In contemporary sciences, it is of great interest to study supervised and unsupervised learning problems of high-dimensional tensor data. In this dissertation, we develop new methods for tensor classification and clustering problems, and discuss algorithms to enhance their performance. For supervised learning, we propose CATCH model, in short for Covariate-Adjusted Tensor Classification in High-dimensions, which efficiently integrates the low-dimensional covariates and the tensor to perform classification and variable selection. The CATCH model preserves and utilizes the structures of the data for maximum interpretability and optimal prediction. We propose a penalized approach to select a subset of tensor predictor entries that has direct discriminative effects after adjusting for covariates. Theoretical results confirm that our approach achieves variable selection consistency and optimal classification accuracy. For unsupervised learning, we consider clustering problem on high-dimensional tensor data. we propose an efficient procedure based on EM algorithm. It directly estimates the sparse discriminant vector from a penalized objective function and provides computationally efficient rules to update all other parameters. Meanwhile, the algorithm takes advantage of the tensor structure to reduce the number of parameters, which leads to lower storage costs. The performance of our method over existing methods is demonstrated in simulated and real data examples. Moreover, based on tensor computation, we propose a novel algorithm referred to as the SMORE algorithm for differential network analysis. The SMORE algorithm has low storage cost and high computation speed, especially in the presence of strong sparsity. It also provides a unified framework for binary and multiple network problems. In addition, we note that the SMORE algorithm can be applied to high-dimensional quadratic discriminant analysis problems, providing a new approach for multiclass high-dimensional quadratic discriminant analysis. In the end, we discuss some directions of the future work, including new approaches, applications and relaxing assumptions. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 16, 2019. / classification, clustering, high-dimension, tensor, variable selection / Includes bibliographical references. / Qing Mai, Professor Co-Directing Dissertation; Xin Zhang, Professor Co-Directing Dissertation; Weikuan Yu, University Representative; Elizabeth Slate, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_709804 |
| Contributors | Pan, Yuqing (author), Mai, Qing (Professor Co-Directing Dissertation), Zhang, Xin (Professor Co-Directing Dissertation), Yu, Weikuan (University Representative), Slate, Elizabeth H. (Committee Member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (140 pages), computer, application/pdf |
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