1. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques1 Data Preprocessing — Chapter 2 —

2. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques2 Data Preprocessing Step in KDD Process Relevant Data Data Preprocessing Data Mining Evaluation/InterpretationPattern Knowledge Databases

3. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Introduction to Data Mining3 Main Steps of a KDD Process (Fully) Domain knowledge Acquisition Learning relevant prior knowledge and goals of application Data collection and preprocessing (may take 60% of effort!) Data selection and integration : creating a target data set Data cleaning, data transformation, and data reduction Data mining Choosing functions of data mining association, classification, clustering, regression, summarization. Choosing the mining algorithm(s) Searching for patterns of interest Pattern evaluation and knowledge presentation visualization, transformation, removing redundant patterns, etc. Use of discovered knowledge

4. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques4 Chapter 2: Data Preprocessing Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation Summary

5. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques5 Why Data Preprocessing? Data in the real world is dirty incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data noisy: containing errors or outliers inconsistent: containing discrepancies in codes or names No quality data, no quality mining results! Quality decisions must be based on quality data Data quality is important to data mining

6. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques6 Multi-Dimensional Measure of Data Quality A well-accepted multidimensional view: ( 人、事、時、地、物 ) Accuracy Completeness Consistency Timeliness Believability Value added Interpretability Accessibility

7. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques7 Major Tasks in Data Preprocessing Data cleaning Process missing values and noisy data Data integration Integration of multiple files, tables, databases, or DBMSs’ DBs Data transformation Normalization and aggregation Data reduction Reducing data representation in volume but produces the same or similar analytical results (especially for Cloud computing) Data discretization Part of data reduction. Reducing the number of attribute values (especially for numerical attributes)

8. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques8 Forms of data preprocessing

9. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques9 Chapter 2: Data Preprocessing Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation Summary

10. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques10 Data Cleaning Data cleaning tasks mainly include Fill in missing values Identify outliers and smooth out noisy data Correct inconsistent data

11. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques11 Missing Data Data is not always available e.g., many tuples may 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 e.g., data may not be considered important at the time of entry not registered history or changes of the data Missing data may need to be inferred.

12. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques12 How to Handle Missing Data? Ignore the tuple: usually done when class label is missing (assuming the task is 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 value! Use the attribute mean 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, decision tree or linear regression

13. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques13 Noisy Data Noise: random error or variance in a measured variable Incorrect attribute values may due to faulty data collection instruments data entry problems data transmission problems technology limitation inconsistency in naming convention Other data problems which requires data cleaning duplicate records incomplete data inconsistent data

14. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques14 How to Handle Noisy Data? Binning method: first sort data and partition data 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 Example

15. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques15 Simple Discretization Methods: Binning Equal-width (distance) partitioning: The most straightforward method It divides the range of the attribute value into N intervals of equal size. If A and B are the lowest and highest values of the attribute, the width of intervals will be: W = (B -A)/N. Outliers may dominate the presentation Skewed data cannot be handled well. Equal-depth (frequency) partitioning: It divides the range into N intervals. Each interval contains approximately a same number of samples Good data scaling Managing categorical attributes can be tricky.

16. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques16 Data Smoothing for Equal-Depth Binning 1). Sorted data for price : 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 2). Partition into 3 (equi-depth) bins: - Bin 1: - Bin 2: - Bin 3: 3). Smoothing * Smoothing by bin means: - Bin 1: - Bin 2: - Bin 3: * Smoothing by bin boundaries: - Bin 1: - Bin 2: - Bin 3: 9, 9, 9, 9 23, 23, 23, 23 29, 29, 29, 29 4, 4, 4, 15 21, 21, 25, 25 26, 26, 26, 34 4, 8, 9, 15 21, 21, 24, 25 26, 28, 29, 34

17. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques17 Detect Outliers by Cluster Analysis 1. Cluster analysis  2. Outlier detection X Y Z Points X, Y, and Z are outliers

18. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques18 Data Smoothing by Regression x y y = x + 1 X1 Y1 1. Regression 2. Detect outlier 3. Outlier smoothing Y1’ (X1,Y1)  (X1,Y1’) According to y = x + 1

19. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques19 Chapter 2: Data Preprocessing Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation Summary

20. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques20 Data Integration Data integration of various source combines data from multiple sources into a coherent store (multiple files, databases, or DBMSs’ DBs) Schema (table) 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 may be different possible reasons: different representations, different scales, e.g., metric vs. British units

21. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques21 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, total price Redundant data may be able to be detected by correlational analysis Careful integration of the data from multiple sources may help reduce/avoid data redundancies and inconsistencies and improve mining speed and quality

22. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques22 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

23. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques23 Data Transformation: Normalization min-max normalization for Attribute A z-score normalization for Attribute A normalization by decimal scaling for Attribute A Where j is the smallest integer such that Max(| |)<1

24. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques24 Chapter 2: Data Preprocessing Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation Summary

25. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques25 Data Reduction Strategies Data warehouse/Cloud may store terabytes of data Complex data analysis/mining may take a very long time to run on a complete data set Data reduction Obtains a reduced representation of the data set that is much smaller in volume but yet produces the same (or almost the same) analytical results Data reduction strategies Dimensionality reduction Numerosity reduction Discretization and concept hierarchy generation

26. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques26 Dimensionality Reduction Feature selection (i.e., attribute subset selection): Select a minimum set of features from the original features such that the class probability distribution using the minimal features is as close as possible to the distribution using the original features Heuristic methods (due to exponential # of choices): decision-tree induction step-wise forward selection step-wise backward elimination combining forward selection and backward elimination principal component analysis

27. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques27 Example of Decision Tree Induction Initial attribute set: {A1, A2, A3, A4, A5, A6} A4 ? A1? A6? Class 1 Class 2 Class 1 Class 2 Reduced attribute set: {A1, A4, A6}

28. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques28 Other Heuristic Feature Selection Methods There are 2 d possible subsets of d features Several heuristic feature selection methods: Best/Worst single feature : choose by significance tests (under the feature independence assumption) Best step-wise feature selection: The best single-feature is picked first Then pick the next best feature given the first feature,... Step-wise feature elimination: Repeatedly eliminate the worst feature Best combined feature selection and elimination: Optimal branch and bound: Use feature elimination and backtracking

29. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques29 Given N data vectors from k dimensions, find c (c <= k) k-dimensional orthogonal vectors that can be best used to represent the data Transformation of data representation: O(N × k) → O(N × c) Each original data vector is represented by a linear combination of the c principal component vectors Each original vector is transformed into a c-dimensional vector The original data set is reduced to a new data set consisting of N data vectors on c principal components Space complexity of representation : O(N × k) → O(N × c) Works for numeric data only Used when the number of dimensions is large Principal Component Analysis Example

30. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques30 X Y α β Principal Component Analysis ( Data Representation Transformation : X Y  αβ ) X, Y : old coordinates α, β : new coordinates a b (a, b) a’ b’ (a’, b’) (a, b) → (a’, b’) (c, d) c d (c’, d’) d’ c’ (c, d) → (c’, d’)

31. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques31 Numerosity Reduction (Especially for Big Data Analysis) Parametric methods Assume the data fits a certain model, estimate model parameters, store only the parameters, and discard the data (except possible outliers) Example: In linear regression, if a set of points (x 1, y 1 ), (x 2, y 2 ) …, (x n, y n ) is approximated by a line Y=  +  X, then  and  represent the given points Non-parametric methods Do not assume models Major families: histograms, clustering, sampling Example

32. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques32 Numerosity Reduction by Regression Given n sets (classes) of data : S 1, S 2, …S i, …, S n Linear regression: The i-th set of data is modeled to fit a straight line : Y = a i X + b i Therefore, S i is represented by The n data sets are translated into,,…, Multiple regression: Y=a 10 +a 11 x 1 +a 12 x 2 +…+a 1n x n =A 1 X Where, A 1 =, X= The i-th set of data is modeled to fit a straight line Therefore, S i is represented by A i The n data sets are translated into n data vectors : A 1, A 2,…, A n

33. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques33 Numerosity Reduction by Histograms ( Non-parametric methods ) A popular data reduction technique Divide data into buckets and store average (sum) & count for each bucket Related to quantization problems.

34. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques34 Numerosity Reduction by Clustering (Non-parametric methods) Partition data set into clusters, and store cluster representations only Can be very effective if data is clustered, but not if data is “smeared” There are many choices of clustering definitions and clustering algorithms, further detailed in Chapter 7 Example

35. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Introduction to Data Mining 35 A B C Use A, B, C to represent the data set Represent Data by Cluster Centers (For Numerosity Reduction ) A, B, C are cluster representations of data

36. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques36 Sampling (Non-parametric methods) Allow a mining algorithm to run in complexity that depends on the sample size, not the size of the data Choose a representative subset of the data Note that simple random sampling may have very poor performance in the presence of skew Adaptive sampling method Stratified sampling ( 分層抽樣 ): Approximate the percentage of each class (or subpopulation) in the overall data Used in conjunction with skewed data 2 methods Example

37. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques37 Simple Random Sampling SRSWOR (simple random sampling without replacement) Raw Data SRSWR After a sample is drawn, it is placed back so that it may be drawn again

38. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques38 Example of Stratified Sampling Raw Data Stratified Samples

39. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques39 Chapter 2: Data Preprocessing Why preprocess the data? Data cleaning Data integration and transformation Data reduction Discretization and concept hierarchy generation Summary

40. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques40 Discretization (Reduce the Number of Attribute Values) Consider 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 Each interval is denoted by a new categorical value Reduce the total number of attribute values Some classification algorithms only accept categorical attributes. Prepare for further analysis

41. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques41 Discretization and Concept Hierarchy Reduce the number of different values for a given attribute Discretization (for continuous attribute ) reduce the number of different values for a given continuous attribute by dividing the data range of the attribute into intervals. Then, interval labels is used to replace actual data values. Concept hierarchies (for nominal attribute ) reduce the number of different values for a given nominal attribute by replacing low level concepts (such as low-fat milk, 2% milk, coke, orange juice) by higher level concepts (such as milk, drink).

42. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques42 Discretization and Concept Hierarchy Generation for Numeric Data Binning (see sections before) Histogram analysis (see sections before) Clustering analysis (see sections before) Entropy-based discretization Segmentation by natural partitioning

43. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques43 Entropy-Based Discretization Given a set of samples S, if S is partitioned into two intervals S 1 and S 2 using boundary T for a continuous attribute A, the entropy after partitioning is The boundary that minimizes the entropy function over all possible boundaries is selected as a binary discretization. The process is recursively applied to the obtained partitions until some stopping criterion is met, e.g., Experiments show that it may reduce data size and improve classification accuracy

44. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques44 Segmentation by natural partitioning 3-4-5 rule can be used to segment numeric data into relatively uniform, “natural” intervals. * If an interval covers 3, 6, 7 or 9 distinct values at the most significant decimal digit, partition the range into 3 equi-width intervals * If it covers 2, 4, or 8 distinct values at the most significant digit, partition the range into 4 intervals * If it covers 1, 5, or 10 distinct values at the most significant digit, partition the range into 5 intervals

45. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques45 Example of 3-4-5 rule (Generation of Concept Hierarchy for Profits) (-$400 -$5,000) (-$400 - 0) (-$400 - -$300) (-$300 - -$200) (-$200 - -$100) (-$100 - 0) (0 - $1,000) (0 - $200) ($200 - $400) ($400 - $600) ($600 - $800) ($800 - $1,000) ($2,000 - $5, 000) ($2,000 - $3,000) ($3,000 - $4,000) ($4,000 - $5,000) ($1,000 - $2, 000) ($1,000 - $1,200) ($1,200 - $1,400) ($1,400 - $1,600) ($1,600 - $1,800) ($1,800 - $2,000) msd = 1,000Low = -$1,000High = $2,000 Step 2: Step 4: Step 1: -$351-$159profit $1,838 $4,700 Min Low (i.e, 5%-tile) High (i.e, 95%- tile) Max count (-$1,000 - $2,000) (-$1,000 - 0) (0 -$ 1,000) Step 3: ($1,000 - $2,000) Generate concept hierarchy according to Low and High Adjust left/right boundaries according to Min and Max Step 3 Step 4

46. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques46 Automatic Generation of Concept Hierarchy Alternative Methods Specification of a partial ordering of attributes explicitly at the schema level by users or experts, e.g. day->month->quarter->year Specification of a portion of a hierarchy by explicit data grouping, e.g, day->month, quarter->year, … Specification of a set of attributes, but not of their partial ordering, in the hierarchy. The system can then try to automatically generate the concept hierarchy

47. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques47 Specification of a set of attributes Concept hierarchy can be automatically generated based on the number of distinct values per attribute in the given attribute set. The attribute with the most distinct values is placed at the lowest level of the hierarchy. country province_or_ state city street 15 distinct values 65 distinct values 3567 distinct values 674,339 distinct values

48. 2015年11月6日星期五 2015年11月6日星期五 2015年11月6日星期五 Data Mining: Concepts and Techniques48 Summary Data preparation is a big issue for both warehousing and mining Data preparation includes Data cleaning, data integration, data transformation Data reduction and feature selection Discretization A lot a methods have been developed but still an active area of research