Doctor of Philosophy (PhD) / This thesis addresses the problem of building statistical models for multi-sensor perception in unstructured outdoor environments. The perception problem is divided into three distinct tasks: recognition, representation and association. Recognition is cast as a statistical classification problem where inputs are images or a combination of images and ranging information. Given the complexity and variability of natural environments, this thesis investigates the use of Bayesian statistics and supervised dimensionality reduction to incorporate prior information and fuse sensory data. A compact probabilistic representation of natural objects is essential for many problems in field robotics. This thesis presents techniques for combining non-linear dimensionality reduction with parametric learning through Expectation Maximisation to build general representations of natural features. Once created these models need to be rapidly processed to account for incoming information. To this end, techniques for efficient probabilistic inference are proposed. The robustness of localisation and mapping algorithms is directly related to reliable data association. Conventional algorithms employ only geometric information which can become inconsistent for large trajectories. A new data association algorithm incorporating visual and geometric information is proposed to improve the reliability of this task. The method uses a compact probabilistic representation of objects to fuse visual and geometric information for the association decision. The main contributions of this thesis are: 1) a stochastic representation of objects through non-linear dimensionality reduction; 2) a landmark recognition system using a visual and ranging sensors; 3) a data association algorithm combining appearance and position properties; 4) a real-time algorithm for detection and segmentation of natural objects from few training images and 5) a real-time place recognition system combining dimensionality reduction and Bayesian learning. The theoretical contributions of this thesis are demonstrated with a series of experiments in unstructured environments. In particular, the combination of recognition, representation and association algorithms is applied to the Simultaneous Localisation and Mapping problem (SLAM) to close large loops in outdoor trajectories, proving the benefits of the proposed methodology.

This report shows how knowledge about the visual world can be built into a shape representation in the form of a descriptive vocabulary making explicit the important geometrical relationships comprising objects' shapes. Two computational tools are offered: (1) Shapestokens are placed on a Scale-Space Blackboard, (2) Dimensionality-reduction captures deformation classes in configurations of tokens. Knowledge lies in the token types and deformation classes tailored to the constraints and regularities ofparticular shape worlds. A hierarchical shape vocabulary has been implemented supporting several later visual tasks in the two-dimensional shape domain of the dorsal fins of fishes.

This thesis concerns and combines the results of experimental studies of magnetocaloric, multiferroic and spin-glass materials, using SQUID magnetometry as the main characteriza-tion technique.  The magnetocaloric effect offers an interesting new technology for cooling and heating applications. The studies of magnetocaloric materials in this thesis are focused on experimen-tal characterization of fundamental magnetic properties of Fe2P-based materials. These are promising magnetocaloric materials with potential industrial use. It is found that the magneto-caloric properties of Fe2P can be optimally tuned by substitution of manganese for iron and silicon for phosphorus. Furthermore, a simple device to measure the magnetocaloric effect in terms of the adiabatic temperature change was constructed.  Materials that simultaneously exhibit different types of ferroic order, for example magnetic and electrical order, are rare in nature. Among these multiferroic materials, those in which the ferroelectricity is magnetically-induced, or vice versa the magnetism is electrically-induced, are intensively studied due to a need for new functionalities in future data storage and logic devices. This thesis presents results on two materials: Co3TeO6 and Ba3NbFe3Si2O14, which belong to the group of magnetically-induced ferroelectrics and exhibit strong coupling be-tween the magnetic and the electrical order parameter. Their ordering properties were studied using magnetic and electrical measurement techniques. The coupling between the magnetic and electronic degrees of freedom was investigated using high-field and low-temperature Raman spectroscopy.  Spin-glass materials exhibit complex magnetism and disorder. The influence of the spin dimensionality on the low and high magnetic field properties of spin glasses was investigated by studying model Heisenberg, XY and Ising spin-glass systems. Significant differences were found between the non-equilibrium dynamics and the hysteresis behavior of Heisenberg systems compared to those of XY and Ising spin glasses.

The present work applies well-known data mining techniques in a digital learning media environment in order to identify groups of students based on their pro le. We generate identi able clusters where some interesting patterns and rules are observed. We generate a neural network predictive model intended to predict the success of the students in the digital media learning environment. One of the goals of this study is to identify a subset of variables that have the biggest impact in student performance with respect to the learning assessments of the digital media learning environment. Three approaches are used to perform the dimensionality reduction of our dataset. The experiments were conducted with over 69 students of health science courses who used the digital media learning environment. / UOIT

This thesis researches techniques for modelling static facial expressions, as well as the dynamics of continuous facial motion. We demonstrate how static and dynamic properties of facial expressions can be represented within a linear and nonlinear context, respectively. These two representations do not act in isolation, but are mutually reinforcing in conceding a cohesive framework for the analysis, animation, and manipulation of expressive faces. We derive a basis for the linear space of expressions through Principal Components Analysis (PCA). We introduce and formalize the notion of "expression manifolds", manifolds residing in PCA space that model motion dynamics for semantically similar expressions. We then integrate these manifolds into an animation workflow by performing Nonlinear Dimensionality Reduction (NLDR) on the expression manifolds. This operation yields expression maps that encode a wealth of information relating to complex facial dynamics, in a low dimensional space that is intuitive to navigate and efficient to manage.

This thesis researches techniques for modelling static facial expressions, as well as the dynamics of continuous facial motion. We demonstrate how static and dynamic properties of facial expressions can be represented within a linear and nonlinear context, respectively. These two representations do not act in isolation, but are mutually reinforcing in conceding a cohesive framework for the analysis, animation, and manipulation of expressive faces. We derive a basis for the linear space of expressions through Principal Components Analysis (PCA). We introduce and formalize the notion of "expression manifolds", manifolds residing in PCA space that model motion dynamics for semantically similar expressions. We then integrate these manifolds into an animation workflow by performing Nonlinear Dimensionality Reduction (NLDR) on the expression manifolds. This operation yields expression maps that encode a wealth of information relating to complex facial dynamics, in a low dimensional space that is intuitive to navigate and efficient to manage.

Harnessing the power of DNA microarray technology requires the existence of analysis methods that accurately interpret microarray data. Current literature abounds with algorithms meant for the investigation of microarray data. However, there is need for an efficient approach that combines different techniques of microarray data analysis and provides a viable solution to dimensionality reduction of microarray data. Reducing the high dimensionality of microarray data is one approach in striving to better understand the information contained within the data. We propose a novel approach for dimensionality reduction of microarray data that effectively combines different techniques in the study of DNA microarrays. Our method, <strong><em>KAS</em></strong> (<em>kernel alignment with semidefinite embedding</em>), aids the visualization of microarray data in two dimensions and shows improvement over existing dimensionality reduction methods such as PCA, LLE and Isomap.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.

Harnessing the power of DNA microarray technology requires the existence of analysis methods that accurately interpret microarray data. Current literature abounds with algorithms meant for the investigation of microarray data. However, there is need for an efficient approach that combines different techniques of microarray data analysis and provides a viable solution to dimensionality reduction of microarray data. Reducing the high dimensionality of microarray data is one approach in striving to better understand the information contained within the data. We propose a novel approach for dimensionality reduction of microarray data that effectively combines different techniques in the study of DNA microarrays. Our method, <strong><em>KAS</em></strong> (<em>kernel alignment with semidefinite embedding</em>), aids the visualization of microarray data in two dimensions and shows improvement over existing dimensionality reduction methods such as PCA, LLE and Isomap.

Metric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.