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Data Integration Process

 Data mining often requires data integration, the merging of data from multiple data source.

Entity Identification Problem

When matching attributes from one database to another during integration, special attention must be paid to the structure of the data. This is to ensure that any attribute functional dependencies and referential constraints in the source system match those in the target system.

Redundancy and Correlation Analysis

Some redundancies can be detected by correlation analysis.

For nominal data, we use the X2 (chi-square) test. For numeric attributes, the correlation coefficient and covariance can be used.

Chi-Square Correlation Test (Pearson Statistic Test)

where 

oij is the observed frequency (actual count)

eij is the expected frequency

where

n is the number of data tuples

If there is no correlation between A & B, then they are independent. The cells that contribute the most to the chi-square value are those for which the actual count is very different from that expected.

Correlation Coefficient for Numeric data (Pearson’s product moment coefficient)

where

n - number of tuples

ai & bi respective values of A & B in tuple i

A & B - mean value of A & B

oA & oB - standard deviation of A & B

If rA,B is greater than 0, then A & B are positively correlated. Higher the value, the stronger the correlation.

If the value is equal to zero, then A and B are independent and no correlation.

If the value is less than zero, then A & B are negatively correlated.

Covariance of Numeric data

The mean values of A and B, respectively, are also known as the expected values on A and B, that is,

The covariance between A and B is defined as
If we compare rA,B (correlation coefficient) with covariance,
For two attributes A and B that tend to change together, if A is larger than the expected value of A, then B is likely to be larger than the expected value of B. Therefore, the covariance between A and B is positive. 
On the other hand, if one of the attributes tends to be above its expected value when the other attribute is below its expected value, then the covariance of A and B is negative.
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