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Multivariate kernel methods in the a...

Purdom, Elizabeth.

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Multivariate kernel methods in the analysis of graphical structures.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Multivariate kernel methods in the analysis of graphical structures./
作者:	Purdom, Elizabeth.
面頁冊數:	209 p.
附註:	Adviser: Susan Holmes.
Contained By:	Dissertation Abstracts International67-09B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3235325
ISBN:	9780542895401

Multivariate kernel methods in the analysis of graphical structures.
Purdom, Elizabeth.

Multivariate kernel methods in the analysis of graphical structures. - 209 p.

Adviser: Susan Holmes.

Thesis (Ph.D.)--Stanford University, 2006.

Increasingly, current knowledge of a biological process is summarized in the form of a graph or a network. However, graphical structures are difficult to incorporate into a standard data analysis. In particular, it is difficult to relate the information in a graph to new experimental data. Various authors have suggested kernel approaches to these problems. Such kernel methods adapt classical multivariate statistical techniques for more general types of data. Rather than require numerical description of the data, kernel techniques require only a particular type of measure of similarity between objects. For biological graphs, different authors have used a measure of similarity between nodes of a graph to analyze graphs with kernel techniques. However, the kernel methods in use only generally describe the relationship between the graph and the experiment without being explicitly predictive; in particular, they derive from the classical technique of Canonical Correlation Analysis (CCA).

ISBN: 9780542895401Subjects--Topical Terms:

517247
Statistics.

Multivariate kernel methods in the analysis of graphical structures.
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520 $a Increasingly, current knowledge of a biological process is summarized in the form of a graph or a network. However, graphical structures are difficult to incorporate into a standard data analysis. In particular, it is difficult to relate the information in a graph to new experimental data. Various authors have suggested kernel approaches to these problems. Such kernel methods adapt classical multivariate statistical techniques for more general types of data. Rather than require numerical description of the data, kernel techniques require only a particular type of measure of similarity between objects. For biological graphs, different authors have used a measure of similarity between nodes of a graph to analyze graphs with kernel techniques. However, the kernel methods in use only generally describe the relationship between the graph and the experiment without being explicitly predictive; in particular, they derive from the classical technique of Canonical Correlation Analysis (CCA).
520 $a In this work, we turn instead to explicitly predictive multivariate regression techniques. We extend multivariate regression to the kernel framework and show that this provides a method more appropriate for these tasks, which are generally predictive in nature. In doing so, we also show how the CCA and regression framework are related through regularization of the problem. We illustrate how these kernel techniques are equivalent to classical statistical techniques, if the "data" for an observation consists of the similarity of the observation to the training set. This is a different interpretation of the kernel techniques and can be more convenient for those already familiar with classical statistics. We demonstrate our techniques for two different types of graphs: (1) a yeast metabolic network and (2) a phylogenetic tree. For the metabolic network, we use a network and related experimental data that has been previously analyzed the literature using kernel methods. For the phylogenetic tree, we analyze ecological data collected on bacteria and their estimated phylogenetic tree. For the latter set of data, we suggest a different type of similarity appropriate for phylogenetic trees, and we connect this type of analysis to others in the literature.
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