Business Systems Intelligence: 2. Data Preparation

1. Dr. Brian Mac Namee (www.comp.dit.ie/bmacnamee) Business Systems Intelligence:2. Data Preparation

2. Acknowledgments • These notes are based (heavily) on those provided by the authors to accompany “Data Mining: Concepts & Techniques” by Jiawei Han and Micheline Kamber • Some slides are also based on trainer’s kits provided by More information about the book is available at:www-sal.cs.uiuc.edu/~hanj/bk2/ And information on SAS is available at:www.sas.com

3. Data Preprocessing • Today we will look at data preprocessing and in particular: • Descriptive data summarization • What kind of data are we talking about? • Why preprocess data? • Data cleaning • Data integration and transformation • Data reduction • Discretization and concept hierarchy generation • Summary

4. Descriptive Data Summarization • Descriptive data summarization techniques can be used to identify the typical properties of your data • We will take a look at: • Mean, median, mode and midrange • Quartiles, interquartilerange and variance • We will also introduce the notions of a distributive measure, an algebraic measure and a holistic measure • For all of these measures we will assume a set of attribute observations x1, x2, x3,…,xN

5. Measuring The Central Tendency • The central tendency of a data set can be considered a measure of the middle of the data • The most simple, and commonly used is the arithmetic mean • The mean is calculated as: • The arithmetic mean can be upset by noise and outliers

6. Measuring The Central Tendency (cont…) • For skewed data the median can be a better measure than the mean • Given a sorted numerical data set of N distinct values: • If N is odd the median is the middle value • If N is even it is the average of the two middle values • The mode of a data set is the value that occurs most frequently in the set • The mode may correspond to more than one value

7. Measuring The Dispersion Of Data • The degree to which a data set is spread out is known as the dispersion or variance of the data • Typical measure of dispersion invclude: • Range • Interquartile range • Five-number summary • Standard deviation • The range of a set of observations is the difference between the largest and the smallest values

8. Percentiles & Quartiles • The kth percentile of a set of data in numerical order is the value xi having the property that k percent of the observations lie at or below xi • The median is the 50th percentile • The most important percentiles are the median and the quartiles • The first quartile, Q1, is the 25th percentile • The third quartile, Q3, is the 75th percentile • The interquartile range (IQR) is the difference between the third and first quartiles • IQR = Q3 - Q1

9. The Five Number Summary • To describe a set of observations the five number summary is often used • The five number summary consists of: • The minimum • Q1 • The median • Q3 • The maximum • Box plots are used to display the summary

10. Variance & Standard Deviation • The variance of N observations x1, x2, x3,…,xN is given as: • The standard deviation, σ is the square root of the variance

11. What Kind Of Data Are We Talking About? Variables/Features Class/Target Tuples/Records

12. 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

13. 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 processing of data • Collection • Entry • Transmission • Inconsistent data comes from • Different data sources • Functional dependency violation

14. 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 warehouses need consistent integration of quality data “Data extraction, cleaning, and transformation comprises the majority of the work of building a data warehouse” —Bill Inmon

15. 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

16. Forms Of Data Preprocessing

17. Data Cleaning • Data cleaning tasks • Fill in missing values • Identify outliers and smooth out noisy data • Correct inconsistent data • Resolve redundancy caused by data integration “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

18. Data Cleaning Example

19. 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 registering history or changes of the data

20. How To Handle Missing Data? • Ignore the tuple • Usually done when class label is missing • Fill in the missing value manually • Tedious & infeasible? • Fill in the missing value automatically • Use a global constant, e.g. “unknown” • Use the attribute mean • Use the attribute mean for all samples belonging to the same class • Use the most probable value

21. Noisy Data • Noise: Random error or variance in a measured variable • Incorrect attribute values may be due to: • Faulty data collection instruments • Data entry problems • Data transmission problems • Technology limitation • Inconsistency in naming convention

22. 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

23. Simple Discretization Methods: Binning • Equal-depth (frequency) partitioning: • Divides the range into N intervals, each containing approximately same number of samples • Good data scaling • Managing categorical attributes can be tricky • Equal-width (distance) partitioning: • 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.

24. Cluster Analysis

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

26. 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 v imperial

27. Handling Redundancy In Data Integration • Redundant data occur often through 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 correlation analysis • Careful integration of the data from multiple sources may help reduce/avoid redundancies and inconsistencies and improve mining speed and quality

28. Data Transformation • Smoothing: remove noise from data • Aggregation: summarization, data cube construction • Generalization: concept hierarchy climbing • Normalization: scaled to fall within a small, specified range • Min-max normalization • Z-score normalization • Normalization by decimal scaling • Attribute/feature construction • New attributes constructed from the given ones

29. Where j is the smallest integer such that Max(| |)<1 Data Transformation: Normalization • Min-max normalization • Z-score normalization • Normalization by decimal scaling

30. Data Reduction • A data warehouse may store terabytes of data • Complex data analysis/mining may take a very long time to run on the complete data set • Data reduction • Obtain a reduced representation of the data set that is much smaller in volume but yet produces the same (or almost the same) analytical results

31. Data Reduction Strategies • Data reduction strategies include: • Data cube aggregation • Dimensionality reduction—remove unimportant attributes • Data Compression • Numerosity reduction—fit data into models • Discretization and concept hierarchy generation

32. Data Cube Aggregation • The lowest level of a data cube • The aggregated data for an individual entity of interest • E.g. a customer in a phone calling data warehouse • Multiple levels of aggregation in data cubes • Further reduce the size of data to deal with • Reference appropriate levels • Use the smallest representation which is enough to solve the task • Queries regarding aggregated information should be answered using data cube, when possible

33. Data Cube Aggregation (cont…)

34. Dimensionality Reduction • Feature selection (i.e., attribute subset selection): • Select a minimum set of features such that the probability distribution of different classes given the values for those features is as close as possible to the original distribution given the values of all features • Reduce # of patterns in the patterns, easier to understand • How can we do this?

35. Dimensionality Reduction (cont…) • There are 2d possible sub-features of d features • Heuristic methods (due to exponential # of choices): • Step-wise forward selection • Step-wise backward elimination • Combining forward selection and backward elimination • Decision-tree induction

36. Example Of Decision Tree Induction • Initial attribute set: {A1, A2, A3, A4, A5, A6} • => Reduced attribute set: {A1, A4, A6} A4? A1? A6? Class 1 Class 2 Class 1 Class 2

37. Data Compression • String compression • There are extensive theories and well-tuned algorithms • Typically lossless compression is used • Only limited manipulation is possible without expansion • Audio/video compression • Typically lossy compression, with progressive refinement • Sometimes small fragments of signal can be reconstructed without reconstructing the whole

38. Data Compression Types Original Data Compressed Data lossless Original Data Approximated lossy

39. Data Compression Techniques • Data compression techniques include: • Wavelet transformations • Principle components analysis • Numerosity reduction • Parametric methods • Assume the data fits some model, estimate model parameters, store only the parameters, and discard the data (except possible outliers) • Non-parametric methods • Do not assume models • Major families: histograms, clustering, sampling

40. Parametric Methods: Regression • Linear regression • Data are modeled to fit a straight line • Often uses the least-square method to fit the line • Multiple regression • Allows a response variable Y to be modeled as a linear function of multidimensional feature vector

41. Regression Analysis • Linear regression: Y =  +  X • Two parameters,  and  specify the line and are estimated by using the data at hand • Using the least squares criterion to the known values of Y1, Y2, …, X1, X2, …. • Multiple regression: Y = b0 + b1 X1 + b2 X2 • Many nonlinear functions can be transformed into the above

42. Non-Parametric Methods:Histograms • A popular data reduction technique • Divide data into buckets and store average for each bucket • Can be constructed optimally in one dimension using dynamic programming • Related to quantization problems

43. Non-Parametric Methods:Clustering • Partition data set into clusters, and store cluster representation only • Can be very effective if data is clustered but not if data is “smeared” • Can have hierarchical clustering and be stored in multi-dimensional index tree structures • There are many choices of clustering definitions and clustering algorithms • We’ll talk loads more about clustering later on

44. Non-Parametric Methods:Sampling • Allow a mining algorithm to run in complexity that is potentially sub-linear to the size of the data • Choose a representative subset of the data • Simple random sampling may have very poor performance in the presence of skew • Develop adaptive sampling methods • Stratified sampling: • Approximate the percentage of each class (or subpopulation of interest) in the overall database • Used in conjunction with skewed data

45. Raw Data Sampling (cont…) SRSWOR (simple random sample without replacement) SRSWR

46. Sampling (cont…) Cluster/Stratified Sample Raw Data

47. Non-Parametric Methods:Hierarchical Reduction • Use multi-resolution structure with different degrees of reduction • Hierarchical clustering is often performed but tends to define partitions of data sets rather than “clusters” • Parametric methods are usually not amenable to hierarchical representation • Hierarchical aggregation • An index tree hierarchically divides a data set into partitions by value range of some attributes • Each partition can be considered as a bucket • Thus an index tree with aggregates stored at each node is a hierarchical histogram

48. Data Discretization • Three types of attributes: • Nominal — values from an unordered set • Ordinal — values from an ordered set • Continuous — real numbers • Discretization: • Divide the range of a continuous attribute into intervals • Some classification algorithms only accept categorical attributes • Reduce data size by discretization • Prepare for further analysis

49. Discretization & Concept Hierachy • Discretization • Reduce the number of values for a given continuous attribute by dividing the range of the attribute into intervals • Interval labels can then be used to replace actual data values • Concept hierarchies • Reduce the data by collecting and replacing low level concepts (such as numeric values for the attribute age) by higher level concepts (such as young, middle-aged, or senior)

50. Discretization & Concept Hierarchy Generation For Numeric Data • Binning (see sections before) • Histogram analysis (see sections before) • Clustering analysis (see sections before) • Entropy-based discretization • We’ll talk about this when we look at decision trees • Segmentation by natural partitioning