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Preprocessing Step in Data Cleaning - Data Mining

preprocessing data in data mining

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1 Data Mining: Concepts and Techniques (3rd ed.) — Chapter 3 — Jiawei Han, Micheline Kamber, and Jian Pei University of Illinois at Urbana-Champaign & Simon Fraser University ©2011 Han, Kamber & Pei. All rights reserved.
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 Data Quality: Why Preprocess the Data? ■ Measures for data quality: A multidimensional view ■ Accuracy: correct or wrong, accurate or not ■ Completeness: not recorded, unavailable, … ■ Consistency: some modified but some not, dangling, … ■ Timeliness: timely update? ■ Believability: how trustable the data are correct? ■ Interpretability: how easily the data can be understood?
4 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 reduction ■ Dimensionality reduction ■ Numerosity reduction ■ Data compression ■ Data transformation and data discretization ■ Normalization ■ Concept hierarchy generation
5 5 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
6 Data Cleaning ■ Data in the Real World Is Dirty: Lots of potentially incorrect data, e.g., instrument faulty, human or computer error, transmission error ■ incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data ■ e.g., Occupation=“ ” (missing data) ■ noisy: containing noise, errors, or outliers ■ e.g., Salary=“−10” (an error) ■ inconsistent: containing discrepancies in codes or names, e.g., ■ Age=“42”, Birthday=“03/07/2010” ■ Was rating “1, 2, 3”, now rating “A, B, C” ■ discrepancy between duplicate records ■ Intentional (e.g., disguised missing data) ■ Jan. 1 as everyone’s birthday?
7 Incomplete (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
8 How to Handle Missing Data? ■ Ignore the tuple: usually done when class label is missing (when doing classification)—not effective when the % of missing values per attribute varies considerably ■ Fill in the missing value manually: tedious + infeasible? ■ Fill in it automatically with ■ a global constant : e.g., “unknown”, a new class?! ■ the attribute mean ■ the attribute mean for all samples belonging to the same class: smarter ■ the most probable value: inference-based such as Bayesian formula or decision tree
9 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 ■ Other data problems which require data cleaning ■ duplicate records ■ incomplete data ■ inconsistent data
10 How to Handle Noisy Data? ■ Binning ■ first sort data and partition into (equal-frequency) bins ■ then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc. ■ Regression ■ smooth by fitting the data into regression functions ■ Clustering ■ detect and remove outliers ■ Combined computer and human inspection ■ detect suspicious values and check by human (e.g., deal with possible outliers)
11 Data Cleaning as a Process ■ Data discrepancy detection ■ Use metadata (e.g., domain, range, dependency, distribution) ■ Check field overloading ■ Check uniqueness rule, consecutive rule and null rule ■ Use commercial tools ■ Data scrubbing: use simple domain knowledge (e.g., postal code, spell-check) to detect errors and make corrections ■ Data auditing: by analyzing data to discover rules and relationship to detect violators (e.g., correlation and clustering to find outliers) ■ Data migration and integration ■ Data migration tools: allow transformations to be specified ■ ETL (Extraction/Transformation/Loading) tools: allow users to specify transformations through a graphical user interface ■ Integration of the two processes ■ Iterative and interactive (e.g., Potter’s Wheels)
12 12 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
13 13 Data Integration ■ Data integration: ■ Combines data from multiple sources into a coherent store ■ Schema integration: e.g., A.cust-id ≡ B.cust-# ■ Integrate metadata from different sources ■ Entity identification problem: ■ 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
14 14 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
15 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
16 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 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
17 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(ai bi ) 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
18 Visually Evaluating Correlation Scatter plots showing the similarity from –1 to 1.
19 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
20 Covariance (Numeric Data) ■ Covariance is similar to correlation 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 Correlation coefficient:
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.
Example ■ Let's say you want to know if gender has anything to do with political party preference. You poll 440 voters in a simple random sample to find out which political party they prefer. The results of the survey are shown in the table below: ■ To see if gender is linked to political party preference, perform a Chi-Square test * Data Mining: Concepts and Techniques 22
23 23 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
24 Data Reduction Strategies ■ 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 ■ Why data reduction? — A database/data warehouse may store terabytes of data. Complex data analysis may take a very long time to run on the complete data set. ■ Data reduction strategies ■ Dimensionality reduction, e.g., remove unimportant attributes ■ Wavelet transforms ■ Principal Components Analysis (PCA) ■ Feature subset selection, feature creation ■ Numerosity reduction (some simply call it: Data Reduction) ■ Regression and Log-Linear Models ■ Histograms, clustering, sampling ■ Data cube aggregation ■ Data compression
25 Clustering ■ Partition data set into clusters based on similarity, and store cluster representation (e.g., centroid and diameter) 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 ■ Cluster analysis will be studied in depth in Chapter 10
26 Sampling ■ Sampling: obtaining a small sample s to represent the whole data set N ■ Allow a mining algorithm to run in complexity that is potentially sub-linear to the size of the data ■ Key principle: Choose a representative subset of the data ■ Simple random sampling may have very poor performance in the presence of skew ■ Develop adaptive sampling methods, e.g., stratified sampling: ■ Note: Sampling may not reduce database I/Os (page at a time)
27 Types of Sampling ■ Simple random sampling ■ There is an equal probability of selecting any particular item ■ Sampling without replacement ■ Once an object is selected, it is removed from the population ■ Sampling with replacement ■ A selected object is not removed from the population ■ Stratified sampling: ■ Partition the data set, and draw samples from each partition (proportionally, i.e., approximately the same percentage of the data) ■ Used in conjunction with skewed data
28 Sampling: With or without Replacement SRSWOR (simple random sample without replacement) SRSWR Raw Data
29 Sampling: Cluster or Stratified Sampling Raw Data Cluster/Stratified Sample
30 Data Cube Aggregation ■ The lowest level of a data cube (base cuboid) ■ 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
31 Data Reduction 3: Data Compression ■ String compression ■ There are extensive theories and well-tuned algorithms ■ Typically lossless, but 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 ■ Time sequence is not audio ■ Typically short and vary slowly with time ■ Dimensionality and numerosity reduction may also be considered as forms of data compression
32 Data Compression Original Data Compressed Data lossless Original Data Approximated lossy
33 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
34 Data Transformation ■ A function that maps the entire set of values of a given attribute to a new set of replacement values s.t. each old value can be identified with one of the new values ■ Methods ■ Smoothing: Remove noise from data ■ Attribute/feature construction ■ New attributes constructed from the given ones ■ Aggregation: Summarization, data cube construction ■ Normalization: Scaled to fall within a smaller, specified range ■ min-max normalization ■ z-score normalization ■ normalization by decimal scaling ■ Discretization: Concept hierarchy climbing
35 Normalization ■ Min-max normalization: to [new_minA , new_maxA ] ■ Ex. Let income range $12,000 to $98,000 normalized to [0.0, 1.0]. Then $73,000 is mapped to ■ Z-score normalization (μ: mean, σ: standard deviation): ■ Ex. Let μ = 54,000, σ = 16,000. Then ■ Normalization by decimal scaling Where j is the smallest integer such that Max(|ν’|) < 1
36 Discretization ■ Three types of attributes ■ Nominal—values from an unordered set, e.g., color, profession ■ Ordinal—values from an ordered set, e.g., military or academic rank ■ Numeric—real numbers, e.g., integer or real numbers ■ Discretization: Divide the range of a continuous attribute into intervals ■ Interval labels can then be used to replace actual data values ■ Reduce data size by discretization ■ Supervised vs. unsupervised ■ Split (top-down) vs. merge (bottom-up) ■ Discretization can be performed recursively on an attribute ■ Prepare for further analysis, e.g., classification
37 Data Discretization Methods ■ Typical methods: All the methods can be applied recursively ■ Binning ■ Top-down split, unsupervised ■ Histogram analysis ■ Top-down split, unsupervised ■ Clustering analysis (unsupervised, top-down split or bottom-up merge) ■ Decision-tree analysis (supervised, top-down split) ■ Correlation (e.g., χ2 ) analysis (unsupervised, bottom-up merge)
38 Simple Discretization: Binning ■ 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 ■ 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
39 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 equal-frequency (equi-depth) bins: • Smoothing by bin means: • Smoothing by bin boundaries:
40 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 equal-frequency (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
41 Discretization Without Using Class Labels (Binning vs. Clustering) Data Equal interval width (binning) Equal frequency (binning) K-means clustering leads to better results
42 Discretization by Classification & Correlation Analysis ■ Classification (e.g., decision tree analysis) ■ Supervised: Given class labels, e.g., cancerous vs. benign ■ Using entropy to determine split point (discretization point) ■ Top-down, recursive split ■ Details to be covered in Chapter 7 ■ Correlation analysis (e.g., Chi-merge: χ2 -based discretization) ■ Supervised: use class information ■ Bottom-up merge: find the best neighboring intervals (those having similar distributions of classes, i.e., low χ2 values) to merge ■ Merge performed recursively, until a predefined stopping condition
43 Concept Hierarchy Generation ■ Concept hierarchy organizes concepts (i.e., attribute values) hierarchically and is usually associated with each dimension in a data warehouse ■ Concept hierarchies facilitate drilling and rolling in data warehouses to view data in multiple granularity ■ Concept hierarchy formation: Recursively reduce the data by collecting and replacing low level concepts (such as numeric values for age) by higher level concepts (such as youth, adult, or senior) ■ Concept hierarchies can be explicitly specified by domain experts and/or data warehouse designers ■ Concept hierarchy can be automatically formed for both numeric and nominal data. For numeric data, use discretization methods shown.
44 Concept Hierarchy Generation for Nominal Data ■ Specification of a partial/total ordering of attributes explicitly at the schema level by users or experts ■ street < city < state < country ■ Specification of a hierarchy for a set of values by explicit data grouping ■ {Urbana, Champaign, Chicago} < Illinois ■ Specification of only a partial set of attributes ■ E.g., only street < city, not others ■ Automatic generation of hierarchies (or attribute levels) by the analysis of the number of distinct values ■ E.g., for a set of attributes: {street, city, state, country}
45 Automatic Concept Hierarchy Generation ■ Some hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the data set ■ The attribute with the most distinct values is placed at the lowest level of the hierarchy ■ Exceptions, e.g., weekday, month, quarter, year country province_or_ state city street 15 distinct values 365 distinct values 3567 distinct values 674,339 distinct values
46 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
47 Summary ■ Data quality: accuracy, completeness, consistency, timeliness, believability, interpretability ■ Data cleaning: e.g. missing/noisy values, outliers ■ Data integration from multiple sources: ■ Entity identification problem ■ Remove redundancies ■ Detect inconsistencies ■ Data reduction ■ Dimensionality reduction ■ Numerosity reduction ■ Data compression ■ Data transformation and data discretization ■ Normalization ■ Concept hierarchy generation
48 References ■ D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Comm. of ACM, 42:73-78, 1999 ■ A. Bruce, D. Donoho, and H.-Y. Gao. Wavelet analysis. IEEE Spectrum, Oct 1996 ■ T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003 ■ J. Devore and R. Peck. Statistics: The Exploration and Analysis of Data. Duxbury Press, 1997. ■ H. Galhardas, D. Florescu, D. Shasha, E. Simon, and C.-A. Saita. Declarative data cleaning: Language, model, and algorithms. VLDB'01 ■ M. Hua and J. Pei. Cleaning disguised missing data: A heuristic approach. KDD'07 ■ H. V. Jagadish, et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical Committee on Data Engineering, 20(4), Dec. 1997 ■ H. Liu and H. Motoda (eds.). Feature Extraction, Construction, and Selection: A Data Mining Perspective. Kluwer Academic, 1998 ■ J. E. Olson. Data Quality: The Accuracy Dimension. Morgan Kaufmann, 2003 ■ D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999 ■ V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and Transformation, VLDB’2001 ■ T. Redman. Data Quality: The Field Guide. Digital Press (Elsevier), 2001 ■ R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans. Knowledge and Data Engineering, 7:623-640, 1995

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Preprocessing Step in Data Cleaning - Data Mining

  • 1.
    1 Data Mining: Concepts andTechniques (3rd ed.) — Chapter 3 — Jiawei Han, Micheline Kamber, and Jian Pei University of Illinois at Urbana-Champaign & Simon Fraser University ©2011 Han, Kamber & Pei. All rights reserved.
  • 2.
    2 2 Chapter 3: DataPreprocessing ■ 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 Data Quality: WhyPreprocess the Data? ■ Measures for data quality: A multidimensional view ■ Accuracy: correct or wrong, accurate or not ■ Completeness: not recorded, unavailable, … ■ Consistency: some modified but some not, dangling, … ■ Timeliness: timely update? ■ Believability: how trustable the data are correct? ■ Interpretability: how easily the data can be understood?
  • 4.
    4 Major Tasks inData 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 reduction ■ Dimensionality reduction ■ Numerosity reduction ■ Data compression ■ Data transformation and data discretization ■ Normalization ■ Concept hierarchy generation
  • 5.
    5 5 Chapter 3: DataPreprocessing ■ Data Preprocessing: An Overview ■ Data Quality ■ Major Tasks in Data Preprocessing ■ Data Cleaning ■ Data Integration ■ Data Reduction ■ Data Transformation and Data Discretization ■ Summary
  • 6.
    6 Data Cleaning ■ Datain the Real World Is Dirty: Lots of potentially incorrect data, e.g., instrument faulty, human or computer error, transmission error ■ incomplete: lacking attribute values, lacking certain attributes of interest, or containing only aggregate data ■ e.g., Occupation=“ ” (missing data) ■ noisy: containing noise, errors, or outliers ■ e.g., Salary=“−10” (an error) ■ inconsistent: containing discrepancies in codes or names, e.g., ■ Age=“42”, Birthday=“03/07/2010” ■ Was rating “1, 2, 3”, now rating “A, B, C” ■ discrepancy between duplicate records ■ Intentional (e.g., disguised missing data) ■ Jan. 1 as everyone’s birthday?
  • 7.
    7 Incomplete (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
  • 8.
    8 How to HandleMissing Data? ■ Ignore the tuple: usually done when class label is missing (when doing classification)—not effective when the % of missing values per attribute varies considerably ■ Fill in the missing value manually: tedious + infeasible? ■ Fill in it automatically with ■ a global constant : e.g., “unknown”, a new class?! ■ the attribute mean ■ the attribute mean for all samples belonging to the same class: smarter ■ the most probable value: inference-based such as Bayesian formula or decision tree
  • 9.
    9 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 ■ Other data problems which require data cleaning ■ duplicate records ■ incomplete data ■ inconsistent data
  • 10.
    10 How to HandleNoisy Data? ■ Binning ■ first sort data and partition into (equal-frequency) bins ■ then one can smooth by bin means, smooth by bin median, smooth by bin boundaries, etc. ■ Regression ■ smooth by fitting the data into regression functions ■ Clustering ■ detect and remove outliers ■ Combined computer and human inspection ■ detect suspicious values and check by human (e.g., deal with possible outliers)
  • 11.
    11 Data Cleaning asa Process ■ Data discrepancy detection ■ Use metadata (e.g., domain, range, dependency, distribution) ■ Check field overloading ■ Check uniqueness rule, consecutive rule and null rule ■ Use commercial tools ■ Data scrubbing: use simple domain knowledge (e.g., postal code, spell-check) to detect errors and make corrections ■ Data auditing: by analyzing data to discover rules and relationship to detect violators (e.g., correlation and clustering to find outliers) ■ Data migration and integration ■ Data migration tools: allow transformations to be specified ■ ETL (Extraction/Transformation/Loading) tools: allow users to specify transformations through a graphical user interface ■ Integration of the two processes ■ Iterative and interactive (e.g., Potter’s Wheels)
  • 12.
    12 12 Chapter 3: DataPreprocessing ■ Data Preprocessing: An Overview ■ Data Quality ■ Major Tasks in Data Preprocessing ■ Data Cleaning ■ Data Integration ■ Data Reduction ■ Data Transformation and Data Discretization ■ Summary
  • 13.
    13 13 Data Integration ■ Dataintegration: ■ Combines data from multiple sources into a coherent store ■ Schema integration: e.g., A.cust-id ≡ B.cust-# ■ Integrate metadata from different sources ■ Entity identification problem: ■ 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
  • 14.
    14 14 Handling Redundancy inData 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
  • 15.
    15 Correlation Analysis (NominalData) ■ 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
  • 16.
    16 Chi-Square Calculation: AnExample ■ 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 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
  • 17.
    17 Correlation Analysis (NumericData) ■ 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(ai bi ) 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
  • 18.
    18 Visually Evaluating Correlation Scatterplots showing the similarity from –1 to 1.
  • 19.
    19 Correlation (viewed aslinear relationship) ■ Correlation measures the linear relationship between objects ■ To compute correlation, we standardize data objects, A and B, and then take their dot product
  • 20.
    20 Covariance (Numeric Data) ■Covariance is similar to correlation 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 Correlation coefficient:
  • 21.
    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.
  • 22.
    Example ■ Let's sayyou want to know if gender has anything to do with political party preference. You poll 440 voters in a simple random sample to find out which political party they prefer. The results of the survey are shown in the table below: ■ To see if gender is linked to political party preference, perform a Chi-Square test * Data Mining: Concepts and Techniques 22
  • 23.
    23 23 Chapter 3: DataPreprocessing ■ Data Preprocessing: An Overview ■ Data Quality ■ Major Tasks in Data Preprocessing ■ Data Cleaning ■ Data Integration ■ Data Reduction ■ Data Transformation and Data Discretization ■ Summary
  • 24.
    24 Data Reduction Strategies ■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 ■ Why data reduction? — A database/data warehouse may store terabytes of data. Complex data analysis may take a very long time to run on the complete data set. ■ Data reduction strategies ■ Dimensionality reduction, e.g., remove unimportant attributes ■ Wavelet transforms ■ Principal Components Analysis (PCA) ■ Feature subset selection, feature creation ■ Numerosity reduction (some simply call it: Data Reduction) ■ Regression and Log-Linear Models ■ Histograms, clustering, sampling ■ Data cube aggregation ■ Data compression
  • 25.
    25 Clustering ■ Partition dataset into clusters based on similarity, and store cluster representation (e.g., centroid and diameter) 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 ■ Cluster analysis will be studied in depth in Chapter 10
  • 26.
    26 Sampling ■ Sampling: obtaininga small sample s to represent the whole data set N ■ Allow a mining algorithm to run in complexity that is potentially sub-linear to the size of the data ■ Key principle: Choose a representative subset of the data ■ Simple random sampling may have very poor performance in the presence of skew ■ Develop adaptive sampling methods, e.g., stratified sampling: ■ Note: Sampling may not reduce database I/Os (page at a time)
  • 27.
    27 Types of Sampling ■Simple random sampling ■ There is an equal probability of selecting any particular item ■ Sampling without replacement ■ Once an object is selected, it is removed from the population ■ Sampling with replacement ■ A selected object is not removed from the population ■ Stratified sampling: ■ Partition the data set, and draw samples from each partition (proportionally, i.e., approximately the same percentage of the data) ■ Used in conjunction with skewed data
  • 28.
    28 Sampling: With orwithout Replacement SRSWOR (simple random sample without replacement) SRSWR Raw Data
  • 29.
    29 Sampling: Cluster orStratified Sampling Raw Data Cluster/Stratified Sample
  • 30.
    30 Data Cube Aggregation ■The lowest level of a data cube (base cuboid) ■ 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
  • 31.
    31 Data Reduction 3:Data Compression ■ String compression ■ There are extensive theories and well-tuned algorithms ■ Typically lossless, but 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 ■ Time sequence is not audio ■ Typically short and vary slowly with time ■ Dimensionality and numerosity reduction may also be considered as forms of data compression
  • 32.
    32 Data Compression Original DataCompressed Data lossless Original Data Approximated lossy
  • 33.
    33 Chapter 3: DataPreprocessing ■ Data Preprocessing: An Overview ■ Data Quality ■ Major Tasks in Data Preprocessing ■ Data Cleaning ■ Data Integration ■ Data Reduction ■ Data Transformation and Data Discretization ■ Summary
  • 34.
    34 Data Transformation ■ Afunction that maps the entire set of values of a given attribute to a new set of replacement values s.t. each old value can be identified with one of the new values ■ Methods ■ Smoothing: Remove noise from data ■ Attribute/feature construction ■ New attributes constructed from the given ones ■ Aggregation: Summarization, data cube construction ■ Normalization: Scaled to fall within a smaller, specified range ■ min-max normalization ■ z-score normalization ■ normalization by decimal scaling ■ Discretization: Concept hierarchy climbing
  • 35.
    35 Normalization ■ Min-max normalization:to [new_minA , new_maxA ] ■ Ex. Let income range $12,000 to $98,000 normalized to [0.0, 1.0]. Then $73,000 is mapped to ■ Z-score normalization (μ: mean, σ: standard deviation): ■ Ex. Let μ = 54,000, σ = 16,000. Then ■ Normalization by decimal scaling Where j is the smallest integer such that Max(|ν’|) < 1
  • 36.
    36 Discretization ■ Three typesof attributes ■ Nominal—values from an unordered set, e.g., color, profession ■ Ordinal—values from an ordered set, e.g., military or academic rank ■ Numeric—real numbers, e.g., integer or real numbers ■ Discretization: Divide the range of a continuous attribute into intervals ■ Interval labels can then be used to replace actual data values ■ Reduce data size by discretization ■ Supervised vs. unsupervised ■ Split (top-down) vs. merge (bottom-up) ■ Discretization can be performed recursively on an attribute ■ Prepare for further analysis, e.g., classification
  • 37.
    37 Data Discretization Methods ■Typical methods: All the methods can be applied recursively ■ Binning ■ Top-down split, unsupervised ■ Histogram analysis ■ Top-down split, unsupervised ■ Clustering analysis (unsupervised, top-down split or bottom-up merge) ■ Decision-tree analysis (supervised, top-down split) ■ Correlation (e.g., χ2 ) analysis (unsupervised, bottom-up merge)
  • 38.
    38 Simple Discretization: Binning ■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 ■ 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
  • 39.
    39 Binning Methods forData Smoothing ❑ Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 * Partition into equal-frequency (equi-depth) bins: • Smoothing by bin means: • Smoothing by bin boundaries:
  • 40.
    40 Binning Methods forData Smoothing ❑ Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34 * Partition into equal-frequency (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
  • 41.
    41 Discretization Without UsingClass Labels (Binning vs. Clustering) Data Equal interval width (binning) Equal frequency (binning) K-means clustering leads to better results
  • 42.
    42 Discretization by Classification& Correlation Analysis ■ Classification (e.g., decision tree analysis) ■ Supervised: Given class labels, e.g., cancerous vs. benign ■ Using entropy to determine split point (discretization point) ■ Top-down, recursive split ■ Details to be covered in Chapter 7 ■ Correlation analysis (e.g., Chi-merge: χ2 -based discretization) ■ Supervised: use class information ■ Bottom-up merge: find the best neighboring intervals (those having similar distributions of classes, i.e., low χ2 values) to merge ■ Merge performed recursively, until a predefined stopping condition
  • 43.
    43 Concept Hierarchy Generation ■Concept hierarchy organizes concepts (i.e., attribute values) hierarchically and is usually associated with each dimension in a data warehouse ■ Concept hierarchies facilitate drilling and rolling in data warehouses to view data in multiple granularity ■ Concept hierarchy formation: Recursively reduce the data by collecting and replacing low level concepts (such as numeric values for age) by higher level concepts (such as youth, adult, or senior) ■ Concept hierarchies can be explicitly specified by domain experts and/or data warehouse designers ■ Concept hierarchy can be automatically formed for both numeric and nominal data. For numeric data, use discretization methods shown.
  • 44.
    44 Concept Hierarchy Generation forNominal Data ■ Specification of a partial/total ordering of attributes explicitly at the schema level by users or experts ■ street < city < state < country ■ Specification of a hierarchy for a set of values by explicit data grouping ■ {Urbana, Champaign, Chicago} < Illinois ■ Specification of only a partial set of attributes ■ E.g., only street < city, not others ■ Automatic generation of hierarchies (or attribute levels) by the analysis of the number of distinct values ■ E.g., for a set of attributes: {street, city, state, country}
  • 45.
    45 Automatic Concept HierarchyGeneration ■ Some hierarchies can be automatically generated based on the analysis of the number of distinct values per attribute in the data set ■ The attribute with the most distinct values is placed at the lowest level of the hierarchy ■ Exceptions, e.g., weekday, month, quarter, year country province_or_ state city street 15 distinct values 365 distinct values 3567 distinct values 674,339 distinct values
  • 46.
    46 Chapter 3: DataPreprocessing ■ Data Preprocessing: An Overview ■ Data Quality ■ Major Tasks in Data Preprocessing ■ Data Cleaning ■ Data Integration ■ Data Reduction ■ Data Transformation and Data Discretization ■ Summary
  • 47.
    47 Summary ■ Data quality:accuracy, completeness, consistency, timeliness, believability, interpretability ■ Data cleaning: e.g. missing/noisy values, outliers ■ Data integration from multiple sources: ■ Entity identification problem ■ Remove redundancies ■ Detect inconsistencies ■ Data reduction ■ Dimensionality reduction ■ Numerosity reduction ■ Data compression ■ Data transformation and data discretization ■ Normalization ■ Concept hierarchy generation
  • 48.
    48 References ■ D. P.Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments. Comm. of ACM, 42:73-78, 1999 ■ A. Bruce, D. Donoho, and H.-Y. Gao. Wavelet analysis. IEEE Spectrum, Oct 1996 ■ T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003 ■ J. Devore and R. Peck. Statistics: The Exploration and Analysis of Data. Duxbury Press, 1997. ■ H. Galhardas, D. Florescu, D. Shasha, E. Simon, and C.-A. Saita. Declarative data cleaning: Language, model, and algorithms. VLDB'01 ■ M. Hua and J. Pei. Cleaning disguised missing data: A heuristic approach. KDD'07 ■ H. V. Jagadish, et al., Special Issue on Data Reduction Techniques. Bulletin of the Technical Committee on Data Engineering, 20(4), Dec. 1997 ■ H. Liu and H. Motoda (eds.). Feature Extraction, Construction, and Selection: A Data Mining Perspective. Kluwer Academic, 1998 ■ J. E. Olson. Data Quality: The Accuracy Dimension. Morgan Kaufmann, 2003 ■ D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999 ■ V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning and Transformation, VLDB’2001 ■ T. Redman. Data Quality: The Field Guide. Digital Press (Elsevier), 2001 ■ R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE Trans. Knowledge and Data Engineering, 7:623-640, 1995