Mixture-Based Clustering for High-Dimensional Count Data Using Minorization-Maximization Approaches

The Multinomial distribution has been widely used to model count data. To increase clustering efficiency, we use an approximation of the Fisher Scoring as a learning algorithm, which is more robust to the choice of the initial parameter values. Moreover, we consider the generalization of the multinomial model obtained by introducing the Dirichlet as prior, which is called the Dirichlet Compound Multinomial (DCM). Even though DCM can address the burstiness phenomenon of count data, the presence of Gamma function in its density function usually leads to undesired complications. In this thesis, we use two alternative representations of DCM distribution to perform clustering based on finite mixture models, where the mixture parameters are estimated using minorization-maximization algorithm. Moreover, we propose an online learning technique for unsupervised clustering based on a mixture of Neerchal- Morel distributions. While the novel mixture model is able to capture overdispersion due to a weight parameter assigned to each feature in each cluster, online learning is able to overcome the drawbacks of batch learning in such a way that the mixture’s parameters can be updated instantly for any new data instances. Finally, by implementing a minimum message length model selection criterion, the weights of irrelevant mixture components are driven towards zero, which resolves the problem of knowing the number of clusters beforehand. To evaluate and compare the performance of our proposed models, we have considered five challenging real-world applications that involve high dimensional count vectors, namely, sentiment analysis, topic detection, facial expression recognition, human action recognition and medical diagnosis. The results show that the proposed algorithms increase the clustering efficiency remarkably as compared to other benchmarks, and the best results are achieved by the models able to accommodate over-dispersed count data

Mixture-Based Clustering for High-Dimensional Count Data Using Minorization-Maximization Approaches

The Multinomial distribution has been widely used to model count data. To increase clustering efficiency, we use an approximation of the Fisher Scoring as a learning algorithm, which is more robust to the choice of the initial parameter values. Moreover, we consider the generalization of the multinomial model obtained by introducing the Dirichlet as prior, which is called the Dirichlet Compound Multinomial (DCM). Even though DCM can address the burstiness phenomenon of count data, the presence of Gamma function in its density function usually leads to undesired complications. In this thesis, we use two alternative representations of DCM distribution to perform clustering based on finite mixture models, where the mixture parameters are estimated using minorization-maximization algorithm. Moreover, we propose an online learning technique for unsupervised clustering based on a mixture of Neerchal- Morel distributions. While, the novel mixture model is able to capture overdispersion due to a weight parameter assigned to each feature in each cluster, online learning is able to overcome the drawbacks of batch learning in such a way that the mixture’s parameters can be updated instantly for any new data instances. Finally, by implementing a minimum message length model selection criterion, the weights of irrelevant mixture components are driven towards zero, which resolves the problem of knowing the number of clusters beforehand. To evaluate and compare the performance of our proposed models, we have considered five challenging real-world applications that involve high-dimensional count vectors, namely, sentiment analysis, topic detection, facial expression recognition, human action recognition and medical diagnosis. The results show that the proposed algorithms increase the clustering efficiency remarkably as compared to other benchmarks, and the best results are achieved by the models able to accommodate over-dispersed count data

Count Data Modeling and Classification Using Statistical Hierarchical Approaches and Multi-topic Models

In this thesis, we propose and develop various statistical models to enhance and improve the efficiency of statistical modeling of count data in various applications. The major emphasis of the work is focused on developing hierarchical models. Various schemes of hierarchical structures are thus developed and analyzed in this work ranging from purely static hierarchies to dynamic models. The second part of the work concerns itself with the development of multitopic statistical models. It has been shown that these models provide more realistic modeling characteristics in comparison to mono topic models. We proceed with developing several multitopic models and we analyze their performance against benchmark models. We show that our proposed models in the majority of instances improve the modeling efficiency in comparison to some benchmark models, without drastically increasing the computational demands. In the last part of the work, we extend our proposed multitopic models to include online learning capability and again we show the relative superiority of our models in comparison to the benchmark models. Various real world applications such as object recognition, scene classification, text classification and action recognition, are used for analyzing the strengths and weaknesses of our proposed models