Algorithms for Similarity Relation Learning from High Dimensional Data

The notion of similarity plays an important role in machine learning and artificial intelligence. It is widely used in tasks related to a supervised classification, clustering, an outlier detection and planning [7, 22, 57, 89, 153, 166]. Moreover, in domains such as information retrieval or case-based reasoning, the concept of similarity is essential as it is used at every phase of the reasoning cycle [1]. The similarity itself, however, is a very complex concept that slips out from formal definitions. A similarity of two objects can be different depending on a considered context. In many practical situations it is difficult even to evaluate the quality of similarity assessments without considering the task for which they were performed. Due to this fact the similarity should be learnt from data, specifically for the task at hand. In this dissertation a similarity model, called Rule-Based Similarity, is described and an algorithm for constructing this model from available data is proposed. The model utilizes notions from the rough set theory [108, 110, 113, 114, 115] to derive a similarity function that allows to approximate the similarity relation in a given context. The construction of the model starts from the extraction of sets of higher-level features. Those features can be interpreted as important aspects of the similarity. Having defined such features it is possible to utilize the idea of Tversky’s feature contrast model [159] in order to design an accurate and psychologically plausible similarity function for a given problem. Additionally, the dissertation shows two extensions of Rule-Based Similarity which are designed to efficiently deal with high dimensional data. They incorporate a broader array of similarity aspects into the model. In the first one it is done by constructing many heterogeneous sets of features from multiple decision reducts. To ensure their diversity, a randomized reduct computation heuristic is proposed. This approach is particularly well-suited for dealing with the few-objects-many-attributes problem, e.g. the analysis of DNA microarray data. A similar idea can be utilized in the text mining domain. The second of the proposed extensions serves this particular purpose. It uses a combination of a semantic indexing method and an information bireducts computation technique to represent texts by sets of meaningful concepts. The similarity function of the proposed model can be used to perform an accurate classification of previously unseen objects in a case-based fashion or to facilitate clustering of textual documents into semantically homogeneous groups. Experiments, whose results are also presented in the dissertation, show that the proposed models can successfully compete with the state-of-the-art algorithms.