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Tensor generalizations of the singul...

The University of Texas at Austin., Physics.

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Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data./
Author:	Omberg, Lars Gustaf.
Description:	115 p.
Notes:	Advisers: Orly Alter; Greg O. Sitz.
Contained By:	Dissertation Abstracts International68-12B.
Subject:	Biology, Bioinformatics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290840
ISBN:	9780549348856

Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data.
Omberg, Lars Gustaf.

Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data. - 115 p.

Advisers: Orly Alter; Greg O. Sitz.

Thesis (Ph.D.)--The University of Texas at Austin, 2007.

The structure of large-scale molecular biological data is often of an order higher than that of a matrix, especially when integrating data from different studies. Flattened into a matrix format, much of the information in the data is lost. I describe the use of higher-order generalizations of singular value decomposition (SVD) - both the higher-order singular value decomposition (HOSVD) and Parallel Factorization (PARAFAC) - in transforming tensors into simplified spaces. I apply these transformations to a series of DNA microarray datasets from different studies tabulated in a tensor of genes x time x conditions, specifically an integration of genome-scale mRNA expression data from three yeast-cell cycle time courses. One of the time courses was under exposure to the oxidative stress agent hydrogen peroxide (HP); another was exposed to menadione (MD) and the third was unstressed[45].

ISBN: 9780549348856Subjects--Topical Terms:

1018415
Biology, Bioinformatics.

Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data.
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020 $a 9780549348856
035 $a (UMI)AAI3290840
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100 1 $a Omberg, Lars Gustaf. $3 1018660
245 1 0 $a Tensor generalizations of the singular value decomposition for integrative analysis of large-scale molecular biological data.
300 $a 115 p.
500 $a Advisers: Orly Alter; Greg O. Sitz.
500 $a Source: Dissertation Abstracts International, Volume: 68-12, Section: B, page: 7747.
502 $a Thesis (Ph.D.)--The University of Texas at Austin, 2007.
520 $a The structure of large-scale molecular biological data is often of an order higher than that of a matrix, especially when integrating data from different studies. Flattened into a matrix format, much of the information in the data is lost. I describe the use of higher-order generalizations of singular value decomposition (SVD) - both the higher-order singular value decomposition (HOSVD) and Parallel Factorization (PARAFAC) - in transforming tensors into simplified spaces. I apply these transformations to a series of DNA microarray datasets from different studies tabulated in a tensor of genes x time x conditions, specifically an integration of genome-scale mRNA expression data from three yeast-cell cycle time courses. One of the time courses was under exposure to the oxidative stress agent hydrogen peroxide (HP); another was exposed to menadione (MD) and the third was unstressed[45].
520 $a The HOSVD transforms the tensor to a "core tensor" of "eigenarrays"' x "time-eigengenes" x "condition-eigengenes,"' where the eigenarrays, time-eigengenes and condition-eigengenes are unique orthonormal superpositions of the genes, times and conditions, respectively. This HOSVD, also known as N-mode SVD, formulates the tensor as a linear superposition of all possible outer products of an eigenarray, a time-eigengene and a condition-eigengene, i.e., rank-1 "subtensors," the superposition coefficients of which are tabulated in the core tensor. Each coefficient indicates the significance of the corresponding subtensor in terms of the overall information it captures in the data. PARAFAC reformulates the same data tensor into a sum of rank-1 tensor of F elements that best approximate the data tensor in a least square sense.
520 $a I show that significant rank-1 subtensors can be associated with independent biological processes, which are manifested in the data tensor. Subtensors of the HOSVD capture the subprocesses: stress response, pheromone response and developmental stage. The data suggests that the conserved genes YKU70, MRE11, AIF1 and ZWF1, as well as the genes involved in the processes of retrotransposition, apoptosis and the oxidative pentose phosphate cycle may play significant, yet previously unrecognized, roles in the differential effects of HP and MD on cell cycle progression. Subtensors of PARAFAC capture the same biological processes as the 2 most significant HOSVD subtensors. A genome-wide correlation between DNA replication and initiation of RNA transcription, which is equivalent to a recently discovered correlation and might be due to a previously unknown mechanism of regulation, is independently uncovered.
590 $a School code: 0227.
650 4 $a Biology, Bioinformatics. $3 1018415
650 4 $a Biology, Biostatistics. $3 1018416
690 $a 0308
690 $a 0715
710 2 $a The University of Texas at Austin. $b Physics. $3 1018659
773 0 $t Dissertation Abstracts International $g 68-12B.
790 $a 0227
790 1 0 $a Alter, Orly, $e advisor
790 1 0 $a Sitz, Greg O., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3290840