Amplifying the Block Matrix Structure for Spectral Clustering

Spectral clustering methods perform well in cases where classical methods (K-means, single linkage, etc.) fail. However, for very non-compact clusters, they also tend to have problems. In this paper, we propose three improvements which we show that perform better in such cases. We suggest that spectral decomposition is merely a method for determining the block structure of the affinity matrix. Consequently, it is advantageous for clustering techniques if the affinity matrix has a clear block structure. We propose two independent steps to achieve this goal. In the first, which we term context-dependent affinity, we compute point affinities by taking their neighborhoods into account. In the second, the conductivity method, we aim at amplifying the block structure of the affinity matrix. Combining these two enables us to achieve a clear block-diagonal structure, despite starting with very weak affinities. For the last step, clustering spectral images, K-means is commonly used. Instead, as a third improvement, we suggest using our K-lines algorithm. When compared to other clustering algorithms, our methods display promising performance on both artificial and real-world data sets.