Data preprocessing

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Data preprocessing techniques

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Data preprocessing

  1. 1. A Brief Presentation on Data Mining Jason Rodrigues Data Preprocessing
  2. 2. • Introduction • Why data proprocessing? • Data Cleaning • Data Integration and Transformation • Data Reduction • Discretization and concept Heirarchy generation • Takeaways Agenda
  3. 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  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 warehouse needs consistent integration of quality data A multi-dimensional measure of data quality  A well-accepted multi-dimensional view:  accuracy, completeness, consistency, timeliness, believability, value added, interpretability, accessibility Broad categories  intrinsic, contextual, representational, and accessibility
  4. 4. Data Preprocessing Major Tasks of 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, files, or notes Data trasformation  Normalization (scaling to a specific range)  Aggregation Data reduction  Obtains reduced representation in volume but produces the same or similar analytical results  Data discretization: with particular importance, especially for numerical data  Data aggregation, dimensionality reduction, data compression, generalization
  5. 5. Data Preprocessing Major Tasks of Data Preprocessing Data Cleaning Data Integration Databases Data Warehouse Task-relevant Data Selection Data Mining Pattern Evaluation
  6. 6. Data Cleaning Tasks of Data Cleaning  Fill in missing values  Identify outliers and smooth noisy data  Correct inconsistent data
  7. 7. Data Cleaning Manage Missing Data  Ignore the tuple: usually done when class label is missing (assuming the task is classification—not effective in certain cases)  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 to fill in the missing value  Use the attribute mean for all samples of 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 regression, Bayesian formula, decision tree
  8. 8. Data Cleaning Manage 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 Semi Automated  Computer and Manual Intervention Regression  Use regression functions
  9. 9. Data Cleaning Cluster Analysis
  10. 10. Data Cleaning Regression Analysis x y y = x + 1 X1 Y1 Y1’ •Linear regression (best line to fit two variables) •Multiple linear regression (more than two variables, fit to a multidimensional surface
  11. 11. Data Cleaning Inconsistant Data  Manual correction using external references  Semi-automatic using various tools − To detect violation of known functional dependencies and data constraints − To correct redundant data
  12. 12. Data integration and transformation Tasks of Data Integration and transformation  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, different currency
  13. 13. Manage Data Integration Data integration and transformation  Redundant data occur often when integrating multiple DBs − 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 • Careful integration can help reduce/avoid redundancies and inconsistencies and improve mining speed and quality BA BA n BBAA r σσ)1( ))(( , − −−Σ =
  14. 14. Manage Data Transformation Data integration and transformation  Smoothing: remove noise from data (binning, clustering, regression)  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
  15. 15. Manage Data Reduction Data reduction Data reduction: reduced representation, while still retaining critical information  Data cube aggregation  Dimensionality reduction  Data compression  Numerosity reduction  Discretization and concept hierarchy generation
  16. 16. Data Cube Aggregation Data reduction  Multiple levels of aggregation in data cubes − Further reduce the size of data to deal with  Reference appropriate levels Use the smallest representation capable to solve the task
  17. 17. Data Compression Data reduction  String compression − There are extensive theories and well-tuned algorithms − Typically lossless − But only limited manipulation is possible without expansion  Audio/video, image 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 ``
  18. 18. Decision Tree Data reduction
  19. 19. Similarities and Dissimilarities Proximity  Proximity is used to refer to Similarity or Dissimilarity, since proximity between the object is a function of proximity between the corresponding attributes of two objects.  Similarity: Numeric measure of the degree to which the two objects are alike.  Dissimilarity: Numeric measure of the degree to which the two objects are different.
  20. 20. Dissimilarities between Data Objects?  Similarity − Numerical measure of how alike two data objects are. − Is higher when objects are more alike. − Often falls in the range [0,1]  Dissimilarity − Numerical measure of how different are two data objects − Lower when objects are more alike − Minimum dissimilarity is often 0 − Upper limit varies  Proximity refers to a similarity or dissimilarity
  21. 21. Euclidean Distance  Euclidean Distance Where n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q.  Standardization is necessary, if scales differ. ∑ = −= n k kk qpdist 1 2 )(
  22. 22. Euclidean Distance  Euclidean Distance ∑ = −= n k kk qpdist 1 2 )( 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 0 5 4 3 Column 2
  23. 23. Minkowski Distance  r = 1. City block (Manhattan, taxicab, L1 norm) distance. − A common example of this is the Hamming distance, which is just the number of bits that are different between two binary vectors  r = 2. Euclidean distance  r → ∞. “supremum” (Lmax norm, L∞ norm) distance. − This is the maximum difference between any component of the vectors − Example: L_infinity of (1, 0, 2) and (6, 0, 3) = ?? − Do not confuse r with n, i.e., all these distances are defined for all numbers of dimensions.
  24. 24. Minkowski Distance point x y p1 0 2 p2 2 0 p3 3 1 p4 5 1 L1 p1 p2 p3 p4 p1 0 4 4 6 p2 4 0 2 4 p3 4 2 0 2 p4 6 4 2 0 L2 p1 p2 p3 p4 p1 0 2.828 3.162 5.099 p2 2.828 0 1.414 3.162 p3 3.162 1.414 0 2 p4 5.099 3.162 2 0 L∞ p1 p2 p3 p4 p1 0 2 3 5 p2 2 0 1 3 p3 3 1 0 2 p4 5 3 2 0
  25. 25. Euclidean Distance Properties • Distances, such as the Euclidean distance, have some well known properties. 1. d(x, y) ≥ 0 for all x and y and d(x, y) = 0 only if x = y. (Positive definiteness) 2. d(x, y) = d(y, x) for all x and q. (Symmetry) 3. d(x, y) ≤ d(x, y) + d(y, z) for all points x, y, and z. (Triangle Inequality) where d(x, y) is the distance (dissimilarity) between points (data objects), x and y. • A distance that satisfies these properties is a metric, and a space is called a metric space
  26. 26. Non Metric Dissimilarities – Set Differences  non-metric measures are often robust (resistant to outliers, errors in objects, etc.) − the symmetry and mainly the triangular inequality are often violated  cannot be directly used with MAMs a b a > b + c c a b a ≠ b
  27. 27. Non Metric Dissimilarities – Time  various k-median distances − measure distance between the two (k-th) most similar portions in objects  COSIMIR − back-propagation network with single output neuron serving as a distance, allows training  Dynamic Time Warping distance − sequence alignment technique − minimizes the sum of distances between sequence elements  fractional Lp distances − generalization of Minkowski distances (p<1) − more robust to extreme differences in coordinates
  28. 28. Jaccard Coeffificient  Recall: Jaccard coefficient is a commonly used measure of overlap of two sets A and B jaccard(A,B) = |A ∩ B| / |A ∪ B| jaccard(A,A) = 1 jaccard(A,B) = 0 if A ∩ B = 0  A and B don’t have to be the same size.  JC always assigns a number between 0 and 1.
  29. 29. Takeaways Why Data Preprocessing? Data Cleaning Data Integration and Transformation Data Reduction Discretization and concept Heirarchy generation

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