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Learning rules from incomplete training examples by rough sets

Learning rules from incomplete training examples by rough sets. Tzung-Pei Hong, Li-Huei Tseng, Shyue-Liang Wang Expert Systems with Applications 22(2002) 285-293 2006. 5. 17(Wed). Introduction. deal with the problem of producing a set of certain and possible rules from incomplete data sets

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Learning rules from incomplete training examples by rough sets

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  1. Learning rules from incomplete training examples by rough sets Tzung-Pei Hong, Li-Huei Tseng, Shyue-Liang Wang Expert Systems with Applications 22(2002) 285-293 2006. 5. 17(Wed)

  2. Introduction • deal with the problem of producing a set of certain and possible rules from incomplete data sets • propose a new learning approach based on rough sets • derive rules from incomplete data sets • estimate the missing values in the learning process • Unknown values are first assumed to be any possible values and are gradually redefined according to the incomplete lower & upper approximations • The examples and the approximations interact on each other to derive certain and possible rules and to estimate appropriate unknown values.

  3. Review of the rough set theory

  4. class set : BP possible values : {Low(L), Normal(N), High(H)} • Example 1. • indiscernibility relation and belong to the same equivalence class for SP • equivalence partition for singleton attributes • lower approximation of X • upper approximation of X

  5. Definitions • incomplete equivalence classes • each object is represented as a tuple (obj, symbol) • symbol : certain(c) or uncertain(u) • If an object has a certain value for attribute , then is put in the equivalence class for ; otherwise, is put in each equivalence class of attribute • above definition(for single attributes) can easily be extended to attribute subsets • The set of incomplete equivalence classes for subset B is referred to as B-elementary set

  6. for SP e.g. • Example 3. • the incomplete elementary set of attribute SP • the incomplete elementary set of attribute DP

  7. represents the incomplete equivalence classes in which exists

  8. Example 4. • assume • incomplete lower approximation for attribute SP on X • incomplete upper approximation for attribute SP on X

  9. A rough set based approach to simultaneously estimate missing values and derive rules • proposed learning algorithm

  10. An example • Step 1. partition • Step 2. • the incomplete elementary set of attribute SP • the incomplete elementary set of attribute DP

  11. Step 3. q =1 • Step 4. • incomplete lower approximation • Step 5. • each uncertain object is checked for change to certain objects. e.g. in • the incomplete elementary set of attribute SP

  12. Step 6. q = q+1 = 2, and Steps 4-6 are repeated • incomplete elementary set of attributes {SP,DP} • incomplete lower approximations of {SP,DP}

  13. incomplete elementary set of attributes {SP,DP} • incomplete elementary set of attributes DP

  14. Conclusion and future work • The proposed approach is different from others in that it can derive rules and estimate the missing values at the same time. • The incomplete lower and upper approximations was defined • The interaction between data and approximations helps derive certain and possible rules from incomplete data sets and estimate appropriate unknown values

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