Constrained spectral embedding for K-way data clustering

Spectral clustering methods meet more and more success in machine learning community thanks to their ability to cluster data points of any complex shapes. The problem of clustering is addressed in terms of finding an embedding space in which the projected data are linearly separable by a classical clustering algorithm such as K-means algorithm. Often, spectral algorithm performances are significantly improved by incorporating prior knowledge in their design, and several techniques have been developed for this purpose. In this paper, we describe and compare some recent linear and non-linear projection algorithms integrating instance-level constraints (“must-link” and “cannot-link”) and applied for data clustering. We outline a K-way spectral clustering algorithm able to integrate pairwise relationships between the data samples. We formulate the objective function as a combination of the original spectral clustering criterion and the penalization term based on the instance constraints. The optimization problem is solved as a standard eigensystem of a signed Laplacian matrix. The relevance of the proposed algorithm is highlighted using six UCI benchmarks and two public face databases.

► We describe some recent linear and non-linear projection algorithms integrating constraints.
► We outline a K-way spectral clustering algorithm able to integrate pairwise relationships.
► The criterion is a combination of spectral clustering criterion and a penalization term.
► The optimization problem is solved as a standard eigensystem of a signed Laplacian graph.