Abstract
Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics.
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References
AKAIKE, H. (1974): A new look at the statistical model idenfication. IEEE Transactions on Automatic Control, 19(6), 716–723.
BLAKE, A. and ZISSERMAN, A. (1987): Visual Reconstruction. The MIT Press Series in Artificial Intelligence, MIT Press, Massachusetts, USA.
CAVANAUGH, J.E. (1997): Unifying the derivations for the Akaike and corrected Akaike information criteria. Statistics & Probability Letters, 33, 201–208.
DAVIES, P.L. (1995): Data features. J. of the Netherlands Society for Statistics and Operations Research, 49(2), 185–245.
DAVIES, P.L. and KOVAC, A. (2001): Local extremes, runs, strings and multires-olution. Ann. Stat., 29, 1–65.
DROBYSHEV, A.L, MACHKA, CHR., HORSCH, M., SELTMANN, M., LIEB-SCHER, V, HRABÉ DE ANGELIS, V., and BECKERS, J. (2003): Specificity assessment from fractionation experiments, (SAFE): a novel method to evaluate microarray probe specificity based on hybridization stringencies. Nucleic Acids Res., 31(2), 1–10.
FRIEDRICH, F. (2003a): Stochastic Simulation and Bayesian Inference for Gibbs fields. CD-ROM, Springer Verlag, Heidelberg, New York.
FRIEDRICH, F. (2003b): AntsInFields: Stochastic simulation and Bayesian inference for Gibbs fields, URL: http://www.AntsInFields.de.
KEMPE, A. (2003): Statistical analysis of the Potts model and applications in biomedical imaging. Thesis, Institute of Biomathematics and Biometry, National Research Center for Environment and Health Munich, Germany.
MUMFORD, D. and SHAH, J. (1989): Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math., 42, 577–685.
SCHWARZ, G. (1978): Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.
SERRA, J. (1982, 1988): Image analysis and mathematical morphology. Vol. I, II. Acad. Press, London.
WINKLER, G. (2003): Image Analysis, Random Fields and Markov Chain Monte Carlo Methods. A Mathematical Introduction. volume 27 of Applications of Mathematics, Springer Verlag, Berlin, Heidelberg, New York, second edition.
WINKLER, G. and LIEBSCHER, V. (2002): Smoothers for Discontinuous Signals. J. Nonpar. Statist., 14(1–2), 203–222.
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Winkler, G., Kempe, A., Liebscher, V., Wittich, O. (2005). Parsimonious Segmentation of Time Series by Potts Models. In: Baier, D., Wernecke, KD. (eds) Innovations in Classification, Data Science, and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26981-9_34
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DOI: https://doi.org/10.1007/3-540-26981-9_34
Publisher Name: Springer, Berlin, Heidelberg
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