Multi-objective SNP selection based on Pareto optimality

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LaTex

@article{GUMUS201323,
title = “Multi objective SNP selection using pareto optimality”,
journal = “Computational Biology and Chemistry”,
volume = “43”,
pages = “23 - 28”,
year = “2013”,
issn = “1476-9271”,
doi = “https://doi.org/10.1016/j.compbiolchem.2012.12.006“,
url = “http://www.sciencedirect.com/science/article/pii/S1476927112001156“,
author = “Ergun Gumus and Zeliha Gormez and Olcay Kursun”,
keywords = “Feature selection, Principal component analysis (PCA), Mutual information (MI), Genomic鈥揼eographical distance, Human Genome Diversity Project SNP dataset”
}

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Ergun Gumus, Zeliha Gormez, Olcay Kursun,
Multi objective SNP selection using pareto optimality,
Computational Biology and Chemistry,
Volume 43,
2013,
Pages 23-28,
ISSN 1476-9271,
https://doi.org/10.1016/j.compbiolchem.2012.12.006.
(http://www.sciencedirect.com/science/article/pii/S1476927112001156)
Keywords: Feature selection; Principal component analysis (PCA); Mutual information (MI); Genomic–geographical distance; Human Genome Diversity Project SNP dataset

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Summary

Biomarker discovery

SNP — single nucleotide polymorphism

Traditional Single Objective - Maximize Classification Accuracy

1 High classification accuracy
2 Correlation between genetic diversity of ethnic groups and geographic distance

main content

Dataset:
Human Genome Diversity Project (HGDP) SNP dataset
1064 individuals
52 populations
Raw data:
1043 individuals
per individual — 660,918 SNPs (163 from mitochondrial DNA, excluded) — with 660,755
each SNP — 2 alleles Gene — code is expressed as:$\left\{ -1, 0, 1 \right\}$

Goal one :

High classification accuracy — mutual information MI

$H$— Entropy of a random variable

Goal two :

Genomic geographic correlations — principal components analysis PCA

Due to higher dimensionality - used a "dimensional trick" for PCA

$C$—$D\times D$dimensional covariance matrix
$Y$—$N \times D$is the central data matrix,$N \ll D$

$k_i$- Feature vector$i$
Multiply both sides$Y$

$v_i = Yk_i$— covariance matrix$YY^T$First$i$Eigenvectors are multiplied
on both sides$Y^T$

Available: