Constrained spectral clustering (CSC) has recently shown great promise in improving clustering accuracy or catering for some specific grouping bias by encoding pairwise constraints into spectral clustering. Essentially, the existing CSC algorithms coarsely lie in two camps in terms of encoding pairwise constraints: (1) they modify the original similarity matrix to encode pairwise constraints; (2) they regularize the spectral embedding to encode pairwise constraints. Those methods have made significant progresses, but little of them takes the extensional sense of pairwise constraints into account, e.g., respective neighbors of two musk-link points lie in a same cluster with certain high probabilities, and respective neighbors of two cannot-link points lie in different clusters with certain high probabilities, etc. In this paper, we use absorbing Markov chains to formulate the extensional sense of instance-level constraints as such, under the assumption that the formulation aids in improving the accuracy of CSC. We describe a new CSC algorithm which could propagates the extensional sense over a partly-labeled affinity graph. Experiments over publicly available datasets verify the performance of our algorithm.
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