User-Informed Clustering for Cell Population Identification in Cytometry and Sequential Outlier Identification for Gaussian Mixture Modelling

Abstract

Whether obscured by scientifically insignificant noise or distorted by the presence of outliers, the true group structure of a data set can often be difficult to uncover in real-world data. In this thesis, we examine a challenging setting in which clustering algorithms have been applied to solve a real-world problem, that of cell population identification in flow cytometry. These data sets present a variety of challenges which can prevent clustering algorithms from identifying biologically meaningful populations. We discuss some of these issues in the context of how model-based clustering methods have been adapted to try to overcome them. Model-based clustering is a statistical, probabilistic approach for data clustering which models heterogeneous data using a mixture of known probability distributions with parameters estimated based on the data. Next, we review several non-model-based methods which have been developed for this problem, and a handful of methods which have been designed to utilise expert knowledge about the cell populations targeted by the researcher. Taking advantage of immunologists' knowledge of the cell populations in their data allows a clustering algorithm to focus on biologically significant differences between cells and to construct a set of cell populations which suits the context of the experiment and the needs of the researcher. We develop our own user-informed clustering method for flow cytometry, gateTree, and demonstrate its ability to accurately identify populations that have been described in simple and biologically meaningful terms. We then extend this user-informed approach to constrained mixture models and discuss their strengths and weaknesses. In the latter part of this thesis, we broaden our focus to examine the general problem of outliers in Gaussian mixture modelling, rather than exclusively dealing with flow cytometry data. We present outlierMBC, a novel method for sequentially identifying outliers in Gaussian mixture models, and then extend it to Gaussian linear cluster-weighted models. We demonstrate its ability to accurately identify outliers and compare it to a range of leading methods for model-based outlier identification. The novel methods developed and presented in this thesis share a common aim to circumvent some of the noisiness and complexity present in real-world data sets and uncover a meaningful and practical clustering solution.