Interactive content analysis : evaluating interactive variants of non-negative Matrix Factorisation and Latent Dirichlet Allocation as qualitative content analysis aids

This thesis addressed issues that have prevented qualitative researchers from using thematic discovery algorithms. The central hypothesis evaluated whether allowing qualitative researchers to interact with thematic discovery algorithms and incorporate domain knowledge improved their ability to address research questions and trust the derived themes. Non-negative Matrix Factorisation and Latent Dirichlet Allocation find latent themes within document collections but these algorithms are rarely used, because qualitative researchers do not trust and cannot interact with the themes that are automatically generated. The research determined the types of interactivity that qualitative researchers require and then evaluated interactive algorithms that matched these requirements. Theoretical contributions included the articulation of design guidelines for interactive thematic discovery algorithms, the development of an Evaluation Model and a Conceptual Framework for Interactive Content Analysis.

Parallel implementation of alternate quadrant interlocking factorisation method on star topology

This paper discusses the parallel implementation of the solution of a set of linear equations using the Alternative Quadrant Interlocking Factorisation Methods (AQIF), on a star topology. Both the AQIF and LU decomposition methods are mapped onto star topology on an IBM SP2 system, with MPI as the internode communicator. Performance parameters such as speedup, efficiency have been obtained through experimental and theoretical means. The studies demonstrate (i) a mismatch of 15% between the theoretical and experimental results, (ii) scalability of the AQIF algorithm, and (iii) faster executing AQIF algorithm.

Speaker and noise factorisation on the AURORA4 task

For many realistic scenarios, there are multiple factors that affect the clean speech signal. In this work approaches to handling two such factors, speaker and background noise differences, simultaneously are described. A new adaptation scheme is proposed. Here the acoustic models are first adapted to the target speaker via an MLLR transform. This is followed by adaptation to the target noise environment via model-based vector Taylor series (VTS) compensation. These speaker and noise transforms are jointly estimated, using maximum likelihood. Experiments on the AURORA4 task demonstrate that this adaptation scheme provides improved performance over VTS-based noise adaptation. In addition, this framework enables the speech and noise to be factorised, allowing the speaker transform estimated in one noise condition to be successfully used in a different noise condition. © 2011 IEEE.

An online expectation-maximisation algorithm for nonnegative matrix factorisation models

In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximation of our online EM algorithm. We show the performance of the proposed method with two numerical examples. © 2012 IFAC.

Multilinear function factorisation for time series feature extraction

This work applies a variety of multilinear function factorisation techniques to extract appropriate features or attributes from high dimensional multivariate time series for classification. Recently, a great deal of work has centred around designing time series classifiers using more and more complex feature extraction and machine learning schemes. This paper argues that complex learners and domain specific feature extraction schemes of this type are not necessarily needed for time series classification, as excellent classification results can be obtained by simply applying a number of existing matrix factorisation or linear projection techniques, which are simple and computationally inexpensive. We highlight this using a geometric separability measure and classification accuracies obtained though experiments on four different high dimensional multivariate time series datasets. © 2013 IEEE.

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

Factorisation de la fonction de partition du modèle d'Ising en deux dimensions défini sur deux régions contiguës

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Les polynômes orthogonaux matriciels et la méthode de factorisation

La méthode de factorisation est appliquée sur les données initiales d'un problème de mécanique quantique déja résolu. Les solutions (états propres et fonctions propres) sont presque tous retrouvés.