Comparison of LEM2 and a Dynamic Reduct Classification Algorithm - PowerPoint PPT Presentation

Lower Approximation – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.27/90

Lower Approximation – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.28/90

Lower Approximation – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.29/90

Upper Approximation – Definition Let X and B be as before. Then the upper approxim- ation to X is the set of objects that are possibly in X , given the information in B . skip example Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.30/90

Upper Approximation – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.31/90

Upper Approximation – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.32/90

Reduct We want to find a more compact description of the data, or a reduced set of attributes describing the things we are interested in (for instance the concept of having high Credibility ) Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.33/90

Reduct – Definition A superreduct B is a set of attributes in an information system such that IND S A IND S B . If B is a su- perreduct such that if one of the attributes is removed from B , the number of objects that are indiscernible from each other (are in the IND S B relation with each other) will increase, then B is a reduct , or proper reduct skip example Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.34/90

Reduct – Example 1 Let B Shoesize Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.35/90

Reduct – Example 1 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.36/90

Reduct – Example 1 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.37/90

Reduct – Example 1 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.38/90

Reduct – Example 1 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.39/90

Reduct – Example 1 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.40/90

Reduct – Example 2 Let B Age Shoesize Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.41/90

Reduct – Example 2 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.42/90

Reduct – Example 2 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.43/90

Reduct – Example 2 Occupation Age Shoesize Credibility u 1 thief 35 42 High u 2 doctor 45 44 Medium u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.44/90

Relative Reduct – Definition A relative reduct B A is a minimal set of attrib- U A d utes in a decision system S such that IND S d IND S B skip example Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.45/90

Relative Reduct – Example Let B Shoesize . Remove u 2 from S Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.46/90

Relative Reduct – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.47/90

Relative Reduct – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.48/90

Relative Reduct – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.49/90

Relative Reduct – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.50/90

Relative Reduct – Example Occupation Age Shoesize Credibility u 1 thief 35 42 High u 3 thief 35 41 Low u 4 farmer 23 46 High u 5 thief 53 46 High u 6 doctor 49 44 Low u 7 doctor 49 44 Low Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.51/90

Dynamic Reducts Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.52/90

Dynamic Reducts Reducts that occur in subtables are good (conjecture) Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

Dynamic Reducts Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

Dynamic Reducts Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables and are also reducts of the whole table. Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

Dynamic Reducts Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables and are also reducts of the whole table. The frequency is called stability Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

Filtering techniques Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.54/90

Filtering techniques Replace missing values Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

Filtering techniques Replace missing values Discretization Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

Filtering techniques Replace missing values Discretization MD-heuristic Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

Filtering techniques Replace missing values Discretization MD-heuristic Dynamic reducts Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

Discretization – Example Suppose we have a number of objects with different values on the numerical attribute Age . Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.56/90

Discretization – Example We want to construct a limited number of intervals. Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.57/90

Discretization – MD-heuristics Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

Discretization – MD-heuristics 1. Get the cut that discerns most object-pairs with different decisions from each other. Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

Discretization – MD-heuristics 1. Get the cut that discerns most object-pairs with different decisions from each other. 2. Separate the data w.r.t. that cut Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

Discretization – MD-heuristics 1. Get the cut that discerns most object-pairs with different decisions from each other. 2. Separate the data w.r.t. that cut 3. If the data in each part does not belong to single decision classes, go to 1. Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

Discretization – Dynamic Reducts Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.59/90

Discretization – Dynamic Reducts 1. Convert the original dataset into a new set with binary attributes. See example Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.60/90

Discretization – Dynamic Reducts 1. Convert the original dataset into a new set with binary attributes. See example 2. Divide this set of data into subsets (suitable number of sets of suitable size) Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.61/90

Discretization – Dynamic Reducts 1. Convert the original dataset into a new set with binary attributes. See example 2. Divide this set of data into subsets (suitable number of sets of suitable size) 3. Extract a number of relative reducts from the table obtained in step 1. Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.62/90

Discretization – Dynamic Reducts 4. Of these, choose the one that most frequently appear the tables obtained in step 2. (most stable reduct) Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.63/90

Discretization – Dynamic Reducts 4. Of these, choose the one that most frequently appear the tables obtained in step 2. (most stable reduct) 5. Convert this reduct into a set of cuts on the old table (revert the process in step 1) Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.64/90

Discretization – Dynamic Reducts 4. Of these, choose the one that most frequently appear the tables obtained in step 2. (most stable reduct) 5. Convert this reduct into a set of cuts on the old table (revert the process in step 1) 6. Use these cuts to discretize the table (see example) Continue Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.65/90

Binary table – Example Discretize the data (on a reduced table) w.r.t. age Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.66/90

Binary table – Example Age Credibility u 1 35 High u 2 45 Medium u 3 35 Low u 4 23 High Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.67/90

Binary table – Example Create cutpoints 29 40 on Age between the values of the instances in the set and make new binary attributes Age 29 Age 40 for each of these cutpoints: if Age u x 0 Age x u if Age u x 1 Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.68/90

Binary table – Example Age 29 Age 40 Credibility u 1 1 0 High u 2 1 1 Medium u 3 1 0 Low u 4 0 0 High return Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.69/90

Discretized table – Example Age 29 Age 40 Credibility u 1 1 0 High u 2 1 1 Medium u 3 1 0 Low u 4 0 0 High Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.70/90

Discretized table – Example Age Credibility u 1 29 40 High ∞ u 2 40 Medium u 3 29 40 Low ∞ u 4 29 High return Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.71/90

Model construction Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.72/90