Manifold K-means with $\ell_{2,p}$-Norm Maximization
Keywords: Clustering, Manifold Learning, K-means, $\ell_{2, p}$-Norm
Abstract: Although a variety of different methods have emerged in the field of clustering, K-means still occupies an important position, and many advanced clustering methods even rely on the K-means to achieve effective cluster detection. However, the sensitivity of K-means to the selection of the initial cluster center and its limited ability to handle nonlinear separable data somewhat restrict its clustering performance. In order to overcome the limitations of K-means, we draw inspiration from manifold learning and redefine K-means as a manifold K-means clustering framework. This framework supports various types of distance matrices, thus facilitating the efficient processing of nonlinear separable data. A unique advantage of this approach is that it does not require the calculation of the cluster center, while it maintains the consistency between manifold structure and cluster labels. Additionally, we highlight the significant role of the $\ell_{2,p}$-norm; by maximizing the $\ell_{2,p}$-norm, we can ensure the balance of classes in the clustering process, which is also supported by theoretical analysis. The results from extensive experiments across multiple databases substantiate the superiority of our proposed model.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 133
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