Discovering multi–level structures in bio-molecular data through the Bernstein inequality

<p>Abstract</p> <p>Background</p> <p>The unsupervised discovery of structures (i.e. clusterings) underlying data is a central issue in several branches of bioinformatics. Methods based on the concept of stability have been recently proposed to assess the reliability of...

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Main Authors: Valentini Giorgio, Bertoni Alberto
Format: Article
Language:English
Published: BMC 2008-03-01
Series:BMC Bioinformatics
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spelling doaj-ec4d3b6b1bcb4cc3a9cc2e687ab4c4f02020-11-24T23:36:36ZengBMCBMC Bioinformatics1471-21052008-03-019Suppl 2S410.1186/1471-2105-9-S2-S4Discovering multi–level structures in bio-molecular data through the Bernstein inequalityValentini GiorgioBertoni Alberto<p>Abstract</p> <p>Background</p> <p>The unsupervised discovery of structures (i.e. clusterings) underlying data is a central issue in several branches of bioinformatics. Methods based on the concept of stability have been recently proposed to assess the reliability of a clustering procedure and to estimate the “optimal” number of clusters in bio-molecular data. A major problem with stability-based methods is the detection of multi-level structures (e.g. hierarchical functional classes of genes), and the assessment of their statistical significance. In this context, a chi-square based statistical test of hypothesis has been proposed; however, to assure the correctness of this technique some assumptions about the distribution of the data are needed.</p> <p>Results</p> <p>To assess the statistical significance and to discover multi-level structures in bio-molecular data, a new method based on Bernstein's inequality is proposed. This approach makes no assumptions about the distribution of the data, thus assuring a reliable application to a large range of bioinformatics problems. Results with synthetic and DNA microarray data show the effectiveness of the proposed method.</p> <p>Conclusions</p> <p>The Bernstein test, due to its loose assumptions, is more sensitive than the chi-square test to the detection of multiple structures simultaneously present in the data. Nevertheless it is less selective, that is subject to more false positives, but adding independence assumptions, a more selective variant of the Bernstein inequality-based test is also presented. The proposed methods can be applied to discover multiple structures and to assess their significance in different types of bio-molecular data.</p>
collection DOAJ
language English
format Article
sources DOAJ
author Valentini Giorgio
Bertoni Alberto
spellingShingle Valentini Giorgio
Bertoni Alberto
Discovering multi–level structures in bio-molecular data through the Bernstein inequality
BMC Bioinformatics
author_facet Valentini Giorgio
Bertoni Alberto
author_sort Valentini Giorgio
title Discovering multi–level structures in bio-molecular data through the Bernstein inequality
title_short Discovering multi–level structures in bio-molecular data through the Bernstein inequality
title_full Discovering multi–level structures in bio-molecular data through the Bernstein inequality
title_fullStr Discovering multi–level structures in bio-molecular data through the Bernstein inequality
title_full_unstemmed Discovering multi–level structures in bio-molecular data through the Bernstein inequality
title_sort discovering multi–level structures in bio-molecular data through the bernstein inequality
publisher BMC
series BMC Bioinformatics
issn 1471-2105
publishDate 2008-03-01
description <p>Abstract</p> <p>Background</p> <p>The unsupervised discovery of structures (i.e. clusterings) underlying data is a central issue in several branches of bioinformatics. Methods based on the concept of stability have been recently proposed to assess the reliability of a clustering procedure and to estimate the “optimal” number of clusters in bio-molecular data. A major problem with stability-based methods is the detection of multi-level structures (e.g. hierarchical functional classes of genes), and the assessment of their statistical significance. In this context, a chi-square based statistical test of hypothesis has been proposed; however, to assure the correctness of this technique some assumptions about the distribution of the data are needed.</p> <p>Results</p> <p>To assess the statistical significance and to discover multi-level structures in bio-molecular data, a new method based on Bernstein's inequality is proposed. This approach makes no assumptions about the distribution of the data, thus assuring a reliable application to a large range of bioinformatics problems. Results with synthetic and DNA microarray data show the effectiveness of the proposed method.</p> <p>Conclusions</p> <p>The Bernstein test, due to its loose assumptions, is more sensitive than the chi-square test to the detection of multiple structures simultaneously present in the data. Nevertheless it is less selective, that is subject to more false positives, but adding independence assumptions, a more selective variant of the Bernstein inequality-based test is also presented. The proposed methods can be applied to discover multiple structures and to assess their significance in different types of bio-molecular data.</p>
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