Hyper-rectangle-based Discriminative Data Generalization and Applications in Data Mining

The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as human-comprehensible patterns from which end-users can gain intuitions and insights. Axis-parallel hyper-rectangles provide interpretable generalizations for multi-dimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectangle-based discriminative data generalization in the context of several useful data mining applications: cluster description, rule learning, and Nearest Rectangle classification. Clustering is one of the most important data mining tasks. However, most clustering methods output sets of points as clusters and do not generalize them into interpretable patterns. We perform a systematic study of cluster description, where we propose novel description formats leading to enhanced expressive power and introduce novel description problems specifying different trade-offs between interpretability and accuracy. We also present efficient heuristic algorithms for the introduced problems in the proposed formats. If-then rules are known to be the most expressive and human-comprehensible representation of knowledge. Rectangles are essentially a special type of rules with all the attributional conditions specified whereas normal rules appear more compact. Decision rules can be used for both data classification and data description depending on whether the focus is on future data or existing data. For either scenario, smaller rule sets are desirable. We propose a novel rectangle-based and graph-based rule learning approach that finds rule sets with small cardinality. We also consider Nearest Rectangle learning to explore the data classification capacity of generalized rectangles. We show that by enforcing the so-called “right of inference”, Nearest Rectangle learning can potentially become an interpretable hybrid inductive learning method with competitive accuracy.