Conceptual Clustering of Heterogeneous Sequences via Schema Mapping

Abstract

We are concerned with clustering sequences that have been classified according to heterogeneous schema. We adopt a model-based approach that uses a Hidden Markov model (HMM) that has as states the stages of the underlying process that generates the sequences, thus allowing us to handle complex and heterogeneous data. Each cluster is described in terms of a HMM where we seek to find schema mappings between the states of the original sequences and the states of the HMM. The general solution that we propose involves several distinct tasks. Firstly, there is a clustering problem where we seek to group similar sequences; for this we use mutual entropy to identify associations between sequence states. Secondly, because we are concerned with clustering heterogeneous sequences, we must determine the mappings between the states of each sequence in a cluster and the states of an underlying hidden process; for this we compute the most probable mapping. Thirdly, on the basis of these mappings we use maximum likelihood techniques to learn the probabilistic description of the hidden Markov process for each cluster. Finally, we use these descriptions to characterise the clusters by using Dynamic Programming to determine the most probable pathway for each cluster. Such an approach provides an intuitive way of describing the underlying shape of the process by explicitly modelling the temporal aspects of the data; non time-homogeneous HMMs are also considered. The approach is illustrated using gene expression sequences.

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