Rank-constrained spectral clustering with flexible embedding

© 2012 IEEE. Spectral clustering (SC) has been proven to be effective in various applications. However, the learning scheme of SC is suboptimal in that it learns the cluster indicator from a fixed graph structure, which usually requires a rounding procedure to further partition the data. Also, the obtained cluster number cannot reflect the ground truth number of connected components in the graph. To alleviate these drawbacks, we propose a rank-constrained SC with flexible embedding framework. Specifically, an adaptive probabilistic neighborhood learning process is employed to recover the block-diagonal affinity matrix of an ideal graph. Meanwhile, a flexible embedding scheme is learned to unravel the intrinsic cluster structure in low-dimensional subspace, where the irrelevant information and noise in high-dimensional data have been effectively suppressed. The proposed method is superior to previous SC methods in that: 1) the block-diagonal affinity matrix learned simultaneously with the adaptive graph construction process, more explicitly induces the cluster membership without further discretization; 2) the number of clusters is guaranteed to converge to the ground truth via a rank constraint on the Laplacian matrix; and 3) the mismatch between the embedded feature and the projected feature allows more freedom for finding the proper cluster structure in the low-dimensional subspace as well as learning the corresponding projection matrix. Experimental results on both synthetic and real-world data sets demonstrate the promising performance of the proposed algorithm