Probabilistic Modelling of Multiresolution Biological Data

When the measurements from the ever improving measurement technology are accumulated over a period of time, the result is the collection of data in different representations. However, most machine learning and data mining algorithms, in their standard form, are designed to operate on data in single representation. This thesis proposes machine learning and data mining algorithms to analyze data in different representation with respect to the resolution within a single analysis. The novel algorithms proposed to analyze multiresolution data are in the field of probabilistic modelling and semantic data mining. First, three different deterministic data transformation methods are proposed to transform data across different resolutions. After the data transformation, the resulting data in same resolution are integrated and modeled using mixture models. Second, similar mixture components in a mixture model are merged one by one repetitively to generate a chain of mixture models. A new fast approximation of the KL-divergence is derived to determine the similarity of the mixture components. The chain of generated mixture models are useful for comparison, for example, in model selection. Third, mixture components in different resolutions are iteratively merged to model multiresolution data generating models in each modeled resolution that incorporate information from data in other resolution. Fourth, a single multiresolution mixture model with multiresolution mixture components is proposed whose mixture components independently have the capabilities of a Bayesian network. Finally, three-part methodology consisting of clustering using mixture models, rule learning using semantic subgroup discovery, and pattern visualization using banded matrices is developed for comprehensive analysis of multiresolution data. The multiresolution data analysis methods presented in this thesis improves the performance of the methods in comparison with the their single resolution counterparts. Furthermore, developed methods aims to make the results understandable to the domain experts. Therefore, the developed methods are useful addition in the analysis of chromosomal aberration patterns and the cancer research in general.