A semi-supervised approximate spectral clustering algorithm based on HMRF model

Abstract Before clustering, we usually have some background knowledge about the data structure. Pairwise constraints are commonly used background knowledge. For graph partition problems, pairwise constraints can be naturally added to the graph edge. This paper integrates pairwise constraints into the objective function of graph cuts and derive the semi-supervised approximate spectral clustering based on Hidden Markov Random Fields (HMRF). This algorithm utilize the mathematical connection between HMRF semi-supervised clustering and approximate weighted kernel k-means. The approximate weighted kernel k-means is used to calculate the optimal clustering results of HMRF spectral clustering. The effectiveness of the proposed algorithm is verified on several benchmark data sets. Experiments show that adding more pairwise constraints will help improve the clustering performance. Our method has advantages for the challenging clustering tasks of large-scale nonlinear data because of the high efficiency and less memory consumption.