A Hilbert-Schmidt Dependence Maximization Approach to Unsupervised Structure Discovery

In recent work by (Song et al., 2007), it has been proposed to perform clustering by maximizing a Hilbert-Schmidt independence criterion with respect to a predefined cluster structure Y, by solving for the partition matrix. We extend this approach here to the case where the cluster structure Y is not fixed, but is a quantity to be optimized and we use an independence criterion which has been shown to be more sensitive at small sample sizes (the Hilbert-Schmidt Normalized Information Criterion, or HSNIC (Fukumizu et al., 2008)). We demonstrate the use of this framework in two scenarios. In the first, we adopt a cluster structure selection approach in which the HSNIC is used to select a structure from several candidates. In the second, we consider the case where we discover structure by directly optimizing Y.