| Summary: | 博士 === 國立中央大學 === 資訊工程學系 === 106 === In this work, we construct new dimension reduction models for learning low rank projection in the complex domain to obtain both intuitive features and high performance in real applications, particularly face, facial expression recognition and image clustering. Complex matrix factorization (CMF) is a matrix factorization method that decomposes a complex matrix into two complex matrix factors. The proposed models can be performed without limiting the sign of data. These proposed frameworks can be applied to both negative and positive data which yield extension and effectiveness on real-world applications. Therefore, several operations that can extract complex features, such as the short-time Fourier transform, are going to be utilized directly instead of their absolute values (magnitude/power spectrogram).
From the basic framework, CMF, we developed two constrained CMF frameworks by adding graph and sparse constraints to obtain graph regularized complex matrix factorization (GraCMF) and complex matrix factorization with sparsity constraint (SpaCMF).
Besides, we modified the structure of standard CMF to provide more extensions. One of them is exemplar-embed complex matrix factorization (EE-CMF) which a learned base lies within original space (exemplar). Projective complex matrix factorization (ProCMF) was developed as a new learning subspace method that the coefficient of each data point lies within the subspace spanned by the column vectors of one projection complex matrix. Simplical complex matrix factorization (SiCMF), a new model was figured out by convex combining the latent components to reconstruct the original instances.
To satisfy nonnegative requirement, nonnegative matrix factorization (NMF) usually uses various strategies on minimizing a function, which lead to computational complexity. On the contrary, the significant superiority compared to NMF approaches of the proposed complex models is to construct an unconstraint optimization problem that simplified the framework of extracting the basis and intrinsic features.
Wirtinger's calculus is used to compute the derivative of the cost functions. The gradient descent method is used to solve complex optimization problems. The proposed algorithms are proved to provide effective features for a face and facial expression recognition as well as image clustering. Experiments on these tasks reveal that the proposed methods of matrix factorization on complex domain provide consistently better recognition results than standard NMFs.
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