Preprocessing - Data Integration Tuple Duplication
- 1. Datamining & Warehousing Dr.VIDHYA B ASSISTANT PROFESSOR & HEAD Department of Computer Technology Sri Ramakrishna College of Arts and Science Coimbatore - 641 006 Tamil Nadu, India 1 Unit 2 - Preprocessing
- 2. 2 2 Chapter 3: Data Preprocessing Data Preprocessing: An Overview Data Quality Major Tasks in Data Preprocessing Data Cleaning Data Integration Data Reduction Data Transformation and Data Discretization Summary
- 3. 3 3 Data Integration Data integration: Combines data from multiple sources into a coherent store Integration helps to reduce and avoid redundancies and inconsistencies Schema integration: e.g., A.cust-id B.cust-# Integrate metadata from different sources
- 4. 4 4 Data Integration Entity identification problem: Data analysis task will involve data integration, which combines data from multiple sources into a coherent data store, as in data warehousing. These sources may include multiple databases, data cubes, or flat files Issues in data integration: Schema integration and object matching Identify real world entities from multiple data sources, e.g., Bill Clinton = William Clinton Detecting and resolving data value conflicts For the same real world entity, attribute values from different sources are different Possible reasons: different representations, different scales, e.g., metric vs. British units
- 5. 5 5 Handling Redundancy in Data Integration Redundant data occur often when integration of multiple databases Object identification: The same attribute or object may have different names in different databases Derivable data: One attribute may be a “derived” attribute in another table, e.g., annual revenue Redundant attributes may be able to be detected by correlation analysis and covariance analysis Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality
- 6. 6 Correlation Analysis (Nominal Data) Χ2 (chi-square) test The larger the Χ2 value, the more likely the variables are related The cells that contribute the most to the Χ2 value are those whose actual count is very different from the expected count Correlation does not imply causality # of hospitals and # of car-theft in a city are correlated Both are causally linked to the third variable: population Expected Expected Observed 2 2 ) (
- 7. 7 Chi-Square Calculation: An Example Χ2 (chi-square) calculation (numbers in parenthesis are expected counts calculated based on the data distribution in the two categories) It shows that like_science_fiction and play_chess are correlated in the group 93 . 507 840 ) 840 1000 ( 360 ) 360 200 ( 210 ) 210 50 ( 90 ) 90 250 ( 2 2 2 2 2 Play chess Not play chess Sum (row) Like science fiction 250(90) 200(360) 450 Not like science fiction 50(210) 1000(840) 1050 Sum(col.) 300 1200 1500
- 8. 8 Correlation Analysis (Numeric Data) Correlation coefficient (also called Pearson’s product moment coefficient) where n is the number of tuples, and are the respective means of A and B, σA and σB are the respective standard deviation of A and B, and Σ(aibi) is the sum of the AB cross-product. If rA,B > 0, A and B are positively correlated (A’s values increase as B’s). The higher, the stronger correlation. rA,B = 0: independent; rAB < 0: negatively correlated B A n i i i B A n i i i B A n B A n b a n B b A a r ) 1 ( ) ( ) 1 ( ) )( ( 1 1 , A B
- 9. 9 Visually Evaluating Correlation Scatter plots showing the similarity from –1 to 1.
- 10. 10 Correlation (viewed as linear relationship) Correlation measures the linear relationship between objects To compute correlation, we standardize data objects, A and B, and then take their dot product ) ( / )) ( ( ' A std A mean a a k k ) ( / )) ( ( ' B std B mean b b k k ' ' ) , ( B A B A n correlatio
- 11. 11 Covariance (Numeric Data) Covariance is similar to correlation used for assessing the change in two attributes. where n is the number of tuples, and are the respective mean or expected values of A and B, σA and σB are the respective standard deviation of A and B. Positive covariance: If CovA,B > 0, then A and B both tend to be larger than their expected values. Negative covariance: If CovA,B < 0 then if A is larger than its expected value, B is likely to be smaller than its expected value. Independence: CovA,B = 0 but the converse is not true: Some pairs of random variables may have a covariance of 0 but are not independent. Only under some additional assumptions (e.g., the data follow multivariate normal distributions) does a covariance of 0 imply independence A B Correlation coefficient:
- 12. Co-Variance: An Example It can be simplified in computation as Suppose two stocks A and B have the following values in one week: (2, 5), (3, 8), (5, 10), (4, 11), (6, 14). Question: If the stocks are affected by the same industry trends, will their prices rise or fall together? E(A) = (2 + 3 + 5 + 4 + 6)/ 5 = 20/5 = 4 E(B) = (5 + 8 + 10 + 11 + 14) /5 = 48/5 = 9.6 Cov(A,B) = (2×5+3×8+5×10+4×11+6×14)/5 − 4 × 9.6 = 4 Thus, A and B rise together since Cov(A, B) > 0.
- 13. 13 Tuple Duplication Apart from detecting redundancies between attributes, detecting duplicates at tuple level is equally important. Denormalized tables is another source of data redundancy. Inconsistencies occur due to inaccurate data entry
- 14. 14 Data Value Conflict Detection and Resolution Data integration involves detection and resolution of data value conflicts. For instance, a weight attribute may be stored in metric units in one system and British imperial units in another. For a hotel chain, the price of rooms in different cities may involve not only different currencies but also different services (e.g., free breakfast) and taxes. When exchanging information between schools, for example, each school may have its own curriculum and grading scheme.
- 15. 15 Data Value Conflict Detection and Resolution Attributes may also differ on the abstraction level, where an attribute in one system is recorded at, say, a lower abstraction level than the “same” attribute in another.