  The performance of most the clustering methods hinges on the used pairwise
affinity, which is usually denoted by a similarity matrix. However, the
pairwise similarity is notoriously known for its vulnerability of noise
contamination or the imbalance in samples or features, and thus hinders
accurate clustering. To tackle this issue, we propose to use information among
samples to boost the clustering performance. We proved that a simplified
similarity for pairs, denoted by a fourth order tensor, equals to the Kronecker
product of pairwise similarity matrices under decomposable assumption, or
provide complementary information for which the pairwise similarity missed
under indecomposable assumption. Then a high order similarity matrix is
obtained from the tensor similarity via eigenvalue decomposition. The high
order similarity capturing spatial information serves as a robust complement
for the pairwise similarity. It is further integrated with the popular pairwise
similarity, named by IPS2, to boost the clustering performance. Extensive
experiments demonstrated that the proposed IPS2 significantly outperformed
previous similarity-based methods on real-world datasets and it was capable of
handling the clustering task over under-sampled and noisy datasets.
