Tk-merge: Computationally Efficient Robust Clustering Under General Assumptions

Bayesian Clustering for Continuous-Time Hidden Markov Models

We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out finite and infinite mixture model-based clustering for a CTHMM and achieve inference using Markov chain Monte Carlo (MCMC). For a finite mixture model with prior on the number of components, we implement reversible-jump MCMC to facilitate the trans-dimensional move between different number of clusters. For a Dirichlet process mixture model, we utilize restricted Gibbs sampling split-merge propo…

Improved initialisation of model-based clustering using Gaussian hierarchical partitions

Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among the several approaches available in the literature, model-based agglomerative hierarchical clustering is used to provide initial partitions in the popular MCLUST R package. This choice is computationally convenient and often yields good clustering partitions. However, in certain circumstances, poor initial partitions may cause the EM algorithm to converge to…

Merging $K$-means with hierarchical clustering for identifying general-shaped groups

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure but suffers from computational complexity in large datasets while $K$-means clustering is efficient but designed to identify homogeneous spherically-shaped clusters. We present a hybrid non-parametric clustering approach that amalgamates the two methods to identify general-shaped …

Whole-Volume Clustering of Time Series Data from Zebrafish Brain Calcium Images via Mixture Modeling

Calcium is a ubiquitous messenger in neural signaling events. An increasing number of techniques are enabling visualization of neurological activity in animal models via luminescent proteins that bind to calcium ions. These techniques generate large volumes of spatially correlated time series. A model-based functional data analysis methodology via Gaussian mixtures is suggested for the clustering of data from such visualizations is proposed. The methodology is theoretically justified and a computationally efficient approach to estimation is suggested. An example analysis of a zebrafish imaging…

A Data-Driven Approach to Estimating the Number of Clusters in Hierarchical Clustering

We propose two new methods for estimating the number of clusters in a hierarchical clustering framework in the hopes of creating a fully automated process with no human intervention. The methods are completely data-driven and require no input from the researcher, and as such are fully automated. They are quite easy to implement and not computationally intensive in the least. We analyze performance on several simulated data sets and the Biobase Gene Expression Set, comparing our methods to the established Gap statistic and Elbow methods and outperforming both in multi-cluster scenarios.

块信号下的高维聚类与信号恢复

High-dimensional Clustering and Signal Recovery under Block Signals

本文针对块信号结构下的高维聚类与信号恢复问题，提出CFA-PCA和MA-PCA两种自适应方法，分别处理稀疏与稠密块信号，并证明其达到计算极小化极大下界，在更弱信号条件下实现一致聚类与恢复。