Advances in mining complex data: modeling and clustering

Abstract

In the last years, there has been a great production of data that come from di®erent application contexts. However, although technological progress pro- vides several facilities to digitally encode any type of event, it is important to de¯ne a suitable representation model which underlies the main character- istics of the data. This aspect is particularly relevant in ¯elds and contexts where data to be archived can not be represented in a ¯x structured scheme, or that can not be described by simple numerical values. We hereinafter refer to these data with the term complex data. Although it is important de¯ne ad-hoc representation models for complex data, it is also crucial to have analysis systems and data exploration tech- niques. Analysts and system users need new instruments that support them in the extraction of patterns and relations hidden in the data. The entire process that aims to extract useful information and knowledge starting from raw data takes the name of Knowledge Discovery in Databases (KDD). It starts from raw data and consists in a set of speci¯c phases that are able to transform and manage data to produce models and knowledge. There have been many knowledge extraction techniques for traditional structured data, but they are not suitable to handle complex data. Investigating and solving representation problems for complex data and de¯ning proper algorithms and techniques to extract models, patterns and new information from such data in an e®ective and e±cient way are the main challenges which this thesis aims to face. In particular, two main aspects related to complex data management have been investigated, that are the way in which complex data can be modeled (i.e., data modeling), and the way in which homogeneous groups within complex data can be identi¯ed (i.e., data clustering). The application contexts that have been objective of such studies are time series data, uncertain data, text data, and biomedical data. It is possible to illustrate research contributions of this thesis by dividing them into four main parts, each of which concerns with one speci¯c area and data type: vi Abstract Time Series | A time series representation model has been developed, which is conceived to support accurate and fast similarity detection. This model is called Derivative time series Segment Approximation (DSA), as it achieves a concise yet feature-rich time series representation by com- bining the notions of derivative estimation, segmentation and segment approximation. Uncertain Data | Research in uncertain data mining went into two di- rections. In a ¯rst phase, a new proposal for partitional clustering has been de¯ned by introducing the Uncertain K-medoids (UK-medoids) al- gorithm. This approach provides a more accurate way to handle uncertain objects in a clustering task, since a cluster representative is an uncertain object itself (and not a deterministic one). In addition, e±ciency issue has been addressed by de¯ning a distance function between uncertain objects that can be calculated o²ine once per dataset. In a second phase, research activities aimed to investigate issues related to hierarchical clustering of uncertain data. Therefore, an agglomera- tive centroid-based linkage hierarchical clustering framework for uncer- tain data (U-AHC) has been proposed. The key point lies in equipping such scheme with a more accurate distance measure for uncertain objects. Indeed, it has been resorted to information theory ¯eld to ¯nd a mea- sure able to compare probability distributions of uncertain objects used to model uncertainty. Text Data |Research results on text data can be summarized in two main contributions. The ¯rst one regards clustering of multi-topic documents, and a framework for hard clustering of documents according to their mix- tures of topics has been proposed. Documents are assumed to be modeled by a generative process, which provides a mixture of probability mass functions (pmfs) to model the topics that are discussed within any spe- ci¯c document. The framework combines the expressiveness of generative models for document representation with a properly chosen information- theoretic distance measure to group the documents. The second proposal concerns distributional clustering of XML documents, focusing on a the development of a distributed framework for e±ciently clustering XML documents. The distributed environment consists of a peer-to-peer network where each node in the network has access to a portion of the whole document collection and communicates with all the other nodes to perform a clustering task in a collaborative fashion. The proposed framework is based on modeling and clustering XML documents by structure and content. Indeed, XML documents are transformed into transactional data based on the notion of tree tuple. The framework is based on the well-known paradigm of centroid-based partitional clustering to conceive the distributed, transactional clustering algorithm. Biomedical Data | Research results on time series and uncertain data have been involved to support e®ective and e±cient biomedical data man- agement. The focus regarded both proteomics and genomics, investigat- Abstract vii ing Mass Spectrometry (MS) data and microarray data. In the speci¯c, a Mass Spectrometry Data Analysis (MaSDA) system has been de¯ned. The key idea consists in exploiting temporal information implicitly contained in MS data and model such data as time series. The major advantages of this solution are the dimensionality and the noise reduction. As re- gards micrarray data, U-AHC has been employed to perform clustering of microarray data with probe-level uncertainty. A strategy to model probe- level uncertainty has been de¯ned, together with a hierarchical clustering scheme for analyzing such data. This approach performs a gene-based clustering to discover clustering solutions that are well-suited to capture the underlying gene-based patterns of microarray data. The e®ectiveness and the e±ciency of the proposed techniques in clus- tering complex data are demonstrated by performing intense and exhaustive experiments, in which such proposals are extensively compared with the main state-of-the-art competitors.