Cluster validation and discovery of multiple clusterings

© 2016 Dr. Yang LeiCluster analysis is an important unsupervised learning process in data analysis. It aims to group data objects into clusters, so that the data objects in the same group are more similar and the data objects in different groups are more dissimilar. There are many open challenges in this area. In this thesis, we focus on two: discovery of multiple clusterings and cluster validation. Many clustering methods focus on discovering one single ‘best’ solution from the data. However, data can be multi-faceted in nature. Particularly when datasets are large and complex, there may be several useful clusterings existing in the data. In addition, users may be seeking different perspectives on the same dataset, requiring multiple clustering solutions. Multiple clustering analysis has attracted considerable attention in recent years and aims to discover multiple reasonable and distinctive clustering solutions from the data. Many methods have been proposed on this topic and one popular technique is meta-clustering. Meta-clustering explores multiple reasonable and distinctive clusterings by analyzing a large set of base clusterings. However, there may exist poor quality and redundant base clustering which will affect the generation of high quality and diverse clustering views. In addition, the generated clustering views may not all be relevant. It will be time and energy consuming for users to check all the returned solutions. To tackle these problems, we propose a filtering method and a ranking method to achieve higher quality and more distinctive clustering solutions. Cluster validation refers to the procedure of evaluating the quality of clusterings, which is critical for clustering applications. Cluster validity indices (CVIs) are often used to quantify the quality of clusterings. They can be generally classified into two categories: external measures and internal measures, which are distinguished in terms of whether or not external information is used during the validation procedure. In this thesis, we focus on external cluster validity indices. There are many open challenges in this area. We focus two of them: (a) CVIs for fuzzy clusterings and, (b) Bias issues for CVIs. External CVIs are often used to quantify the quality of a clustering by comparing it against the ground truth. Most external CVIs are designed for crisp clusterings (one data object only belongs to one single cluster). How to evaluate the quality of soft clusterings (one data object can belong to more than one cluster) is a challenging problem. One common way to achieve this is by hardening a soft clustering to a crisp clustering and then evaluating it using a crisp CVI. However, hardening may cause information loss. To address this problem, we generalize a class of popular information-theoretic based crisp external CVIs to directly evaluate the quality of soft clusterings, without the need for a hardening step. There is an implicit assumption when using external CVIs for evaluating the quality of a clustering, that is, they work correctly. However, if this assumption does not hold, then misleading results might occur. Thus, identifying and understanding the bias behaviors of external CVIs is crucial. Along these lines, we identify novel bias behaviors of external CVIs and analyze the type of bias both theoretically and empirically