Basic statistics for distributional symbolic variables: a new metric-based approach

Advances in Data Analysis and Classification

Volumn 9, Issue 2, 2015, Pages 143-175

  Irpino, Antonio ^a   Verde, Rosanna ^a  

^a SECOND UNIVERSITY OF NAPLES   (Italy)

Author keywords

Basic statistics; Distribution valued data; Histogram data; Symbolic data; Wasserstein metric

Indexed keywords

DATA MINING; DISTRIBUTION FUNCTIONS;

BIVARIATE STATISTICS; CONCEPTUAL FRAMEWORKS; DISTRIBUTION-VALUED DATUM; EMPIRICAL DISTRIBUTION FUNCTIONS; HISTOGRAM DATA; SYMBOLIC DATA; SYMBOLIC DATA ANALYSIS; WASSERSTEIN METRIC;

STATISTICS;

EID: 84929951596     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-014-0176-4     Document Type: Article

References (30)

1. Aitchison J (1986) The statistical analysis of compositional data. Chapman Hall, New York
2. Bacelar-Nicolau H (1987) On the distribution equivalence in cluster analysis. In: Devijver PA, Kittler J (eds) Pattern recognition theory and applications, NATO ASI SeriesF, vol 30. Springer Verlag, Berlin, pp 73–79
3. Bacelar-Nicolau H (1988) Two probabilistic models for classification of variables in frequency tables. In: Bock HH (ed) Classification and related methods. North-Holland, Amsterdam, pp 181–189
4. Barrio E, Matran C, Rodriguez-Rodriguez J, Cuesta-Albertos JA (1999) Tests of goodness of fit based on the L2-Wasserstein distance. Ann Stat 27:1230–1239
5. Bertrand P, Goupil F (2000) Descriptive statistics for symbolic data. In: Bock HH, Diday E (eds) Analysis of symbolic data: exploratory methods for extracting statistical information from complex data. Springer, Berlin, pp 103–124
6. Billard L (2007) Dependencies and variation components of symbolic interval-valued data. In: Brito P, Bertrand P, Cucumel G, de Carvalho FAT (eds) Selected contributions in data analysis and classification. Springer, Berlin, pp 3–12
7. Billard L (2008) Sample covariance function for complex quantitative data. In: Proceedings of IASC 2008, Yokohama, Japan, pp 157–163
8. Billard L, Diday E (2003) From the statistics of data to the statistics of knowledge: symbolic data analysis. J Am Stat Assoc 98(462):470–487
9. Billard L, Diday E (2006) Symbolic data analysis: conceptual statistics and data mining. Wiley, Chirchester
10. Bock HH, Diday E (2000) Analysis of symbolic data, exploratory methods for extracting statistical information from complex data. Studies in Classification, Data Analysis and Knowledge Organisation. Springer-Verlag, Berlin
11. Brito P (2007) On the analysis of symbolic data. In: Brito P, Bertrand P, Cucumel G, de Carvalho FAT (eds) Selected contributions in data analysis and classification. Springer, Berlin, pp 13–22
12. Chisini O (1929) Sul concetto di media. Periodico di Matematiche 4:106–116
13. Diday E (2013) Principal component analysis for bar charts and metabins tables. Stat Anal Data Min 6(5):403–430
14. Frühwirth-Schnatter S (2006) Finite mixture and Markov switching models. Springer, Berlin
15. Gibbs AL, Su FE (2002) On choosing and bounding probability metrics. Int Stat Rev 7(3):419–435
16. Gilchrist WG (2000) Statistical modelling with quantile functions. Chapman and Hall/CRC, London
17. Ginestet CE, Simmons A, Kolaczyk ED (2012) Weighted Frechet means as convex combinations in metric spaces: properties and generalized median inequalities. Stat Probab Lett 82(10):1859–1863
18. Ichino M (2011) The quantile method for symbolic principal component analysis. Stat Anal Data Min 4(2):184–198
19. Irpino A, Lechevallier Y, Verde R (2006) Dynamic clustering of histograms using Wasserstein metric. In: Rizzi A, Vichi M (eds) COMPSTAT 2006. Physica-Verlag, Berlin, pp 869–876
20. Irpino A, Verde R (2006) A new Wasserstein based distance for the hierarchical clustering of histogram symbolic data. In: Batanjeli V, Bock HH, Ferligoj A, Ziberna A (eds) Data science and classification, IFCS 2006. Springer, Berlin, pp 185–192
21. Irpino A, Verde R (2008a) Dynamic clustering of interval data using a Wasserstein-based distance. Pattern Recogn Lett 29:1648–1658
22. Irpino A, Verde R (2008) Comparing histogram data using a Mahalanobis-Wasserstein distance. In: Brito P (ed) COMPSTAT 2008. Physica-Verlag, Heidelberg, pp 77–89
23. Kim J, Billard L (2013) Dissimilarity measures for histogram-valued observations. Commun Stat-Theor M 42:283–303
24. Matusita K (1951) On the theory of statistical decision functions. Ann I Stat Math 3(1):1–30
25. Moore RE (1966) Interval analysis. Prentice Hall, Englewood Cliffs
26. Moore R, Lodwick W (2003) Interval analysis and fuzzy set theory. Fuzzy Set Syst 135(1):5–9
27. Noirhomme-Fraiture M, Brito P (2012) Far beyond the classical data models: symbolic data analysis. Stat Anal Data Min 4(2):157–170
28. Nielsen F, Nock R (2009) Sided and symmetrized Bregman centroids. IEEE T Inform Theory 55(6):2882–2904
29. Rüschendorf L (2001) Wasserstein metric. In: Hazewinkel M (ed) Encyclopedia of mathematics. Springer, New York
30. Verde R, Irpino A (2007) Dynamic clustering of histogram data: using the right metric. In: Brito P, Bertrand P, Cucumel G, de Carvalho FAT (eds) Selected contributions in data analysis and classification. Springer, Berlin, pp 123–134