Abstract
The assessment of the reliability of clusters discovered in bio-molecular data is a central issue in several bioinformatics problems. Several methods based on the concept of stability have been proposed to estimate the reliability of each individual cluster as well as the ”optimal” number of clusters. In this conceptual framework a clustering ensemble is obtained through bootstrapping techniques, noise injection into the data or random projections into lower dimensional subspaces. A measure of the reliability of a given clustering is obtained through specific stability/reliability scores based on the similarity of the clusterings composing the ensemble. Classical stability-based methods do not provide an assessment of the statistical significance of the clustering solutions and are not able to directly detect multiple structures (e.g. hierarchical structures) simultaneously present in the data. Statistical approaches based on the chi-square distribution and on the Bernstein inequality, show that stability-based methods can be successfully applied to the statistical assessment of the reliability of clusters, and to discover multiple structures underlying complex bio-molecular data. In this paper we provide an overview of stability based methods, focusing on stability indices and statistical tests that we recently proposed in the context of the analysis of gene expression data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dopazo, J.: Functional interpretation of microarray experiments. OMICS 3 (2006)
Gasch, P., Eisen, M.: Exploring the conditional regulation of yeast gene expression through fuzzy k-means clustering. Genome Biology 3 (2002)
Dyrskjøt, L., Thykjaer, T., Kruhøffer, M., Jensen, J., Marcussen, N., Hamilton-Dutoit, S., Wolf, H., Ørntoft, T.: Identifying distinct classes of bladder carcinoma using microarrays. Nature Genetics 33, 90–96 (2003)
Kaplan, N., Friedlich, M., Fromer, M., Linial, M.: A functional hierarchical organization of the protein sequence space. BMC Bioinformatics 5 (2004)
Jain, A., Murty, M., Flynn, P.: Data Clustering: a Review. ACM Computing Surveys 31, 264–323 (1999)
Kasturi, J., Acharya, R.: Clustering of diverse genomic data using information fusions. Bioinformatics 21, 423–429 (2005)
Avogadri, R., Valentini, G.: Fuzzy ensemble clustering based on random projections for dna microarray data analysis. Artificial Intelligence in Medicine (2008), doi:10.1016/j.artmed.2008.07.014
Swift, S., Tucker, A., Liu, X.: An analysis of scalable methods for clustering high-dimensional gene expression data. Annals of Mathematics, Computing and Teleinformatics 1, 80–89 (2004)
Napolitano, F., Raiconi, G., Tagliaferri, R., Ciaramella, A., Staiano, A., Miele, G.: Clustering and visualization approaches for human cell cycle gene expression data analysis. Int. J. Approx. Reasoning 47, 70–84 (2008)
Azuaje, F., Dopazo, J.: Data Analysis and Visualization in Genomics and Proteomics. Wiley, Chichester (2005)
Giardine, B., Riemer, C., Hardison, R., Burhans, R., Elnitski, L., Shah, P., Zhang, Y., Blankenberg, D., Albert, I., Taylor, J., Miller, W., Kent, W., Nekrutenko, A.: Galaxy: a platform for interactive large-scale genome analysis. Genome Res. 15, 1451–1455 (2005)
Ciaramella, A., Cocozza, S., Iorio, F., Miele, G., Napolitano, F., Pinelli, M., Raiconi, G., Tagliaferri, R.: Interactive data analysis and clustering of genomic data. Neural Networks 21, 368–378 (2008)
Handl, J., Knowles, J., Kell, D.: Computational cluster validation in post-genomic data analysis. Bioinformatics 21, 3201–3215 (2005)
Dudoit, S., Fridlyand, J.: Bagging to improve the accuracy of a clustering procedure. Bioinformatics 19, 1090–1099 (2003)
Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. Journal of Computational Biology 6, 281–297 (1999)
Ben-Hur, A., Ellisseeff, A., Guyon, I.: A stability based method for discovering structure in clustered data. In: Altman, R., Dunker, A., Hunter, L., Klein, T., Lauderdale, K. (eds.) Pacific Symposium on Biocomputing, Lihue, Hawaii, USA, vol. 7, pp. 6–17. World Scientific, Singapore (2002)
Dudoit, S., Fridlyand, J.: A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biology 3, 1–21 (2002)
Yeung, K., Haynor, D., Ruzzo, W.: Validating clustering for gene expression data. Bioinformatics 17, 309–318 (2001)
Kerr, M., Curchill, G.: Bootstrapping cluster analysis: assessing the reliability of conclusions from microarray experiments. PNAS 98, 8961–8965 (2001)
McShane, L., Radmacher, D., Freidlin, B., Yu, R., Li, M., Simon, R.: Method for assessing reproducibility of clustering patterns observed in analyses of microarray data. Bioinformatics 18, 1462–1469 (2002)
Smolkin, M., Gosh, D.: Cluster stability scores for microarray data in cancer studies. BMC Bioinformatics 36 (2003)
Bittner, M., Meltzer, P., Chen, Y., Jiang, Y., Seftor, E., Hendrix, M., Radmacher, M., Simon, R., Yakhini, Z., Ben-Dor, A., Sampas, N., Dougherty, E., Wang, E., Marincola, F., Gooden, C., Lueders, J., Glatfelter, A., Pollock, P., Carpten, J., Gillanders, E., Leja, D., Dietrich, K., Beaudry, C., Berens, M., Alberts, D., Sondak, V.: Molecular classification of malignant melanoma by gene expression profiling. Nature 406, 536–540 (2000)
Monti, S., Tamayo, P., Mesirov, J., Golub, T.: Consensus Clustering: A Resampling-based Method for Class Discovery and Visualization of Gene Expression Microarray Data. Machine Learning 52, 91–118 (2003)
Lange, T., Roth, V., Braun, M., Buhmann, J.: Stability-based validation of clustering solutions. Neural Computation 16, 1299–1323 (2004)
Valentini, G.: Clusterv: a tool for assessing the reliability of clusters discovered in DNA microarray data. Bioinformatics 22, 369–370 (2006)
Bertoni, A., Valentini, G.: Model order selection for bio-molecular data clustering. BMC Bioinformatics 8 (2007)
Bertoni, A., Valentini, G.: Randomized maps for assessing the reliability of patients clusters in DNA microarray data analyses. Artificial Intelligence in Medicine 37, 85–109 (2006)
Bertoni, A., Valentini, G.: Discovering Significant Structures in Clustered Bio-molecular Data Through the Bernstein Inequality. In: Apolloni, B., Howlett, R.J., Jain, L. (eds.) KES 2007, Part III. LNCS, vol. 4694, pp. 886–891. Springer, Heidelberg (2007)
Bertoni, A., Valentini, G.: Discovering multi-level structures in bio-molecular data through the Bernstein inequality. BMC Bioinformatics 9 (2008)
Valentini, G.: Mosclust: a software library for discovering significant structures in bio-molecular data. Bioinformatics 23, 387–389 (2007)
Bertoni, A., Valentini, G.: Randomized embedding cluster ensembles for gene expression data analysis. In: SETIT 2007 - IEEE International Conf. on Sciences of Electronic, Technologies of Information and Telecommunications, Hammamet, Tunisia (2007)
Rand, W.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66, 846–850 (1971)
Jain, A., Dubes, R.: Algorithms for clustering data. Prentice Hall, Englewood Cliffs (1988)
Achlioptas, D.: Database-friendly random projections. In: Buneman, P. (ed.) Proc. ACM Symp. on the Principles of Database Systems. Contemporary Mathematics, pp. 274–281. ACM Press, New York (2001)
Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)
Bertoni, A., Valentini, G.: Assessment of clusters reliability for high dimensional genomic data. In: BITS 2007, Bioinformatics Italian Society Meeting, Napoli Italy (2007)
Hoeffding, W.: Probability inequalities for sums of independent random variables. J. Amer. Statist. Assoc. 58, 13–30 (1963)
Indyk, P.: Algorithmic Applications of Low-Distortion Geometric Embeddings. In: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, Washington DC, USA, pp. 10–33. IEEE Computer Society, Los Alamitos (2001)
Johnson, W., Lindenstrauss, J.: Extensions of Lipshitz mapping into Hilbert space. In: Conference in modern analysis and probability. Contemporary Mathematics, Amer. Math. Soc., vol. 26, pp. 189–206 (1984)
Valentini, G., Ruffino, F.: Characterization of lung tumor subtypes through gene expression cluster validity assessment. RAIRO - Theoretical Informatics and Applications 40, 163–176 (2006)
Bertoni, A., Valentini, G.: In: Random projections for assessing gene expression cluster stability. In: IJCNN 2005, The IEEE-INNS International Joint Conference on Neural Networks, Montreal (2005)
Ben-David, S., von Luxburg, U., Pal, D.: A sober look at clustering stability. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS, vol. 4005, pp. 5–19. Springer, Heidelberg (2006)
Ben-David, S., von Luxburg, U.: Relating clustering stability to properties of cluster boundaries. In: 21st Annual Conference on Learning Theory (COLT 2008). LNCS, pp. 379–390. Springer, Heidelberg (2008)
Harris, M., et al.: The Gene Ontology (GO) database and informatics resource. Nucleic Acid Res. 32, D258–D261 (2004)
Brehelin, L., Gascuel, O., Martin, O.: Using repeated measurements to validate hierarchical gene clusters. Bioinformatics 24, 682–688 (2008)
Avogadri, R., Brioschi, M., Ruffino, F., Ferrazzi, F., Beghini, A., Valentini, G.: An algorithm to assess the reliability of hierarchical clusters in gene expression data. In: Lovrek, I., Howlett, R.J., Jain, L.C. (eds.) KES 2008, Part III. LNCS, vol. 5179, pp. 764–770. Springer, Heidelberg (2008)
Filippone, M., Masulli, F., Rovetta, S.: Stability and Performances in Biclustering Algorithms. In: Masulli, F., Tagliaferri, R., Verhivker, G.M. (eds.) CIBB 2008. LNCS (LNBI), vol. 5488, pp. 91–101. Springer, Heidelberg (2009)
Troyanskaya, O., et al.: A Bayesian framework for combining heterogeneous data sources for gene function prediction (in saccharomices cerevisiae). Proc. Natl. Acad. Sci. USA 100, 8348–8353 (2003)
Guan, Y., Myers, C., Hess, D., Barutcuoglu, Z., Caudy, A., Troyanskaya, O.: Predicting gene function in a hierarchical context with an ensemble of classifiers. Genome Biology 9 (2008)
Alizadeh, A., Eisen, M., Davis, R., Ma, C., Lossos, I., Rosenwald, A., Boldrick, J., Sabet, H., Tran, T., Yu, X., Powell, J., Yang, L., Marti, G., Moore, T., Hudson, J., Lu, L., Lewis, D., Tibshirani, R., Sherlock, G., Chan, W., Greiner, T., Weisenburger, D., Armitage, J., Warnke, R., Levy, R., Wilson, W., Grever, M., Byrd, J., Botstein, D., Brown, P., Staudt, L.: Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature 403, 503–511 (2000)
Lapointe, J., Li, C., Higgins, J., van de Rijn, M., Bair, E., Montgomery, K., Ferrari, M., Egevad, L., Rayford, W., Bergerheim, U., Ekman, P., DeMarzo, A., Tibshirani, R., Botstein, D., Brown, P., Brooks, J., Pollack, J.: Gene expression profiling identifies clinically relevant subtypes of prostate cancer. PNAS 101, 811–816 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bertoni, A., Valentini, G. (2009). Unsupervised Stability-Based Ensembles to Discover Reliable Structures in Complex Bio-molecular Data. In: Masulli, F., Tagliaferri, R., Verkhivker, G.M. (eds) Computational Intelligence Methods for Bioinformatics and Biostatistics. CIBB 2008. Lecture Notes in Computer Science(), vol 5488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02504-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-02504-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02503-7
Online ISBN: 978-3-642-02504-4
eBook Packages: Computer ScienceComputer Science (R0)