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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, II. 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.
@inproceedings{5179, title = {A Hilbert-Schmidt Dependence Maximization Approach to Unsupervised Structure Discovery}, journal = {Proceedings of the 6th International Workshop on Mining and Learning with Graphs (MLG 2008)}, booktitle = {MLG 2008}, abstract = {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, II. 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.}, pages = {1-3}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, month = jul, year = {2008}, slug = {5179}, author = {Blaschko, MB. and Gretton, A.}, month_numeric = {7} }
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