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- 1. 1 Data Preprocessing
- 2. 2 Introduction Real World databases Huge size Noisy, Missing and Inconsistent Data Preprocessing Data Cleaning Data Integration Data Transformation Data Reduction
- 3. 3 Need for Data Preprocessing Incomplete Data Lacking certain attributes of interest May not have been considered important during data entry Equipment Malfunctioning Deleted due to clashes with other data Only aggregate data maybe present
- 4. 4 Need for Data Preprocessing Noisy data Incorrect attribute values Errors or outliers e.g., Salary=“-10” Data collection instruments – faulty Data entry errors Transmission errors – limited buffer size Inconsistent Containing discrepancies in codes or names e.g., Age=“42” Birthdate=“03/07/1997” Different data sources Functional dependency violation (e.g., modify some linked data) Duplicate records also need data cleaning
- 5. 5 Need for Data Preprocessing Quality data 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. 6 Major Tasks in Data Preprocessing Data cleaning Fill in missing values Smooth noisy data Identify or remove outliers Resolve inconsistencies Data integration Integration of multiple databases, data cubes, or files Attributes may have different names Eliminating redundancies Some attributes can be inferred from others
- 7. 7 Major Tasks in Data Preprocessing Data transformation Normalization and aggregation Data reduction Obtains reduced representation in volume but produces the same or similar analytical results Data Aggregation Dimension Reduction Data Compression Numerosity Reduction Generalization Data discretization Part of data reduction but with particular importance, especially for numerical data
- 8. 8 Forms of Data Preprocessing
- 9. 9 Data Cleaning Importance “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
- 10. 10 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 need to be inferred.
- 11. 11 Handling 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
- 12. 12 Handling Missing Data 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
- 13. 13 Noisy Data Noise: random error or variance in a measured variable Binning first sort data and partition into 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)
- 14. 14 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 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
- 15. 15 Binning 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
- 16. 16 Regression x y y = x + 1 X1 Y1 Y1’
- 17. 17 Cluster Analysis
- 18. 18 Human Inspection Combined Computer and Human Inspection Outliers in Handwritten character recognition Surprise value Garbage / Outliers Human identification
- 19. 19 Inconsistent Data Data discrepancy detection Use metadata (e.g., domain, range, dependency) Check Functional dependency relationships Use commercial tools Data scrubbing: use simple domain knowledge 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) Discrepancy detection and transformation
- 20. 20 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 Other Issues Detecting redundancy (tuple level and attribute level) 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
- 21. 21 Handling Redundancy Redundant data occur often during 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 detected by correlation analysis Careful integration - helps to reduce/avoid redundancies and inconsistencies and improve mining speed and quality
- 22. 22 Correlation Analysis 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 If rA,B > 0, A and B are positively correlated (A’s values increase as B’s). The higher the value, the stronger the correlation. rA,B = 0: independent; rA,B < 0: negatively correlated BAn BBAA r BA σσ)1( ))(( , − −− = ∑ A B
- 23. 23 Correlation Analysis Chi-square test χ2 = ∑ i=1 c ∑ j=1 r (oij – eij)2 / eij c – Number of possibilities for attribute 1; r – for attribute 2 eij =Expected Frequency : count(A=ai) x count(B=bj) / N o – Observed Frequency e – Expected Frequency Compare χ2 value with table and decide (r-1) x (c-1) : degrees of freedom
- 24. Chi-square test Male Female Total Fiction 250 (90) 200 (360) 450 Non-fiction 50 (210) 1000 (840) 1050 Total 300 1200 1500 24 χ2 = (250-90)2 /90 + (200-360)2 /360 + (50-210)2 /210 + (1000-840)2 /840 = 507.93 Hypothesis: Gender and preferred reading are independent 507.83 > 10.83 So hypothesis is rejected Conclusion: Gender and preferred_reading are strongly correlated
- 25. Chi-square test Degrees of freedom (df) χ2 value 1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83 2 0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82 3 0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27 4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.28 18.47 5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52 6 1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46 7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32 8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12 9 3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88 10 3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59 P value (Probability) 0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001 Non-significant Significant 25
- 26. 26 Data Transformation 1. Smoothing: remove noise from data – Binning, Clustering, Regression 2. Normalization: scaled to fall within a small, specified range min-max normalization z-score normalization normalization by decimal scaling 1. Attribute/feature construction New attributes constructed from the given ones 1. Aggregation: summarization, data cube construction 2. Generalization: concept hierarchy climbing
- 27. 27 1. Smoothing Binning Equal-width (distance) partitioning Equal-depth (frequency) partitioning Clustering
- 28. 28 1. Smoothing Regression and Log-Linear Models 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 Log-linear model: approximates multidimensional probability distributions
- 29. 29 Linear regression: Y = w X + b Two regression coefficients, w and b, specify the line and are to be 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 Log-linear models: Approximation of joint probabilities Estimate the probability of each point in a multi-dimensional space from a smaller subset of dimensions 1. Smoothing Regression and Log-Linear Models
- 30. 30 2. 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 $73,600 is mapped to Z-score normalization (μ: mean, σ: standard deviation) Ex. Let μ = 54,000, σ = 16,000. Then for 73600 Normalization by decimal scaling 716.00)00.1( 000,12000,98 000,12600,73 =+− − − AAA AA A minnewminnewmaxnew minmax minv v _)__(' +− − − = A Av v σ µ− =' j v v 10 '= Where j is the smallest integer such that Max(|ν’|) < 1 225.1 000,16 000,54600,73 = −
- 31. 31 3. Attribute Construction New attributes are constructed from given attributes To improve accuracy and understanding of structure Area from height and width Product operator and ‘and’
- 32. 32 4. Aggregation Data Cubes Store Multi-dimensional aggregated information Each cell holds an aggregate data value Concept hierarchies – allow analysis at multiple levels Provide fast access to pre-computed summarized data
- 33. 33 A Sample 3D Data Cube Total annual sales of TV in U.S.A.Date Product Country sum sum TV VCR PC 1Qtr 2Qtr 3Qtr 4Qtr U.S.A Canada Mexico sum
- 34. 34 4. Aggregation Data Cube Aggregation The lowest level of abstraction Base Cuboid Highest level of abstraction Apex Cuboid Multiple levels Lattice of Cuboids
- 35. 35 Cube: A Lattice of Cuboids time,item time,item,location time, item, location, supplier all time item location supplier time,location time,supplier item,location item,supplier location,supplier time,item,supplier time,location,supplier item,location,supplier 0-D(apex) cuboid 1-D cuboids 2-D cuboids 3-D cuboids 4-D(base) cuboid
- 36. 36 5. Generalization - Concept hierarchy 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 young, middle-aged, or senior) Detail lost but more meaningful Mining becomes easier Several concept hierarchies can be defined for the same attribute

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