Spectral clustering via half-quadratic optimization

Spectral clustering has been demonstrated to often outperform K-means clustering in real applications because it improves the similarity measurement of K-means clustering. However, previous spectral clustering method still suffers from the following issues: 1) easily being affected by outliers; 2) constructing the affinity matrix from original data which often contains redundant features and outliers; and 3) unable to automatically specify the cluster number. This paper focuses on address these issues by proposing a new clustering algorithm along with the technique of half-quadratic optimization. Specifically, the proposed method learns the affinity matrix from low-dimensional space of original data, which is obtained by using a robust estimator to remove the influence of outliers as well as a sparsity regularization to remove redundant features. Moreover, the proposed method employs the ℓ_2,1-norm regularization to automatically learn the cluster number according to the data distribution. Experimental results on both synthetic and real data sets demonstrated that the proposed method outperforms the state-of-the-art methods in terms of clustering performance.