Multivariate methods for the analysis of structured data
Abstract/Contents
- Abstract
- We describe methods for incorporating information about variable structure in multivariate analysis. We are motivated by the example of microbiome data, where we have species abundances in addition to information about the evolutionary history of those species. However, the methods we develop are applicable to more general types of structure on the variables, and we expect to find many other applications both in biology and in other fields. We develop a method for structured dimensionality reduction, adaptive gPCA. This method allows for tunable incorporation of the variable structure, so that the fine-scale structure of the variables, the global structure, or anything in between can be brought out. We then move to the problem of incorporating sparsity in addition to the structure to obtain a sparse and structured PCA as well as sparse and structured discriminant analysis for classification problems. The primary motivation behind incorporating sparsity and structure together is to obtain more interpretable results, but we also show that incorporating these two elements can substantially improve classification accuracy in the supervised setting.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Fukuyama, Julia |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Holmes, Susan |
| Thesis advisor | Holmes, Susan |
| Thesis advisor | Relman, David A |
| Thesis advisor | Wong, Wing Hung |
| Advisor | Relman, David A |
| Advisor | Wong, Wing Hung |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Julia Fukuyama. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Julia Anne Fukuyama
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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