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Reducing the Response Time for Data Warehouse Queries Using Rough Set Theory

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Reducing the Response Time for Data Warehouse Queries Using Rough Set Theory

By

Mahmoud Mohamed Al-Bouraie

Yasser Fouad Mahmoud Hassan

Wesam Fathy Jasser

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

- 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).

- It dependents on some concepts like star schema structure as shown in the figure it contents of facttable surrounded by dimension tables. The relationships between them is 1: N.

- 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

- 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.

- 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.

- 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.

- 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.

- 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.

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}

- After deleting all consistent objects we have:

T

T’

The instances containing b0 will not be considered.

U/{a,b}

1. Selecting {a}

R = {a,b}

u5

u3

u6

u4

u7

U/{e}

u3,u5,u6

u4

u7

Also, we select {c} and {d}. Then finally we found:

Result: Subset of attributes＝ {b, d}

- 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 .

- 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.