Integrating Tensor Similarity to Enhance Clustering Performance

Clustering aims to separate observed data into different categories. The performance of popular clustering models relies on the sample-to-sample similarity. However, the pairwise similarity is prone to be corrupted by noise or outliers and thus deteriorates the subsequent clustering. A high-order relationship among samples-to-samples may elaborate the local manifold of the data and thus provide complementary information to guide the clustering. However, few studies have investigated the connection between high-order similarity and usual pairwise similarity. To fill this gap, we first define a high-order tensor similarity to exploit the samples-to-samples affinity relationship. We then establish the connection between tensor similarity and pairwise similarity, proving that the decomposable tensor similarity is the Kronecker product of the usual pairwise similarity and the non-decomposable tensor similarity is generalized to provide complementary information, which pairwise similarity fails to regard. Finally, the high-order tensor similarity and pairwise similarity (IPS2) were integrated collaboratively to enhance clustering performance by enjoying their merits. The proposed IPS2 is shown to perform superior or competitive to state-of-the-art methods on synthetic and real-world datasets. Extensive experiments demonstrated that tensor similarity is capable to boost the performance of the classical clustering method.