Accelerating Bayesian hierarchical clustering of time series data with a randomised algorithm

We live in an era of abundant data. This has necessitated the development of new and innovative statistical algorithms to get the most from experimental data. For example, faster algorithms make practical the analysis of larger genomic data sets, allowing us to extend the utility of cutting-edge statistical methods. We present a randomised algorithm that accelerates the clustering of time series data using the Bayesian Hierarchical Clustering (BHC) statistical method. BHC is a general method for clustering any discretely sampled time series data. In this paper we focus on a particular application to microarray gene expression data. We define and analyse the randomised algorithm, before presenting results on both synthetic and real biological data sets. We show that the randomised algorithm leads to substantial gains in speed with minimal loss in clustering quality. The randomised time series BHC algorithm is available as part of the R package BHC, which is available for download from Bioconductor (version 2.10 and above) via http://bioconductor.org/packages/2.10/bioc/html/BHC.html. We have also made available a set of R scripts which can be used to reproduce the analyses carried out in this paper. These are available from the following URL. https://sites.google.com/site/randomisedbhc/

Innovative Heuristics to Improve the Latent Dirichlet Allocation Methodology for Textual Analysis and a New Modernized Topic Modeling Approach

Natural Language Processing is a complex method of data mining the vast trove of documents created and made available every day. Topic modeling seeks to identify the topics within textual corpora with limited human input into the process to speed analysis. Current topic modeling techniques used in Natural Language Processing have limitations in the pre-processing steps. This dissertation studies topic modeling techniques, those limitations in the pre-processing, and introduces new algorithms to gain improvements from existing topic modeling techniques while being competitive with computational complexity. This research introduces four contributions to the field of Natural Language Processing and topic modeling. First, this research identifies a requirement for a more robust “stopwords” list and proposes a heuristic for creating a more robust list. Second, a new dimensionality-reduction technique is introduced that exploits the number of words within a document to infer importance to word choice. Third, an algorithm is developed to determine the number of topics within a corpus and demonstrated using a standard topic modeling data set. These techniques produce a higher quality result from the Latent Dirichlet Allocation topic modeling technique. Fourth, a novel heuristic utilizing Principal Component Analysis is introduced that is capable of determining the number of topics within a corpus that produces stable sets of topic words