Department Seminar by Jason Hou-Liu

Please Note: This seminar will be given online.

Finding Additional Structure in Gaussian Mixture Models

When we wish to model data that captures more than one sub-population, we often turn to a clustering algorithm that extracts an inter-observation structure over individual units. Building on this, we can also extract further relationships by considering inter-cluster structure. An analogy from biology is that hybrid species tend to exhibit a mixture of parent characteristics, which we can interpret as hybridising parameters between components. We work with the finite Gaussian mixture model framework, used in the model-based clustering of multivariate data, where traditional methods of parameter sharing use geometric redundancies such as volume, shape, and orientation in the covariance matrix. Instead, we explore other techniques such as representing hybrid clusters using the weighted average of parent cluster parameters or constructing subclusters sequentially in a hierarchical style. Additionally, we provide some insights on using the Expectation-Maximization algorithm as the backbone for fitting and estimating parameters in these proposed models. Finally, we juxtapose the proposed methods with parsimonious covariance matrices and demonstrate the method on a selection of real-world datasets, and offer some remarks on remaining challenges.