to represent an image sequence in its intrinsically low‐dimensional space in a noise‐robust and rotation‐robust manner. In this paper, we propose a novel‐ordered sparse subspace clustering algorithm based on a p‐norm to achieve an effective clustering of sequential data under heavy noise conditions. We also use the wavelet‐histogram of oriented gradient (HOG) transform in the kernel view to extract both the global features (with the wavelet process) and the local features (with the HOG process) from the image. In addition, we assign different weights to different features to obtain a sparse coefficient matrix that helps to emphasize the global and local correlations in each sample. Similarly, the clustering algorithm based on the p‐norm for sequential images emphasizes the within‐class correlations amongst samples. Therefore, in this paper, we select additional denoising main components under a Laplacian constraint to achieve a better block‐diagonal structure and highlight the independence of different clusters. Extensive experiments performed on various public datasets (including the ordered face dataset, handwritten recognition dataset, video scene segmentation dataset, and object recognition dataset) demonstrate that the proposed method is more resilient to noise and rotation than other representative sparse subspace clustering methods.