Abstract
In this paper we discuss some issues which arise when applying classical data analysis techniques to interval data, focusing on the notions of dispersion, association and linear combinations of interval variables. We present some methods that have been proposed for analysing this kind of data, namely for clustering, discriminant analysis, linear regression and interval time series analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
BERTRAND, P. and GOUPIL, F. (2000): Descriptive Statistics for Symbolic Data. In: H.-H. Bock and E. Diday (Eds.): Analysis of Symbolic Data. Springer, Heidelberg, 106–124.
BILLARD, L. and DIDAY, E. (2003): From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis. Journal of the American Statistical Association, 98,462, 470–487.
BOCK, H.-H. (2002): Clustering Algorithms and Kohonen Maps for Symbolic Data. Journal of the Japanese Society of Computational Statistics, 15, 1–13.
BOCK, H.-H. and DIDAY, E. (2000): Analysis of Symbolic Data. Springer, Heidelberg.
CHAVENT, M. and LECHEVALLIER, Y. (2002): Dynamical Clustering Algorithm of Interval Data: Optimization of an Adequacy Criterion Based on Hausdorff Distance. In: A. Sokolowski and H.-H. Bock (Eds.): Classification, Clustering and Data Analysis. Springer, Heidelberg, 53–59.
CHOUAKRIA, A., CAZES, P. and DIDAY, E. (2000): Symbolic Principal Component Analysis. In: H.-H. Bock and E. Diday (Eds.): Analysis of Symbolic Data. Springer, Heidelberg, 200–212.
DE CARVALHO, F.A.T., BRITO, P. and BOCK, H.-H. (2006): Dynamic Clustering for Interval Data Based on L 2 Distance. Computational Statistics, 21,2, 231–250.
DIDAY, E. and NOIRHOMME, M. (2006): Symbolic Data Analysis and the SODAS Software. Wiley, to appear.
DIDAY, E. and SIMON, J.J. (1976): Clustering Analysis. In: K.S. Fu (Ed.): Digital Pattern Recognition. Springer, Heidelberg, 47–94.
DUARTE SILVA, A.P. and BRITO, P. (2006): Linear Discriminant Analysis for Interval Data. Computational Statistics, 21,2, 289–308.
LAURO, C. and PALUMBO, F. (2005): Principal Component Analysis for Non-Precise Data. In: M. Vichi et al (Eds.): New Developments in Classification and Data Analysis. Springer, 173–184.
MOORE, R.E. (1966): Interval Analysis. Prentice Hall, New Jersey.
NETO, E.A.L., DE CARVALHO, F.A.T. and TENORIO, C. (2004): Univariate and Multivariate Linear Regression Methods to Predict Interval-Valued Features. In: AI2004:Advances in Artificial Intelligence. Lecture Notes on Artificial Intelligence, Springer, 526–537.
SOUZA, R.M.C.R. and DE CARVALHO, F.A.T. (2004): Clustering of Interval Data Based on City-Block Distances. Pattern Recognition Letters, 25,3, 353–365.
TELES, P. and BRITO, P. (2005): Modeling Interval Time Series Data. In: Proc. of the 3rd World Conference on Computational Statistics and Data Analysis. Limassol, Cyprus.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brito, P. (2007). Modelling and Analysing Interval Data. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-70981-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70980-0
Online ISBN: 978-3-540-70981-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)