Speaker: Hassan Ashtiani, PhD candidate
We address the problem of communicating domain knowledge from a domain expert to the designer of a clustering algorithm. We propose a protocol in which the domain expert provides a clustering of a relatively small random sample of a data set. The algorithm designer then uses that sample to come up with a data representation under which k-means clustering results in a clustering (of the full data set) that is aligned with the domain knowledge. We provide a formal statistical model for analyzing the sample complexity of learning a clustering representation with this paradigm. We then introduce a notion of capacity of a class of possible representations, in the spirit of the VC-dimension, showing that classes of representations that have finite such dimension can be successfully learned with sample size error bounds, and end our discussion with an analysis of that dimension for classes of representations induced by linear embedding.