Importance of Data Preprocessing in Data Warehousing

1. Data Warehousing and Data Mining — Chapter 3 —— Data Preprocessing — 2013/2014 Fall

2. Chapter 3: Data Preprocessing • Why preprocess the data? • Data cleaning • Data integration and transformation • Data reduction • Discretization and concept hierarchy generation • Time-dependent data • Summary

3. Why Data Preprocessing? • Data in the real world is dirty • incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data • e.g., occupation=“” • noisy: containing errors or outliers • e.g., Salary=“-10” • inconsistent: containing discrepancies in codes or names • e.g., Age=“42” Birthday=“03/07/1997” • e.g., Was rating “1,2,3”, now rating “A, B, C” • e.g., discrepancy between duplicate records

4. Why Is Data Dirty? • Incomplete data comes from • n/a data value when collected • different consideration between the time when the data was collected and when it is analyzed. • human/hardware/software problems • Noisy data comes from the process of data • collection • entry • transmission • Inconsistent data comes from • different data sources • functional dependency violation

5. Why Is Data Preprocessing Important? • No quality data, no quality mining results! • Quality decisions must be based on quality data • e.g., duplicate or missing data may cause incorrect or even misleading statistics. • Data warehouse needs consistent integration of quality data • Data extraction, cleaning, and transformation comprises the majority of the work of building a data warehouse

6. Multi-Dimensional Measure of Data Quality • A well-accepted multidimensional view: • Accuracy • Completeness • Consistency • Timeliness • Believability • Value added • Interpretability • Accessibility • Broad categories: • intrinsic, contextual, representational, and accessibility.

7. Major Tasks in Data Preprocessing • Data cleaning • Fill in missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies • Data integration • Integration of multiple databases, data cubes, or files • Data transformation • Normalization and aggregation • Data reduction • Obtains reduced representation in volume but produces the same or similar analytical results • Data discretization • Part of data reduction but with particular importance, especially for numerical data

8. Forms of data preprocessing

9. Chapter 3: Data Preprocessing • Why preprocess the data? • Data cleaning • Data integration and transformation • Data reduction • Discretization and concept hierarchy generation • Time-dependent data • Summary

10. Data Cleaning • Importance • “Data cleaning is one of the three biggest problems in data warehousing”—Ralph Kimball • “Data cleaning is the number one problem in data warehousing”—DCI survey • Data cleaning tasks • Fill in missing values • Identify outliers and smooth out noisy data • Correct inconsistent data • Resolve redundancy caused by data integration

11. Missing Data • Data is not always available • E.g., many tuples have no recorded value for several attributes, such as customer income in sales data • Missing data may be due to • equipment malfunction • inconsistent with other recorded data and thus deleted • data not entered due to misunderstanding • certain data may not be considered important at the time of entry • not register history or changes of the data • Missing data may need to be inferred.

12. How to Handle Missing Data? • Ignore the tuple: usually done when class label is missing (assuming the tasks in classification—not effective when the percentage of missing values per attribute varies considerably. • Fill in the missing value manually: tedious + infeasible? • Use a global constant to fill in the missing value: e.g., “unknown”, a new class?! • Use the attribute mean,median or mode to fill in the missing value • Use the attribute mean for all samples belonging to the same class to fill in the missing value: smarter • Use the most probable value to fill in the missing value: inference-based such as Bayesian formula or decision tree

13. Most Probable Value • Use the most probable value to fill in the missing value: inference-based such as Bayesian formula or decision tree • develop a submodel to predict the category or numerical value of the missing case • income = f(education,sex, age,...) • A neural network model • K-NN model • Decision tree • Regression • ...

14. An Extreme Case • Suppose all values of an attribute is missing • This attribute may be considered as the unknown label in unsupervised learning • Assigning an object into a cluster can be thought of filling the missing values of an attribute

15. Time Series and Spacial Data • Filling missing values in time series and spatial data needs a different tratement Stock index x x data exisits o missing x x o x o x x o x Time in days

16. Noisy Data • Noise: random error or variance in a measured variable • Incorrect attribute values may due to • faulty data collection instruments • data entry problems:human or computer error • data transmission problems • technology limitation • inconsistency in naming convention • duplicate records • Some noice is inavitable and due to variables or factors that can not be measured

17. How to Handle Noisy Data? • Binning method: • first sort data and partition into (equi-depth) bins • then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc. • Clustering • detect and remove outliers • Combined computer and human inspection • detect suspicious values and check by human • Regression • smooth by fitting the data into regression functions

18. Simple Discretization Methods: Binning • Equal-width (distance) partitioning: • It divides the range into N intervals of equal size: uniform grid • if A and B are the lowest and highest values of the attribute, the width of intervals will be: W = (B-A)/N. • The most straightforward • But outliers may dominate presentation • Skewed data is not handled well. • Equal-depth (frequency) partitioning: • It divides the range into N intervals, each containing approximately same number of samples • Managing categorical attributes can be tricky.

19. Binning Methods for Data Smoothing * Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 * Partition into (equi-depth) bins: - Bin 1: 4, 8, 9, 15 - Bin 2: 21, 21, 24, 25 - Bin 3: 26, 28, 29, 34 * Smoothing by bin means: - Bin 1: 9, 9, 9, 9 - Bin 2: 23, 23, 23, 23 - Bin 3: 29, 29, 29, 29 * Smoothing by bin boundaries: - Bin 1: 4, 4, 4, 15 - Bin 2: 21, 21, 25, 25 - Bin 3: 26, 26, 26, 34

20. Cluster Analysis

21. Regression y Y1 y = x + 1 Y1’ x X1

22. Example use of regression to determine outliers • Problem: predict the yearly spending of AE customers from their income. • Y: yearly spending in YTL • X: average montly income in YTL

23. Data set X: income, Y: spending First data is probabliy an outlier But examining only spending data that is Distribution of Y 200 spending of the first Customer can not be identified as an outlier • X Y • 50200 • 10050 • 20070 • 25080 • 30085 • 400120 • 500130 • 700150 • 750150 • 800180 1000200

24. Regression y Y1:200 y = 0.15x + 20 Y1’ x X1:50 X10:1000 Examine residuals Y1-Y1* is high But Y10-Y10* is low So data point 1 is an outlier inccome

25. Notes • Some methods are used for both smoothing and data reduction or discretization • binning • used in decision tress to reduce number of categories • concept hierarchies • Example price a numerical variable • in to concepts as expensive, moderately prised, expensive

26. Inconsistent Data • Inconsistent data may due to • faulty data collection instruments • data entry problems:human or computer error • data transmission problems • Chang in scale over time • 1,2,3 to A, B. C • inconsistency in naming convention • Data integration: • Different units used for the same variable • TL or dollar • Value added tax ıncluded ın one source not in other • duplicate records

27. Mining Data Dispersion Characteristics • Motivation • To better understand the data: central tendency, variation and spread • Data dispersion characteristics • median, max, min, quartiles, outliers, variance, etc. • Numerical dimensions correspond to sorted intervals • Data dispersion: analyzed with multiple granularities of precision • Boxplot or quantile analysis on sorted intervals • Dispersion analysis on computed measures • Folding measures into numerical dimensions • Boxplot or quantile analysis on the transformed cube

28. Measuring the Central Tendency • Mean (algebraic measure): • Weighted arithmetic mean: • Trimmed mean: chopping extreme values • Median: A holistic measure • Middle value if odd number of values, or average of the middle two values otherwise • Estimated by interpolation (for grouped data) • Mode • Value that occurs most frequently in the data • Unimodal, bimodal, trimodal • Empirical formula:

29. Symmetric vs. Skewed Data • Median, mean and mode of symmetric, positively and negatively skewed data

30. Measuring the Dispersion of Data • Quartiles, outliers and boxplots • Quartiles: Q1 (25th percentile), Q3 (75th percentile) • Inter-quartile range: IQR = Q3 –Q1 • Five number summary: min, Q1, M,Q3, max • Boxplot: ends of the box are the quartiles, median is marked, whiskers, and plot outlier individually • Outlier: usually, a value higher/lower than 1.5 x IQR • Variance and standard deviation • Variance s2: (algebraic, scalable computation) • Standard deviation s is the square root of variance s2

31. Properties of Normal Distribution Curve • The normal (distribution) curve • From μ–σ to μ+σ: contains about 68% of the measurements (μ: mean, σ: standard deviation) • From μ–2σ to μ+2σ: contains about 95% of it • From μ–3σ to μ+3σ: contains about 99.7% of it

32. Boxplot Analysis • Five-number summary of a distribution: Minimum, Q1, M, Q3, Maximum • Boxplot • Data is represented with a box • The ends of the box are at the first and third quartiles, i.e., the height of the box is IRQ • The median is marked by a line within the box • Whiskers: two lines outside the box extend to Minimum and Maximum

33. Positively and Negatively Correlated Data

34. Not Correlated Data

35. Graphic Displays of Basic Statistical Descriptions • Histogram: (shown before) • Boxplot: (covered before) • Quantile plot: each value xiis paired with fi indicating that approximately 100 fi % of data are xi • Quantile-quantile (q-q) plot: graphs the quantiles of one univariant distribution against the corresponding quantiles of another • Scatter plot: each pair of values is a pair of coordinates and plotted as points in the plane • Loess (local regression) curve: add a smooth curve to a scatter plot to provide better perception of the pattern of dependence

36. Quantile Plot Displays all of the data (allowing the user to assess both the overall behavior and unusual occurrences) Plots quantile information For a data xidata sorted in increasing order, fiindicates that approximately 100 fi% of the data are below or equal to the value xi Data Mining: Concepts and Techniques 36

37. Quantile-Quantile (Q-Q) Plot Graphs the quantiles of one univariate distribution against the corresponding quantiles of another View: Is there is a shift in going from one distribution to another? Example shows unit price of items sold at Branch 1 vs. Branch 2 for each quantile. Unit prices of items sold at Branch 1 tend to be lower than those at Branch 2. 37

38. Chapter 3: Data Preprocessing • Why preprocess the data? • Data cleaning • Data integration and transformation • Data reduction • Discretization and concept hierarchy generation • Time-dependent data • Summary

39. Data Integration • Data integration: • combines data from multiple sources into a coherent store • Schema integration • integrate metadata from different sources • Entity identification problem: identify real world entities from multiple data sources, e.g., A.cust-id  B.cust-# • 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 • price may include value added tax in one source and not include in the other • Name are entered by different convensıons: • name lastname or lastname name or ...

40. Handling Redundant Data in Data Integration • Redundant data occur often when integration of multiple databases • The same attribute may have different names in different databases • One attribute may be a “derived” attribute in another table, e.g., annual revenue • Redundant data may be able to be detected by correlational analysis • rx,y= ni=1(xi-mean_x)(yi-mean_y)/[(n-1)xy] • where x,y are standard deviation of X and Y • as r1 positive correlation: x y or x y, one is redundant • r  0, X and X are independent • r  -1 negative correlation: x y or x y one is redundant

41. Positively and Negatively Correlated Data

42. Not Correlated Data

43. Exercise • Construct a data set or a functional relationship of two variables X and Y where there is a perfect relation between X and Y: • knowing value of X, Y corresponding to that X can be predicted with no error • but correlation coefficient between X and Y is • ZERO

44. Handling Redundant Data in Data Integration • how to detect redundancy for categorical variables? • Find a measure of association for categorical variables • Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality

45. Correlation Analysis (Categorical 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 2 value are those whose actual count is very different from the expected count

46. Chi-Square Test • Under the null hypothesis that attribute valuea are independent or not correlated •  2 statistics is approximately distributed as chi-square distribution with (kA-1)*(kB-1) degree of freedom • KA and KB are number of distinct values of attribute A and B • Given a confidence level  • Reject null hypothesis of no correlation if •  2> 2(df,)

47. Chi-Square Calculation: An Example •  2 (chi-square) calculation (numbers in parenthesis are expected counts calculated based on the data distribution in the two categories) • 2((2-1)(2-1),0.05)=5.99<507.93 • It shows that like_science_fiction and play_chess are correlated in the group

48. Calculating expected frequencies • Expected values are computed under the independence assumption • E(i,j)=pi*pj*N • pi probability of observing variable A at state i • pj probability of observing variable B at state j • N total number of observations • E.g. E(like_scfic,play_chess) = (450/1500)(300/1500)*1500=90

49. Exercises • What is the limitation of chi-square measure of correlation between categorical variables • Suggest a better way of measuring correlation between categorical variables • Suggest a way of measuring association between a categorical and a numerical variable

50. Correlation and Causation • 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