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The Application of Data Mining Methods In Monitoring of Ecosystems Jiri BILA and Jakub JURA Jiri.Bila@fs.cvut.cz Jakub.Jura@fs.cvut.cz Department of Instrumentation and Control Engineering, Faculty of Mechanical Engineering, CTU in Prague, Technická 4, 166 07 Prague 6

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Monitoring of Ecosystems 11 Measuring Stations 13 variables Sampling period 6 minutes

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Database system for monitoring

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Data Mining Knowledge discovery in data bases is “the nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data ” Fayyad (1996).

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Used Data Mining Methods Conceptual Lattice Rough Sets

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Conceptual Lattice Data Mining Context C = (O, I, R) –O is a set of an objects x –I is a set of an items (attributes) y –R is a binary relation R O I

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Conceptual Lattice Conceptual Lattice L Derived from Data Mining Context C X = x O y Y, x R y Y = y I x X, x R y –X is the largest set of an objects X O –Y is the largest set of an items Y I

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Conceptual Lattice Hasse diagram T he Hasse diagram is constructed by use the partial arrangement "<„. –Edge from the H1 to H2 exist if H1 < H2 and none of element of H3 fulfil condition H1 < H3 < H2. –H1 is an antecedent of element H2 (H2 is the descendant of the element H1). –A pair of X, Y represents a node in Hasse diagram.

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Transformace datab8ze Hasse diagram T he Hasse diagram is constructed by use the partial arrangement "<„. –Edge from the H1 to H2 exist if H1 < H2 and none of element of H3 fulfil condition H1 < H3 < H2. –H1 is an antecedent of element H2 (H2 is the descendant of the element H1). –A pair of X, Y represents a node in Hasse diagram.

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Conceptual Lattice - Example C = ( A 0, A 1, A 2, A 3, A 4 , 3, 4, 7, 8, 9 , R) Where: –C … context of data mining –A 0, A 1, A 2, A 3, A 4 … Monitoring Classes –3, 4, 7, 8, 9 … Situations –R … relation which is represented in the table M G

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Conceptual Lattice MGMG 34789 A0A0 11111 A1A1 11 A2A2 1111 A3A3 111 A4A4 1111 Table M G which represents relation R. Situations Monitoring Classes

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Conceptual Lattice Hass diagram

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Conceptual Lattice Guarantee of the rule’s reliability and validity. Support –supp(Ai, S) = ( (s S Ict(s, Ai))/ ( (S )) –Supp (Ai Aj, S) = supp(Ai Aj, S ) Confidence –Conf (Ai Aj, S) = Supp (Ai Aj, S) / supp(Ai)

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Rule No. iRule r i Supp(r i )Conf (r i ) 1A1 A2A1 A2 0.20.5 2A 1 A 3 0.20.5 3A1 A4A1 A4 0.41 4A2 A3A2 A3 0.5 5A3 A4A3 A4 0.40.66 6A1 A2 A4A1 A2 A4 0.21 7A2 A4 A4A2 A4 A4 0.33 8A2 A3 A4A2 A3 A4 0.20.5 9A2 A4 A3A2 A4 A3 0.20.33 10A1 A3 A4A1 A3 A4 0.21 11A3 A4 A1A3 A4 A1 0.20.5

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Rough Sets Relation of indiscernibility x1, x2 U, (x1 RE(A) x2 )) ⇔ (g(x1, ai) = g(x2, ai)) Where : –U … universe of elements. –A … set of attributes –V ai … sets of values –g: U x A → V

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Rough Sets Which of these elements of universe U and with what certainty approach subset of X ⊂ U, in that we are interested ? Lower Approximation Upper Approximation Border set

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Rough Sets Lower Approximation The Lower Approximation ( positive area PosiRE(X) ) is a set of objects which certain belong to a subset. PosiRE(X) = ∪ { Y Ⅰ (Y ∈ (U/RE)) AND (Y ⊆ X)

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Rough Sets Upper Approximation The set of elements from the U, which may (possibly) belongs to X. PossRE(X) = ∪ { Y Ⅰ (Y ∈ U/RE) AND (Y ∩ X ≠ ∅) }

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Rough Sets Boundary region Difference between the upper and lower approximation X. BoundRE(X) = PossRE(X) - PosiRE(X)

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Rough Sets Rough Set Rough set is a subset X of universe U and this subset is defined using the upper and lower approximation (PossRE(X), PosiRE (X)) and for which: BoundRE(X) ∅

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Rough Sets Rough accuracy of aproximation. RE (X) = card (Posi RE (X)) / card (PossRE(X))

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Conclusion The paper proposed application of two data mining methods. Fragments of a monitoring system database have been used for the data support. The paper emphasises that the use of the original database content is not direct and it is necessary to transform it into forms utilisable by the selected data mining methods. The success of data mining process then strongly depends also on the definition of the monitoring classes and the “operation" situations (formulated by experts).

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©Ian Sommerville 2006Software Engineering, 7th edition. Chapter 14 Slide 1 Object-oriented Design.

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