Domain Decomposed Learning Algorithms and Applications / Jingwei Li.
In machine learning (ML), dimensionality reduction (DR) is a common method to reduce the computational cost, and among the linear DR techniques, principal component analysis (PCA) and linear discriminant analysis (LDA) are widely used for unsupervised and supervised learning. In this thesis, we main...
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| Format: | Thesis Electronic eBook |
| Language: | English |
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ProQuest Dissertations & Theses,
2023.
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| Summary: | In machine learning (ML), dimensionality reduction (DR) is a common method to reduce the computational cost, and among the linear DR techniques, principal component analysis (PCA) and linear discriminant analysis (LDA) are widely used for unsupervised and supervised learning. In this thesis, we mainly propose some new variants of linear reduction methods and an iterative deflation method that addresses some of the limitations of traditional algorithms. For PCA, the reconstruction error is large even when a large number of eigenmodes is used in some applications. In this thesis, we show that an unexpected error source is the pollution effect of a summation operation in the objective function of the PCA algorithm. The summation operator brings together unrelated parts of the data into the same optimization and the result is the reduction of the accuracy of the overall algorithm. To overcome the problem, we introduce a domain decomposed PCA (ddPCA) that improves the accuracy and also increases the parallelism of the algorithm. To demonstrate the accuracy and parallel efficiency of the proposed algorithm, we consider two applications including a face recognition problem, and a brain tumor detection problem using two- and three-dimensional MRI images. For LDA, we propose a domain decomposed method and an iterative deflated method to improve classification accuracy. In the domain decomposed LDA, we decompose the given dataset into subsets and applied LDA separately to each subset for the training phase of the algorithm. In the testing phase, we project the samples into multiple subspaces, contrary to one as in the traditional LDA. From the multiple low-dimensional projections, we determine the class or classes that the sample belongs to. In the iteratively deflated method, the traditional LDA method serves as the initial iteration from which we select separable classes to be deflated from the training dataset, and the remaining samples in the dataset are then used for the next iteration. As the process goes on we generate a sequence of projection matrices that are used to determine which class or classes a sample belongs to using certain classification criteria. With the proper choices of the quantile radii in the separable criteria for the training and testing phases, we show that the proposed method is much more accurate than the traditional LDA. To test these two proposed methods, we consider the CIFAR-10/100 datasets and a gene expression dataset of cancer patients. The results show that the new approaches outperform the traditional LDA by a large margin. |
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| Item Description: | Source: Dissertations Abstracts International, Volume: 84-11, Section: B. Advisors: Cai, Xiao-Chuan Committee members: Brown, Jed; Morrison, Rebecca; Schnabel, Robert; Huang, Yu-Jui. |
| Physical Description: | 1 electronic resource (105 pages) |
| ISBN: | 9798379532482 |
| Access: | This item is not available from ProQuest Dissertations & Theses. |