NEW 2 Tutorial COMPSTAT-1

Lechevallier Yves

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• Publié par: Rupev
• Nombre de lectures: 16
• Langue: English

Extrait

Symbolic Data Analysis Of Complex Data: several directions of research

Edwin Diday CEREMADE Paris Dauphine University

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OUTLINE

What are Complex data? What are “symbolic data”? How “Symbolic Data” are build?   Symbolic Data are Complex data? From Complex Data to Symbolic Data What is “Symbolic Data Analysis” (SDA)? Open directions of research Conclusion: SDA gives a framework for Complex Data Analysis (CDA)

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OUTLINE

What are Complex data? What are “symbolic data”? How “Symbolic Data” are build? Symbolic Data are Complex data? From Complex Data to Symbolic Data What is “Symbolic Data Analysis” (SDA)? Open directions of research SDA gives a framework for Complex Data Analysis (CDA)

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What are Complex data?

Any data which cannot be considered as a standard “observations x variables” data table. Examples • several data tables describing different kind of observations. • Hierarchical Data • Textual Data in each cell of the data table • Time series Data in each cell.

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• • • • • • • •

OUTLINE

What are Complex data? What are “symbolic data”? How “Symbolic Data” are build? Symbolic Data are Complex data? From Complex Data to Symbolic Data What is “Symbolic Data Analysis” (SDA)? Open directions of research SDA gives a framework for Complex Data Analysis (CDA)

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What are “symbolic data”?

Any data taking care on the variation inside classes of standard observation.

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each cell of the data table can contain: A number, a category, an interval, a sequence of categorical values, a sequence of weighted values , a Bar Chart, a histogram, a distribution, …

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Example of SYMBOLIC DATA

  TEAM OF THE WEIGHT NATIONALITY NB OF GOALS FRENCH CUP MARSEILLES [75 , 89 ] {French} {0.8 (0), 0.2 (1)}   LYON [80, (1), …} 0.3 (0), {0.1 Alg, Arg } {Fr, 95]   PARIS-ST G. 95] [76, 0.2 (1), …} {0.4 (0), {Fr, Tun }   NANTES 85] {Fr, [70, (1), …} {0.2 Engl, Arg } 0.5 (0),       Here the variation (of weight, nationality, …) concerns the players of each team.

THIS NEW KIND OF VARIABLES ARE CALLED « SYMBOLIC » BECAUSE THEY ARE NOT PURELY NUMERICAL IN ORDER TO EXPRESS THE INTERNAL VARIATION INSIDE EACH CONCEPT.

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SYMBOLIC DATA TABLE SOFTWARE*

Scoring rows by min, max of intervals or frequencies or barchart is possible.

SYROKKO Company [e-mail]

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SYMBOLIC DATA TABLE SOFTWARE*

Scoring variables is also possible in order to select the most discriminate variables of the rows * SYROKKO Company [e-mail]  

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• • • • • • • •

OUTLINE

What are Complex data? What are “symbolic data”? How symbolic data are build? Symbolic Data are Complex data? Complex data are Symbolic Data after transformation ? What is “Symbolic Data Analysis” (SDA)? SDA gives a framework for Complex Data Analysis (CDA)? Open directions of research.

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First step: From Standard Data TABLE 1 To random variables in each cell TABLE 2

Table 1 Y 1 Y j w 1 w i x ij

Table 2 X 1 X j In each cell I n n u  e m a b c e h r  c o e r  ll a     a  C 1 m doan R leabriVa a   category C i D j C i X ij

w n Standard data table: w i x Y j (Observations) x (Random Variables) a Y j (w mo i )= ng    D x i j j mod ehtY fo nia  = aunbmreo  ra j category

C k Random Variables data table: C i x X j (Classes of Observations) x (Random variables of random variable values) X j (C i ) =X ij is a random variable: X ij (w) =x= a number or a category

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