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Data Preprocessing

Data Preprocessing. CSC 576: Data Science. Today. Data Preprocessing Handling Missing Values Handling Outliers Covariance and Correlation Normalization Binning, Discretization Sampling Aggregation. Data Preprocessing. Data Exploration phase results in finding data quality issues

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Data Preprocessing

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  1. Data Preprocessing CSC 576: Data Science

  2. Today • Data Preprocessing • Handling Missing Values • Handling Outliers • Covariance and Correlation • Normalization • Binning, Discretization • Sampling • Aggregation

  3. Data Preprocessing • Data Exploration phase results in finding data quality issues • Outliers, missing values, … • Data Preprocessing usually delayed until the Modeling phase • Different predictive models require different preprocessing

  4. Handling Missing Data • Motivation: We will frequently encounter missing values, especially in big data. • Lots of fields, lots of observations • Question: how to handle the missing data?

  5. How much data is missing? • Suppose… • Dataset of 30 variables • 5% of data is missing • Missing values are spread evenly throughout data • … • 80% of records would have at least one missing value • Bad solution: Deleting records with any missing data

  6. Handling Missing Values (Approaches) • Drop any features that have missing values. • Might lead to massive loss of data • Drop any instance/record that has a missing value. • Might lead to bias • Derive a missing indicator feature from features with missing values. • Replace with a binary feature, whether the value was missing or not. • Ignore missing values • If data mining method is robust • Replace missing value with some constant (Specified by analyst) • Replace missing value with mean, median, or mode • Replace missing value with value generated at random from the observed variable distribution • Replace missing value with imputed values, based on other characteristics of the record

  7. Handling Missing Values Be careful using imputation on features missing in excess of 30% of their values. • Imputation:replaces missing feature values with a plausible estimated value • Common approach: replace missing values for a feature with a measure of the central tendency of that feature • Mean, median (continuous) • Mode (categorical)

  8. Reclassifying Categorical Variables • Sometimes a categoricalvariable will contain too many factors to be easily analyzable • Example: state field could contain 50 different values • Solution #1: reclassify state into its region: {NorthEast, NorthWest, Central, West, …} • Solution #2: reclassify state by its economic level: {WealthyStates, MiddleStates, PoorestStates} • Up to the analyst to appropriately reclassify

  9. Handling Outliers: Clamp Transformation • Clamps all values above an upper threshold and below a lower threshold to remove outliers • Upper and lower thresholds can be set manually based on domain knowledge • Or: • Lower = 1st quartile -1.5 x inter-quartile range • Upper = 3rd quartile + 1.5 x inter-quartile range Lower and upper are the specific thresholds.

  10. Case Study • What handling strategies would you recommend for the data quality issues found in the motor Insurance fraud dataset (previous slide)? • Num Soft Tissue –imputation (using median) on the 2% of missing values • Claim Amount– clamp transformation on outliers (manually set) • Amount Received – clamp transformation on outliers (manually set)

  11. Covariance and Correlation • Visualpreliminary exploration, comparing two variables, using scatter plots • Quantitativepreliminary exploration using covariance and correlation measures • Covariance:

  12. Covariance • values fall into the range [−∞, ∞] : • negative values indicate a negative relationship • positive values indicate a positive relationship • values near zero indicate that there is little or no relationship between the features

  13. Example • Calculating covariance between the HEIGHT feature and the WEIGHTand AGEfeatures from the basketball players dataset.

  14. Correlation • normalized form of covariance • Values ranges between −1 and +1 • Correlation:

  15. Correlation • values fall into the range [−1, 1] • values close to −1 indicate a very strong negative correlation (or covariance) • values close to 1 indicate a very strong positive correlation • values around 0 indicate no correlation • Features that have no correlation are said to be independent.

  16. Example • Calculating correlation between the HEIGHT feature and the WEIGHT and AGE features from the basketball players dataset.

  17. Covariance and Correlation Matrix • There are usually multiple continuous features in a dataset to explore. • Covariance and Correlation Matrix for the display of every combination of features

  18. Example

  19. Including Correlations in a Scatter Plot Matrix

  20. Correlation does not Imply Linear Relationship • Anscombe’s Quartet: • Each has a correlation value of 0.816 between x and y • Correlation is a good measure of the relationship between two continuous features, • but it is not by any means perfect. • Still need visual analysis.

  21. Correlation does not Imply Causation • Causation can be mistakenly assumed: • Mistaking the order of a causal relationship • Example: Spinning windmills cause wind. • Example: Playing basketball causes people to be tall. • Inferring causation between two features while ignoring a third (hidden) feature. • From Nature, 1999. • “causal relationship between young children sleeping with a night-light turned on and these children developing short-sightedness in later life” • Short-sighted parents, because of poor night vision, tend to favor the use of night-lights; short-sighted parents are more likely to have short-sighted children.

  22. Spurious Correlations • http://tylervigen.com/discover

  23. Data Preparation • Changing the way data is represented just to make it more compatible with certain machine learning algorithms: • Normalization • Binning • Sampling

  24. Normalization Typical ranges used for normalizing feature values are [0,1] and [-1,1]. • change a continuousfeature to fall within a specified range while maintaining the relative differences between the values for the feature • Example: • Customer ages in a dataset: [16, 96] • Customer salaries: [10000, 100000] • Range Normalization:convert a feature value into the range [low , high] Sensitive to the presence of outliers in a dataset.

  25. Standardization Majority of feature values will be in a range of [-1, 1]. • measures how many standard deviations a feature value is from the mean for that feature • mean = 0, standard deviation = 1 • “Standard Scores” • Standardization assumes the feature values are normally distributed. • If not, standardization may introduce some distortions.

  26. Example

  27. Binning • converting a continuousfeature into a categoricalfeature • define a series of ranges (called bins) for the continuous feature that correspond to the levels of the new categorical feature • Approaches: • equal-width binning • equal-frequency binning

  28. Choosing the # of Bins • Need to “manually” decide the number of bins: • Choosing a low number may lose a lot of information • Choosing a very high number might result in a very few instances in each bin or empty bins

  29. Equal-Width Binning • Splits the range of the feature values into b bins each of size • Usually works well • Some near-empty bins when data follows a normal distribution

  30. More accurately models the heavily populated areas of the continuous feature, compared to equal-width. • Slightly less intuitive because bins are of varying sizes. Equal-Frequency Binning • Algorithm: • Sorts the continuous feature values into ascending order • Then places an equal number of instances into each bin, starting with bin 1 • Number of instances placed in each bin =

  31. Data Preparation: Sampling • Sometimes we have too much data! • instead samplea smaller percentage from the larger dataset • Care required when sampling: • Try to ensure that the resulting datasets is still representative of the original data and that no unintended biasis introduced during this process. • If not, any modeling on the sample will not be relevant to the overall dataset.

  32. Sampling: Top Sampling • Select the top s% of instances from a dataset to create a sample. • Top sampling runs a serious risk of introducing bias • the sample will be affected by any ordering of the original dataset • Usually avoided

  33. Sampling: Random Sampling • randomly selects a proportion of s% of the instances from a large dataset to create a smaller set. • good choice in most cases as the random nature of the selection of instances should avoid introducing bias

  34. Other Sampling Forms • Stratified Sampling • Ensures that the relative frequencies of the levels of a specific feature are maintained • Usage: if there are one or more levels of a categorical feature that only have a very small proportion of instances (chance they will omitted by random sampling) • Under-Sampling or Over-Sampling • Sample containing different relative frequencies • Usage: if we want to have a particular categorical feature be represented equally in the sample, even if that was not the distribution in the original dataset

  35. Aggregation • Combining two or more attributes into a single attribute • Or – combining two or more objects into a single object • Purpose: • Data reduction: reduce # of attributes/objects • Change of scale: high-level vs. low-level • Motivations: • Less memory and processing time

  36. Aggregation – Data Reduction

  37. Aggregation – Change in Variability • Less variability at “higher-level” view

  38. When to Remove Variables • Variables that will not help the analysis should be removed • Unary variables: take on a single value • Example: gender variable for students at an all-girls school • Variables that are nearly unary • Example: gender of football athletes at elementary school • 99.95% of the players are male • Some data mining algorithms may treat the variable as unary • Not enough data to investigate the female players anyway…

  39. When to Remove Variables • Think carefully before removing variables because of: • 90% of the values are missing • Strong correlation between two variables

  40. When to Remove Variables • 90% of the values are missing • Are the values that are present representative or not? • If the present values are representative, then either (1) remove the variable or (2) impute the values. • If the present values are non-representative, their presence adds value. • Scenario:donation_dollarsfield in a self-reported survey • Assumption: those who donate a lot are more inclined to report their donation • Could also binarize the variable: donation_flag

  41. When to Remove Variables • Strong correlation between two variables • Inclusion of correlated variables may “double-count” a particular aspect of the analysis, depending on the machine learning technique used. • Example: precipitation and people on a beach • Strategy #1: remove one of the two correlated variables • Strategy #2: use PCA to transform the variables (beyond scope of course)

  42. Id Fields • Id fields have a different value for each record • Won’t be helpful in predictive analysis • If they are, the relationship is usually spurious • Recommended Approach: • Don’t include Id field in modeling • But keep it in the dataset to differentiate between records

  43. References • Fundamentals of Machine Learning for Predictive Data Analytics, Kelleher et al., First Edition

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