Genomic similarity and kernel methods I: Advancements by building on mathematical and statistical foundations

Research output: Contribution to journalReview article

66 Scopus citations

Abstract

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1].

Original languageEnglish (US)
Pages (from-to)109-131
Number of pages23
JournalHuman Heredity
Volume70
Issue number2
DOIs
StatePublished - Jul 1 2010

Keywords

  • Distance
  • Eigenvalue decomposition
  • Nonparametric regression
  • Regularization
  • Similarity kernel
  • Support vector machine

ASJC Scopus subject areas

  • Genetics
  • Genetics(clinical)

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