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Lines of Life for MGS Symbolic Descriptions
Lines of Life for MGS Symbolic Descriptions Mireille Gettler-Summa
I - INTRODUCTION
The IFREMER (French sea research center) oce asked for automatic production of shing activity descriptions from the time tables of all economic units (about 2000 every year) belonging to the six harbors of North Brittany in France. The project is then to follow along many years the evolution of the discovered activities : do some of them disappear, increase or decrease, do new shing tactics appear ... ?
II - MGS APPROACH SOLVES FIRST PROBLEM 2.1 Problem formalization
According to the experts, shing tactics have been formalized as Symbolic descriptions
[1]. Example : Tactic 1 f Tuna sh 0 8]5 tons ; 8 tons ], 0 2 [4 tons ; 5 tons ]g And f Cockle 0 9] 3 tons ; 5 tons ], 0 1 none g And f Spider crab 0 75 ] 6 tons ; 7 tons ], 0 25 none g \0 8" before \] 5 tons ; 8 tons ]" means that the units which have that type of tactic along the year are such that 80 per cent of them catch from 5 tons to 8 tons of tuna sh, whereas 20 per cent of them catch from 4 tons to 5 tons only. :
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2.2 MGS approach
For each year the data table consists of a matrix of tons of sh ; a cell is the total catch of an economic unit ( sh boat owner) for a certain target (prey) during the period. An automatic partition is computed for every year. MGS [5] provides automatic symbolic descriptions for each class of the di erent partitions ; experts validate only some of them as relevant shing tactics on the exhaustive statistic of shing e orts for the concerned period.
III - LINES OF LIFE FOR SYMBOLIC DESCRIPTIONS FROM THREE WAY DATA TABLE 3.1 SODAS description workpackages
SODAS [6] provides tools to describe each tactic because it has a symbolic formalization : 1
SOE displays graphics for each tactic and basic calculations STATS provides histograms and basic statistics on the tactics
These graphics allow a visual comparison of the tactics which are indexed by the year of the date table they come from (by MGS procedure), so that it is possible to see increasing or decreasing of some results, depending on the year which is represented.
3.2 LINES OF LIFE of symbolic descriptions
By computing the number of economic units of date \T + h (h 2 <)" which have some tactic de ned from date \T " data table, a drawing of the evolution of this tactic is available. In the framework of Symbolic Data Analysis, it consists of computing the extension of each symbolic description D on all the data tables to the exclusion of the data table from which MGS has extracted D. De nition : Lines of Life of a Symbolic description consists of the mapping of the frequencies of the above de ned extensions versus the dates.
IV - RESULTS
On three years exhaustive statistics of 6 harbors of North Brittany of France, 38 tactics of shing have been extracted by MGS procedure. 22 of those symbolic descriptions have been validated as Fishing Tactics by the experts of IFREMER Institute. 8 Lines of Life have been drawn to show the evolution of 8 tactics along the three years. Keywords : Clustering, MGS (Marking and Generalization by Symbolic Objects), threeway data table, Symbolic Line of Life.
References [1] DIDAY E., 1995 Probabilistic objects for a symbolic data analysis. DIMACS, Series in Discrete Mathematics and Theorical Computers, vol. 19, (1995). [2] GETTLER-SUMMA M., 1997 Symbolic Marking ; Application on car accident scenarios. Proceedings of Applied Stochastic Models and Data Analysis. (Capri, Italy). [3] GETTLER-SUMMA M., PERINEL E., FERRARIS J., 1994 Automatic aid to symbolic cluster interpretation in New Approaches in Classi cation and Data Analysis. Springer Ed. . [4] M. GETTLER-SUMMA, S. GUEYE, 1998 Image Processing by Symbolic Objects, IFCS 98 (Roma, Italy).
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[5] M. GETTLER-SUMMA, 1998 Approches MGS, Marquage et generalisation symbolique pour de nouvelles aides l'interpretation en Analyse de Donnees. CAHIERS DU CEREMADE No 9830 (Universite Paris-Dauphine, France). [6] SODAS EUROSTAT software project (1997-2000).
Mireille Gettler-Summa Lise CEREMADE - UMR C.N.R.S. 7534 Universite Paris 9 - Dauphine Place du Marechal de Lattre de Tassigny 75775 Paris Cedex 16 - France email: summa@ceremade:dauphine:fr; rosa:summa@wanadoo:fr 3
I - INTRODUCTION
The IFREMER (French sea research center) oce asked for automatic production of shing activity descriptions from the time tables of all economic units (about 2000 every year) belonging to the six harbors of North Brittany in France. The project is then to follow along many years the evolution of the discovered activities : do some of them disappear, increase or decrease, do new shing tactics appear ... ?
II - MGS APPROACH SOLVES FIRST PROBLEM 2.1 Problem formalization
According to the experts, shing tactics have been formalized as Symbolic descriptions
[1]. Example : Tactic 1 f Tuna sh 0 8]5 tons ; 8 tons ], 0 2 [4 tons ; 5 tons ]g And f Cockle 0 9] 3 tons ; 5 tons ], 0 1 none g And f Spider crab 0 75 ] 6 tons ; 7 tons ], 0 25 none g \0 8" before \] 5 tons ; 8 tons ]" means that the units which have that type of tactic along the year are such that 80 per cent of them catch from 5 tons to 8 tons of tuna sh, whereas 20 per cent of them catch from 4 tons to 5 tons only. :
:
:
:
:
:
:
2.2 MGS approach
For each year the data table consists of a matrix of tons of sh ; a cell is the total catch of an economic unit ( sh boat owner) for a certain target (prey) during the period. An automatic partition is computed for every year. MGS [5] provides automatic symbolic descriptions for each class of the di erent partitions ; experts validate only some of them as relevant shing tactics on the exhaustive statistic of shing e orts for the concerned period.
III - LINES OF LIFE FOR SYMBOLIC DESCRIPTIONS FROM THREE WAY DATA TABLE 3.1 SODAS description workpackages
SODAS [6] provides tools to describe each tactic because it has a symbolic formalization : 1
SOE displays graphics for each tactic and basic calculations STATS provides histograms and basic statistics on the tactics
These graphics allow a visual comparison of the tactics which are indexed by the year of the date table they come from (by MGS procedure), so that it is possible to see increasing or decreasing of some results, depending on the year which is represented.
3.2 LINES OF LIFE of symbolic descriptions
By computing the number of economic units of date \T + h (h 2 <)" which have some tactic de ned from date \T " data table, a drawing of the evolution of this tactic is available. In the framework of Symbolic Data Analysis, it consists of computing the extension of each symbolic description D on all the data tables to the exclusion of the data table from which MGS has extracted D. De nition : Lines of Life of a Symbolic description consists of the mapping of the frequencies of the above de ned extensions versus the dates.
IV - RESULTS
On three years exhaustive statistics of 6 harbors of North Brittany of France, 38 tactics of shing have been extracted by MGS procedure. 22 of those symbolic descriptions have been validated as Fishing Tactics by the experts of IFREMER Institute. 8 Lines of Life have been drawn to show the evolution of 8 tactics along the three years. Keywords : Clustering, MGS (Marking and Generalization by Symbolic Objects), threeway data table, Symbolic Line of Life.
References [1] DIDAY E., 1995 Probabilistic objects for a symbolic data analysis. DIMACS, Series in Discrete Mathematics and Theorical Computers, vol. 19, (1995). [2] GETTLER-SUMMA M., 1997 Symbolic Marking ; Application on car accident scenarios. Proceedings of Applied Stochastic Models and Data Analysis. (Capri, Italy). [3] GETTLER-SUMMA M., PERINEL E., FERRARIS J., 1994 Automatic aid to symbolic cluster interpretation in New Approaches in Classi cation and Data Analysis. Springer Ed. . [4] M. GETTLER-SUMMA, S. GUEYE, 1998 Image Processing by Symbolic Objects, IFCS 98 (Roma, Italy).
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[5] M. GETTLER-SUMMA, 1998 Approches MGS, Marquage et generalisation symbolique pour de nouvelles aides l'interpretation en Analyse de Donnees. CAHIERS DU CEREMADE No 9830 (Universite Paris-Dauphine, France). [6] SODAS EUROSTAT software project (1997-2000).
Mireille Gettler-Summa Lise CEREMADE - UMR C.N.R.S. 7534 Universite Paris 9 - Dauphine Place du Marechal de Lattre de Tassigny 75775 Paris Cedex 16 - France email: summa@ceremade:dauphine:fr; rosa:summa@wanadoo:fr 3