Abstract

In recent times, the rapid growth of data in various fields of life has created an immense need for powerful tools to extract useful information from data. This has motivated researchers to explore and devise new ideas and methods in the field of machine learning. Mixture models have gained substantial attention due to their ability to handle high-dimensional data efficiently and effectively. However, when adopting mixture models in such spaces, four crucial issues must be addressed, including the selection of probability density functions, estimation of mixture parameters, automatic determination of the number of components, identification of features that best discriminate the different components, and taking into account the temporal information. The primary objective of this thesis is to propose a unified model that addresses these interrelated problems. Moreover, this thesis proposes a novel approach that incorporates explainability.

This thesis presents innovative mixture-based modelling approaches tailored for diverse applications, such as household energy consumption characterization, energy demand management, fault detection and diagnosis and human activity recognition. The primary contributions of this thesis encompass the following aspects:

Initially, we propose an unsupervised feature selection approach embedded within a finite bounded asymmetric generalized Gaussian mixture model. This model is adept at handling synthetic and real-life smart meter data, utilizing three distinct feature extraction methods. By employing the expectation-maximization algorithm in conjunction with the minimum message length criterion, we are able to concurrently estimate the model parameters, perform model selection, and execute feature selection. This unified optimization process facilitates the identification of household electricity consumption profiles along with the optimal subset of attributes defining each profile. Furthermore, we investigate the impact of household characteristics on electricity usage patterns to pinpoint households that are ideal candidates for demand reduction initiatives.

Subsequently, we introduce a semi-supervised learning approach for the mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. The integration of the uniform distribution within the inner mixture bolsters the model's resilience to outliers. In the unsupervised learning approach, the minimum message length criterion is utilized to ascertain the optimal number of mixture components. The proposed models are validated through a range of applications, including chiller fault detection and diagnosis, occupancy estimation, and energy consumption characterization. Additionally, we incorporate explainability into our models and establish a moderate trade-off between prediction accuracy and interpretability.

Finally, we devise four novel models for human activity recognition (HAR): bounded asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(BAGGM-FSHMM), bounded asymmetric generalized Gaussian mixture-based hidden Markov model~(BAGGM-HMM), asymmetric generalized Gaussian mixture-based hidden Markov model with feature selection~(AGGM-FSHMM), and asymmetric generalized Gaussian mixture-based hidden Markov model~(AGGM-HMM). We develop an innovative method for simultaneous estimation of feature saliencies and model parameters in BAGGM-FSHMM and AGGM-FSHMM while integrating the bounded support asymmetric generalized Gaussian distribution~(BAGGD), the asymmetric generalized Gaussian distribution~(AGGD) in the BAGGM-HMM and AGGM-HMM respectively. The aforementioned proposed models are validated using video-based and sensor-based HAR applications, showcasing their superiority over several mixture-based hidden Markov models~(HMMs) across various performance metrics. We demonstrate that the independent incorporation of feature selection and bounded support distribution in a HAR system yields benefits; Simultaneously, combining both concepts results in the most effective model among the proposed models.