Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^

Subdural electroencephalogram analysis for extracting discriminating measures in epileptogenic data

This dissertation introduces an integrated algorithm for a new application dedicated at discriminating between electrodes leading to a seizure onset and those that do not, using interictal subdural EEG data. The significance of this study is in determining among all of these channels, all containing interictal spikes, why some electrodes eventually lead to seizure while others do not. A first finding in the development process of the algorithm is that these interictal spikes had to be asynchronous and should be located in different regions of the brain, before any consequential interpretations of EEG behavioral patterns are possible. A singular merit of the proposed approach is that even when the EEG data is randomly selected (independent of the onset of seizure), we are able to classify those channels that lead to seizure from those that do not. It is also revealed that the region of ictal activity does not necessarily evolve from the tissue located at the channels that present interictal activity, as commonly believed.^ The study is also significant in terms of correlating clinical features of EEG with the patient's source of ictal activity, which is coming from a specific subset of channels that present interictal activity. The contributions of this dissertation emanate from (a) the choice made on the discriminating parameters used in the implementation, (b) the unique feature space that was used to optimize the delineation process of these two type of electrodes, (c) the development of back-propagation neural network that automated the decision making process, and (d) the establishment of mathematical functions that elicited the reasons for this delineation process. ^

Evaluating the Effectiveness of Discrete Trial Procedures for Teaching Receptive Discrimination to Children with Autism Spectrum Disorders

Research has found that children with autism spectrum disorders (ASD) show significant deficits in receptive language skills (Wiesmer, Lord, & Esler, 2010). One of the primary goals of applied behavior analytic intervention is to improve the communication skills of children with autism by teaching receptive discriminations. Both receptive discriminations and receptive language entail matching spoken words with corresponding objects, symbols (e.g., pictures or words), actions, people, and so on (Green, 2001). In order to develop receptive language skills, children with autism often undergo discrimination training within the context of discrete trial training. This training entails teaching the learner how to respond differentially to different stimuli (Green, 2001). It is through discrimination training that individuals with autism learn and develop language (Lovaas, 2003). The present study compares three procedures for teaching receptive discriminations: (1) simple/conditional (Procedure A), (2) conditional only (Procedure B), and (3) conditional discrimination of two target cards (Procedure C). Six children, ranging in age from 2-years-old to 5-years-old, with an autism diagnosis were taught how to receptively discriminate nine sets of stimuli. Results suggest that the extra training steps included in the simple/conditional and conditional only procedures may not be necessary to teach children with autism how to receptively discriminate. For all participants, Procedure C appeared to be the most efficient and effective procedure for teaching young children with autism receptive discriminations. Response maintenance and generalization probes conducted one-month following the end of training indicate that even though Procedure C resulted in less training sessions overall, no one procedure resulted in better maintenance and generalization than the others. In other words, more training sessions, as evident with the simple/conditional and conditional only procedures, did not facilitate participants’ ability to accurately respond or generalize one-month following training. The present study contributes to the literature on what is the most efficient and effective way to teach receptive discrimination during discrete trial training to children with ASD. These findings are critical as research shows that receptive language skills are predictive of better outcomes and adaptive behaviors in the future.