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Face recognition is a popular research area where there are different approaches studied in the literature. In this thesis, a holistic Principal Component Analysis (PCA) based method, namely Eigenface method is studied in detail and three of the methods based on the Eigenface method are compared. These are the Bayesian PCA where Bayesian classifier is applied after dimension reduction with PCA, the Subspace Linear Discriminant Analysis (LDA) where LDA is applied after PCA and Eigenface where Nearest Mean Classifier applied after PCA. All the three methods are implemented on the Olivetti Research Laboratory (ORL) face database, the Face Recognition Technology (FERET) database and the CNN-TURK Speakers face database. The results are compared with respect to the effects of changes in illumination, pose and aging. Simulation results show that Subspace LDA and Bayesian PCA perform slightly well with respect to PCA under changes in pose / however, even Subspace LDA and Bayesian PCA do not perform well under changes in illumination and aging although they perform better than PCA.

Most of the cardiac structural abnormalities will be examined by echocardiography. With more understanding of heart diseases, it is commonly recognized that heart failures are closely related to left ventricular systolic and diastolic functions. This work discusses the association between gray-scale differences and the risk of heart disease from the changes in left ventricular systole and diastole of ultrasound image. Owing to the large dimension of data matrix, following Chen (2011), we also simplify the influence factors by factor analysis and calculate factor scores to present the characteristics of subjects. Two kinds of classification criteria are used in this work, namely logistic model with distance indicator and discriminant function. According to Guo et al. (2001), we calculate the Mahalanobis distance from each subject to the center of normal and abnormal group, then use logistic model to fit the distances for classification later. This is called logistic model with distance indicator. For the discriminant analysis, the regularized method by Friedman (1989) for estimation of covariance matrix is used, which is more flexible and can improve the covariance matrix estimates when the sample size is small. As far as the cut-point of ROC curve, following the approach as in Hanley et al. (1982), we find the most appropriate cut-point which has good performances for both sensitivity and specificity under the same classification criteria. Then the regularized method and the cut-point of ROC curve are combined to be a new classification criterion. The results under the new classification criterion are presented to classify normal and abnormal groups.

Error estimation must be used to find the accuracy of a designed classifier, an issue that is critical in biomarker discovery for disease diagnosis and prognosis in genomics and proteomics. This dissertation is concerned with the analytical formulation of the joint distribution of the true error of misclassification and two of its commonly used estimators, resubstitution and leave-one-out, as well as their marginal and mixed moments, in the context of the Linear Discriminant Analysis (LDA) classification rule. In the first part of this dissertation, we obtain the joint sampling distribution of the actual and estimated errors under a general parametric Gaussian assumption. Exact results are provided in the univariate case and an accurate approximation is obtained in the multivariate case. We show how these results can be applied in the computation of conditional bounds and the regression of the actual error, given the observed error estimate. In practice the unknown parameters of the Gaussian distributions, which figure in the expressions, are not known and need to be estimated. Using the usual maximum-likelihood estimates for such parameters and plugging them into the theoretical exact expressions provides a sample-based approximation to the joint distribution, and also sample-based methods to estimate upper conditional bounds. In the second part of this dissertation, exact analytical expressions for the bias, variance, and Root Mean Square (RMS) for the resubstitution and leave-one-out error estimators in the univariate Gaussian model are derived. All probabilistic characteristics of an error estimator are given by the knowledge of its joint distribution with the true error. Partial information is contained in their mixed moments, in particular, their second mixed moment. Marginal information regarding an error estimator is contained in its marginal moments, in particular, its mean and variance. Since we are interested in estimator accuracy and wish to use the RMS to measure that accuracy, we desire knowledge of the second-order moments, marginal and mixed, with the true error. In the multivariate case, using the double asymptotic approach with the assumption of knowing the common covariance matrix of the Gaussian model, analytical expressions for the first moments, second moments, and mixed moment with the actual error for the resubstitution and leave-one-out error estimators are derived. The results provide accurate small sample approximations and this is demonstrated in the present situation via numerical comparisons. Application of the results is discussed in the context of genomics.

While all mammals sleep, the functions and implications of sleep are not well understood, and are a strong area of investigation in the research community. Mice are utilized in many sleep studies, with electroencephalography (EEG) signals widely used for data acquisition and analysis. However, since EEG electrodes must be surgically implanted in the mice, the method is high cost and time intensive. This work presents an extension of a previously researched high throughput, low cost, non-invasive method for mouse behavior detection and classification. A novel hierarchical classifier is presented that classifies behavior states including NREM and REM sleep, as well as active behavior states, using data acquired from a Signal Solutions (Lexington, KY) piezoelectric cage floor system. The NREM/REM classification system presented an 81% agreement with human EEG scorers, indicating a useful, high throughput alternative to the widely used EEG acquisition method.

The healthy condition of a rotating machine leads to safe and cheap operation of almost all industrial facilities and mechanical systems. To achieve such a goal, vibration-based condition monitoring has proved to be a well-accepted technique that detects incipient fault symptoms. The conventional way of On-Bearing Vibration Measurement (OBVM) captures symptoms of different faults, however, it requires a relatively expensive setup, an additional space for the auxiliary devices and cabling in addition to an experienced analyst. On-Shaft Vibration Measurement (OSVM) is an emerging method proposed to offer more reliable Faults Diagnosis (FD) tools with less number of sensors, minimal processing time and lower system and maintenance costs. The advancement in sensor and wireless communications technologies enables attaching a MEMS accelerometer with a miniaturised wireless data acquisition unit directly to the rotor without altering the machine dynamics. In this study, OSVM is analysed during constant speed and run-up operations of a test rig. The observations showed response modulation, hence, a Finite Element (FE) analysis has been carried out to help interpret the experimental observations. The FE analysis confirmed that the modulation is due to the rotary motion of the on-shaft sensor. A demodulation method has been developed to solve this problem. The FD capability of OSVM has been compared to that of OBVM using conventional analysis where the former provided more efficient diagnosis with less number of sensors. To incorporate more features, a method has been developed to diagnose faults based on Principal Component Analysis and Nearest Neighbour classifier. Furthermore, the method is enhanced using Linear Discriminant Analysis to do the diagnosis without the need for a classifier. Another faults diagnosis method has been developed that ensures the generalisation of extracted faults features from OSVM data of a specific machine to similar machines mounted on different foundations.

The classification of observations based on repeated measurements performed on the same subject over a given period of time or under different conditions is a common procedure in many disciplines such as medicine, psychology and environmental studies. In this thesis repeated measurements follow the Growth Curve model and are classified using linear discriminant analysis. The aim of this thesis is both to examine the effect of missing data on classification accuracy and to examine the effect of additional data on classification robustness. The results indicate that an increasing amount of missing data leads to a progressive decline in classification accuracy. With regard to the effect of additional data on classification robustness the results show a less predictable effect which can only be characterised as a general tendency towards improved robustness.