Manifold Based Multi-View <i>K</i>-Means

Although numerous clustering algorithms have been developed, many existing methods still rely on the K-means technique to identify clusters of data points. However, the performance of K-means is highly dependent on the accurate estimation of cluster centers, which is challenging to achieve optimally. Furthermore, it struggles to handle linearly non-separable data. To address these limitations, from the perspective of manifold learning, we reformulate multi-view K-means into a manifold-based multi-view clustering formulation that eliminates the need for computing centroid matrix. This reformulation ensures consistency between the manifold structure and the data labels. Building on this, we propose a novel multi-view K-means model incorporating the tensor rank constraint. Our model employs the indicator matrices from different views to construct a third-order tensor, whose rank is minimized via the tensor Schatten p-norm. This approach effectively leverages the complementary information across views. By utilizing different distance functions, our proposed model can effectively handle linearly non-separable data. Extensive experimental results on multiple databases demonstrate the superiority of our proposed model.