title: Discovering multi-level structures in bio-molecular data through the Bernstein inequality.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: DSI, Dipartimento di Scienze dell' Informazione, Universitá degli Studi di Milano, Via Comelico 39, Milano, Italy. bertoni@dsi.unimi.it
authors.forename: Alberto
authors.initials: A
authors.lastname: Bertoni
authors.forename: Giorgio
authors.initials: G
authors.lastname: Valentini
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016208:Databases, Factual; D020869:Gene Expression Profiling / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D020543:Proteome / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D020543:Proteome