Reducing the Response Time for Data Warehouse Queries Using Rough Set Theory By Mahmoud Mohamed Al-Bouraie Yasser Fouad Mahmoud Hassan Wesam Fathy Jasser

Outline Aim Pre-grouping Transformation Hierarchical pre-grouping Attribute Selection A Heuristic Algorithm for Attribute Selection Worked Example Applications Conclusion

Aim To reach to the optimization case. This case is happened when the response time for processing a query become small as possible using –Pre-grouping transformation and –The size of any database become small as possible (using rough set theory).

Pre-grouping Transformation (1) It dependents on some concepts like star schema structure as shown in the figure it contents of fact table surrounded by dimension tables. The relationships between them is 1: N.

Pre-grouping Transformation (2) Another concept that that this transformation dependents on is hierarchical clustering of data. It is based on the idea that the hierarchy of one dimension are encoded into hierarchical surrogates used in the fact table. There is a compact representation of the hierarchy path of a dimension member making it possible to use hierarchy on the fact table without requiring residual joins. The figure shows an example

Hierarchical pre-grouping We assume that the DBMS has information about hierarchical relationships of the dimension attributes. We group on the highest hierarchy level to reduces the number of resulting groups. The groups of the pre-grouping operation are joined with the dimension tables, in order to get the values for the grouping attributes.

Attribute Selection Depending on rough set theory, a database always contains a lot of attributes that are redundant. To eliminate these redundant attributes we use attribute selection that used to find an optimal subset of attributes in a database according to some criterion, so that a classifier with the highest possible accuracy can be induced by learning algorithm using information about data available only from the subset of attributes.

A Heuristic Algorithm for Attribute Selection Let R be a set of the selected attributes, P be the set of unselected condition attributes, U be the set of all objects, X be the set of contradictory objects, Va denotes the attribute a values and EXPECT be the threshold of accuracy. In the initial state, R = CORE(C), k = 0.

Attribute Selection using RSH (1) Step 1. If k >= EXPECT, finish, otherwise calculate the dependency degree, k, Step 2. For each p in P, calculate where max_size denotes the cardinality of the maximal subset.

Attribute Selection using RSH (2) Step 3. Choose the best attribute p with the largest and let Step 4. Remove all consistent instances u in from X. Step 5. Go back to Step 1.

Worked Example of Attribute Selection Condition Attributes: a: Va = {1, 2} b: Vb = {0, 1, 2} c: Vc = {0, 1, 2} d: Vd = {0, 1} Decision Attribute: e: Ve = {0, 1, 2}

R={b} The instances containing b0 will not be considered. TT’ After deleting all consistent objects we have:

1. Selecting {a} R = {a,b} u3,u5,u6 u4 u7 U/{e} u3 u4 u7 U/{a,b} u5 u6

Result: Subset of attributes ＝ {b, d} Also, we select {c} and {d}. Then finally we found:

Application and Result We built a simple database depending on Heart diseases dataset using Excel file. The attributes information and their types will be as following: Attribute Information: 1) age 2) sex 3) chest pain type (4 values) 4) resting blood pressure 5) serum cholesterol in mg/dl 6) fasting blood sugar > 120 mg/dl 7) resting electrocardiograph results (values 0, 1, and 2) 8) maximum heart rate achieved 9) exercise induced angina 10) old peak = ST depression induced by exercise relative to rest 11) the slope of the peak exercise ST segment 12) number of major vessels (0-3) colored by fluoroscopy 13) thal: 3 = normal; 6 = fixed defect; 7 = reversable defect Attributes types Real: 1,4,5,8,10,12 Ordered: 11 Binary: 2,6,9 Nominal: 7,3,13 Using Rosetta software which is used for analyze the data; Then the database reduced. After that we generate the rules on the best reduct. Finally we filtered the rules using Quality filtering loop. The result for our experiment like this in Table.Table

Conclusion The star query: the most common type of query in data warehouse, One of the most promising techniques for efficiently evaluating such queries is the use of fact table organizations that store data clustered according to the dimension hierarchies. –A special hierarchical encoding is imposed on star joins are transformed to multidimensional range queries on the underlying multidimensional structures. The conventional star query evaluation plan changes radically and new processing steps are required.