| dc.description.abstract | In this dissertation, we proposed several new approaches to extend matrix factorization including nonnegative matrix factorization (NMF), complex matrix factorization (CMF), and convolution neural networks (CNN) integrating with principal component analysis (PCA). Our approaches are not only specifically suited for data representation in general and for image analyzing in particular but also outperform to the state-of-the-art in image processing field.
Based on the development of NMF models, the thesis designed two constrained NMF models in order to obtain the sparsity representations. Particularly, for the first model, we constructed a proper simplicial cone base which is compact and has high generalization ability. We named this model is the robust maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). For the second one, we added new constraints to enhance the sparseness of representation. In this, a large basis cone and sparse representation were imposed on non-negative matrix factorization with Kullback-Leibler (KL) divergence (conespaNMF_KL). It achieves sparseness from a large simplicial cone constraint on the base and sparse regularize on the extracted features.
Complex matrix factorization (CMF) models are natural extensions of NMFs, in which the complex data is treated. These models have a wide range of applications, e.g. face recognition and facial expression recognition. Recently, CMF and exemplar-embed complex matrix factorization (EE-CMF) [37] show the powerful data representation in facial expression recognition, in which the real value of pixel intensive is transformed into the complex domain. Follow the work in [37], we developed CMF approaches to enhance the ability of data display by integrating more constraints into EE-CMF model such as graph to obtain the graph regularized exemplar-embed complex matrix factorization (gEE-CMF), and sparsity to achieve the exemplar-embed complex matrix factorization with sparsity constraint (sEE-CMF) models, respectively. We also proposed two schemes of data learning on complex field, namely unsupervised and supervised learning methods on the complex domain (PCMF) and (DPCMF).
Principal component analysis (PCA) is known as a powerful technique for dimensionality reduction and multivariate analysis, whereas convolutional neural networks (CNNs) are powerful visual models that yield hierarchies of features. Taking the advances of these models, we proposed the model (CNN-PCA) by combining them together to acquire a discriminative data representation.
Experiments on face recognition, facial expression recognition, and human action recognition reveal that the proposed methods extract robust features and provide consistently better recognition results than compared methods.
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