DATA MINING Desktop Survival Guide by Graham Williams
Desktop Survival Project Home Introduction Getting Started The Business Problem Data Loading Data Exploring Data Interactive Graphics Statistical Tests Models Network Analysis Text Mining Decision Trees Random Forests Boosting Bagging Support Vector Machine Linear Regression Neural Network Naive Bayes Survival Analysis Evaluation and Deployment Transforming Data Deployment Troubleshooting Issues Moving into R R Getting Help Data Graphics in R Understanding Data Preparing Data Issues Evaluating Models Reporting Fraud Analysis Archetype Analysis Algorithms Bayes Classifier K-Nearest Neighbours Linear Models Open Products AlphaMiner Borgelt Data Mining Suite KNime R Rattle Weka Closed Products Clementine Equbits Foresight GhostMiner InductionEngine ODM Enterprise Miner Statistica Data Miner TreeNet Virtual Predict Installing Rattle Projects Bibliography Index Preface Goals Organisation Features Audience Typographical Conventions A Note on Languages Currency Acknowledgements Introduction Data Mining The Business Problem Types of Analysis Data Mining Applications A Framework for Modelling Agile Data Mining R Rattle Why R and Rattle? Data Preparation Number of Algorithms Repeatability Performance Open Source Data Mining Business Case Sample Business Case Pros and Cons Books on R Getting Started Initial Interaction with R Quitting Rattle and R First Contact Loading a Dataset Building a Model Understanding Our Data Evaluating the Model Evaluating the Model Interacting with R Interacting with Rattle Projects Toolbar Menus Interacting with Plots Keyboard Navigation Summary Command Summary The Business Problem Solar Panel Efficiency Water Collection Others Other Business Problems Fraud Detection Loan Approval Documenting the Business Problem Summary Resources Exercises Data Data Nomenclature Loading Data into Rattle CSV Data Datasets Reading Direct from URL Play Golf Weather Data Other Data Sources ARFF Data ODBC Sourced Data Setting Up a Data Source Name Netezza Setup Teradata Setup R Data R Dataset Data Entry Data Tab Options in Rattle Sampling Data Variable Roles Automatic Role Identification Weights Calculator Manipulating Data Loading Data CSV Data Locating and Loading Data Loading the File CSV Options Basic Data Summary ARFF Data ODBC Sourced Data R Dataset R Data Library Data Options Sampling Data Variable Roles Automatic Role Identification Weights Calculator Command Summary Exploring Data Summarising Data Summary Describe Basics Kurtosis Skewness Missing Exploring Distributions Box Plot Histogram Cumulative Distribution Plot Benford's Law Other Digits Stratified Benford Plots Bar Plot Dot Plot Mosaic Plot GGobi Scatterplot Data Viewer Brushing Identify Multivariate Outliers Other Options Quality Plots Using R Further GGobi Documentation Correlation Analysis Hierarchical Correlation Principal Components Single Variable Overviews Interactive Graphics Interactive Visualisations Latticist GGobi Scatterplot Multiple Plots Brushing Other Plots Data Viewer Brushing Identify Multivariate Outliers Other Options Quality Plots Using R Further GGobi Documentation Documenting Interactive Explorations Code Review Chapter Exercises Command Summary Statistical Tests Documenting Interactive Explorations Code Review Further Resources Chapter Exercises Command Summary Models A Framework for Modelling Descriptive Analytics Predictive Analytics Documenting Models Summary Code Review Exercises Further Resources Command Summary Cluster Analysis Summary Clusters Basic Clustering Hot Spots Alternative Clustering Other Cluster Examples KMeans Export KMeans Clusters Discriminant Coordinates Plot Number of Clusters Hierarchical Clusters Other Cluster Algorithms Association Analysis Summary Overview Algorithm Usage Read Transactions file format sep cols rm.duplicates Summary Apriori data parameter appearance control Inspect Examples Video Marketing Survey Data Other Examples Resources and Further Reading Basket Analysis General Rules Network Analysis Documenting Interactive Explorations Code Review Chapter Exercises Command Summary Text Mining Application to Text Text Mining with R Decision Trees Knowledge Representation Search Heuristic Measures Tutorial Example Rattle R Tuning Parameters Min Split (Rarg[]minsplit) Min Bucket (minbucket) Priors (prior) Loss Matrix Complexity (cp) Other Options Simple Example Convert Tree to Rules Predicting Salary Group Issues Summary Code Review Iris Wine Exercises Resources Command Summary Random Forests Formalities Tutorial Example Tuning Parameters Number of Trees Sample Size Number of Variables Summary Overview Algorithm Usage Random Forest importance classwt Examples Resources and Further Reading Summary Overview Example Algorithm Resources and Further Reading Boosting Formalities Tutorial Example Tuning Parameters Summary Overview AdaBoost Algorithm Examples Step by Step Using gbm Extensions and Variations Alternating Decision Tree Resources and Further Reading Documenting Code Review Further Resources Chapter Exercises Command Summary Bootstrapping Summary Usage Further Information Summary Overview Example Algorithm Resources and Further Reading Bagging Support Vector Machine Formalities Tutorial Example Tuning parameters Examples Resources and Further Reading Overview Examples Resources and Further Reading Linear Regression Linear Regression Formalities Tutorial Example Tuning parameters Generalized Regression Formalities Tutorial Example Tuning parameters Logistic Regression Formalities Tutorial Example Tuning parameters Discussion Probit Regression Formalities Tutorial Example Tuning Parameters Multinomial Regression Formalities Tutorial Example Tuning Parameters Neural Network Formalities Tutorial Example Tuning parameters Documenting Code Review Further Resources Chapter Exercises Command Summary Naive Bayes Summary Code Review Resources Exercises Command Summary Survival Analysis Sample Data Simple Lung Descriptive Analysis Regression survreg Simple Lung coxph Simple Lung Apply to New Data More Input Variables Decision Tree Example from Singer and Willett Other Approaches Design Package Random Survival Forests Prediction on Test Data Evaluation The Evaluate Tab Confusion Matrix Measures Graphical Measures Risk Charts Cost Curves Lift ROC Curves Area Under Curve Precision versus Recall Sensitivity versus Specificity Predicted versus Observed Scoring Documenting Interactive Explorations Code Review Chapter Exercises Command Summary Transforming Data Rescale Data Recenter Scale [0,1] Rank Median/MAD Peer Relativity Profiling Index Impute Zero/Missing Mean/Median/Mode Constant Remap Binning Indicator Variables Join Categorics Math Transforms Outliers Cleanup Delete Ignored Delete Selected Delete Missing Delete Obs with Missing Other Transformations Removing Duplicates Command Summary Deployment Documenting Deployment Code Review Chapter Exercises Command Summary Troubleshooting Cairo A factor has new levels Issues Model Selection Overfitting Imbalanced Classification Sampling Cost Based Learning Model Deployment and Interoperability SQL PMML XML for Data Bibliographic Notes Documenting Code Review Chapter Exercises Command Summary Moving into R Interacting with R Basic Command Line Windows, Icons, Mouse, Pointer--WIMP The Current Rattle State Samples Projects The Rattle Log Further Tuning Models Emacs and ESS Documenting Code Review Chapter Exercises Command Summary R Evaluation Exercises Assignment Libraries and Packages Searching for Objects Package Management Information About a Package Testing Package Availability Packages and Namespaces Basic Programming in R Principles Folders and Files Flow Control If Statement For Loop Functions Apply Methods Objects System Running System Commands System Parameters Misc Internet Memory Management Memory Usage Garbage Collection Errors Frivolous Sudoku Further Resources Using R Specific Purposes Survey Analysis Getting Help R Documentation Data Data Types Numbers Strings Building Strings Splitting Strings Substitution Trim Whitespace Evaluating Strings Logical Dates and Times Space Data Structures Vectors Arrays Lists Sets Matricies Exercises Data Frames Accessing Columns Removing Columns Exercises General Manipulation Factors Elements Rows and Columns Finding Index of Elements Partitions Head and Tail Reverse a List Sorting Unique Values Loading Data Interactive Responses Interactive Data Entry Available Datasets The Iris Dataset CSV Data Used In The Book The Wine Dataset The Cardiac Arrhythmia Dataset The Adult Survey Dataset Foreign Formats Stata Data Conversions Reading Variable Width Data Saving Data Formatted Output Automatically Generate Filenames Reading a Large File Manipulating Data Manipulating Data As SQL Using SQLite ODBC Data Database Connection Excel Access Clipboard Data Spatial Data Simple Map A Density Map Overlays and Point in Polygon Other Data Formats Fixed Width Data Global Positioning System Documenting a Dataset Common Data Problems Graphics in R Basic Plot Controlling Axes Arrow Axes Legends and Points Tables Within Plots Colour Labels in Plots Axis Labels Legend Labels Within Plots Maths in Labels Multiple Plots MatPlot Multiple Plots Using ggplot2 Using GGPlot Networks Symbols Other Graphic Elements Making an Animation Animated Mandelbrot Adding a Logo to a Graphic Graphics Devices Setup Screen Devices Multiple Devices File Devices Multiple Plots Copy and Print Devices Graphics Parameters Plotting Region Locating Points on a Plot Scientific Notation and Plots Understanding Data Single Variable Overviews Textual Summaries Multiple Line Plots Separate Line Plots Pie Chart Fan Plot Stem and Leaf Plots Histogram Barplot Trellis Histogram Histogram Uneven Distribution Bump Chart Density Plot Basic Histogram Basic Histogram with Density Curve Practical Histogram Multiple Variable Overviews Scatterplot Scatterplot with Marginal Histograms Multi-Dimension Scatterplot Correlation Plot Colourful Correlations Fluctuation Plot Heat Map Projection Pursuit RADVIZ Parallel Coordinates Categoric and Numeric Measuring Data Distributions Textual Summaries Boxplot Multiple Boxplots Boxplot by Class Tuning a Boxplot Boxplot Using Lattice Boxplot Using ggplot Violin Plot What Distribution Miscellaneous Plots Line and Point Plots Matrix Data Multiple Plots Aligned Plots Probability Scale Network Plot Sunflower Plot Stairs Plot Graphing Means and Error Bars Bar Charts With Segments Bar Plot With Means 3d Bar Plot Stacks Versus Lines Multi-Line Title Mathematics Plots for Normality Basic Bar Chart Bar Chart Displays Multiple Dot Plots Alternative Multiple Dot Plots 3D Plot Clustered Box Plot Perspective Plots Star Plot Residuals Plot Waterfall Plots Dates and Times Simple Time Series Multiple Time Series Plot Time Series Plot Time Series with Axis Labels Grouping Time Series for Box Plot Time Series Heatmap Textual Summaries Stem and Leaf Plots Histogram Barplot Density Plot Basic Histogram Basic Histogram with Density Curve Practical Histogram Correlation Plot Colourful Correlations Measuring Data Distributions Textual Summaries Boxplot Multiple Boxplots Boxplot by Class Box and Whisker Plot Box and Whisker Plot Clustered Box Plot Further Resources Map Displays Further Resources Preparing Data Data Selection and Extraction Training and Test Datasets Data Cleaning Review Data Selectively Changing Vector Values Replace Indices By Names Missing Values Remove Levels from a Factor Variable Manipulations Remove Columns Reorder Columns Remove Non-Numeric Columns Remove Variables with no Variance Cleaning the Wine Dataset Cleaning the Cardiac Dataset Cleaning the Survey Dataset Imputation Nearest Neighbours Multiple Imputation Data Linking Simple Linking Record Linkage Data Transformation Aggregation Sum of Columns Pivot Tables Normalising Data Binning Interpolation Variable Selection Classification Classification Classification Issues Incremental or Online Modelling Model Tuning Tuning rpart Unbalanced Classification Building Models Temporal Analysis Evaluation Basics Basic Measures Cross Validation Graphical Performance Measures Lift The ROC Curve Other Examples 10 Fold Cross Validation Area Under Curve Calibration Curves Reporting Generating Open Document Format Getting Started with odfWeave OpenOffice.org Macro Support Generating HTML Generating PDF with LATEX Configuration Figure Sizes Fraud Analysis Archetype Analysis

Issues: Under-represented Classes

Consider the problem of fraud investigation, perhaps in insurance claims. Suppose some 10,000 cases have been investigated and of those just 5% (or 500) were found to be fraudulent. This is a typical scenario for numerous organisations. With modelling we wish to improve the deployment of our resources so that the 95% of the cases that were not fraudulent need not all be investigated, yet the 5% still need to be identified. Each case of actual fraud also has a dollar value associated with it, representing the risk (actually, the magnitude of the risk) associated with the case.

The advantage of a decision tree approach is that the resulting tree (and particularly if we traverse each path through the tree to obtain a set of rules) can be easily understood and explained, allowing decision makers the opportunity to understand the changes being suggested.

An aim of modelling here is to present a model which will allow us to identify a caseload tradeoff with coverage whilst maximising the recovery of dollars represented as the risk.

The first step is to build a decision tree. Because of the skewness of the outcome we might ``trick'' rpart into working harder to identify the frauds. As Breiman et al. 1984 indicate, different costs for misclassification can be modelled either by modifying the loss matrix or by using different prior probabilities for the classes, or by using different weights for the response classes. These can be achieve using rpart with the Roption[]parms option which will record the options we want for the tree building. The variables Roption[]loss and Roption[]prior can be set within the Roption[]parms list of variables. Another approach is to use the Roption[]weights (to weight each case) and Roption[]cost (the relative cost of obtaining the variable value, thus can tune the choice of variables in the model) options of rpart.

In using Roption[]prior the relative prior probability assigned to each class can be used to adjust the importance of misclassifications for each class. Thus, priors may be interpreted as case weights, although case weights are treated as case multipliers.

In fraud it is desirable not to misclassify cases of fraud, thus a more accurate classification is desired for some classes over others. This will not be exhibited through the relative class sizes. However, if the criterion for predictive accuracy is misclassification costs, as it often is, then minimising costs amounts to minimising the proportion of misclassified cases when priors are considered proportional to the class sizes and misclassification costs are taken to be equal for every class. A Roption[]loss matrix elaborates the loss incurred if an observation of one decision class (say 1) is erroneously classified by our model as another decision class (say 0).

For the following examples we use the audit dataset from the rattle package. This dataset consists of a bunch of input variables with the target (Adjusted) being in the last column. The outcome is binary (0/1) with the positive case (1) being under-represented. The measure of the risk (Adjustment) is assumed to be in the second last column. The risk is the dollar amount recovered from the review of the fraud and should not be used as an input variable in the modelling (thus we use audit[,-2] to remove this column from the data). The examples here show the R code behind Rattle as presented in Chapter .

Using Roption[]prior to over-emphasize the under-represented outcome:

library(rpart)
library(rattle)
data(audit)
audit.rpart <- rpart(Adjusted ~ .,data=audit[,-12],parms=list(prior=c(.5,.5)))

Using Roption[]loss:

library(rpart)
library(rattle)
data(audit)
loss <- matrix(c(0, 2, 1, 0), byrow=TRUE, ncol=2)
audit.rpart <- rpart(Adjusted ~ ., data=audit[,-12], parms=list(loss=loss))

Using Roption[]weights based on the value of the risk:

library(rpart)
library(rattle)
data(audit)
weight <- abs(audit$Adjustment)/max(audit$Adjustment)*10+1
audit.rpart <- rpart(Adjusted ~ ., data=audit[,-12], weights=weight)

Now we apply the model to the data to obtain probabilistic predictions (note that we are applying the model to the same training set and this is will give us an optimistic estimate - Rattle uses training/test sets to give a better estimate). The result is the probability, for each case, of it being a fraud:

audit.predict <- predict(audit.rpart, audit)

Now, using Rattle (see Chapter ) we can produce a Risk Chart that presents the cases ordered by the probability of being a fraud, and plotting the coverage and risk (percentage of dollars) recovered for each choice of caseload.

library(rattle)
eval <- evaluateRisk(audit.predict, audit$Adjusted, audit$Adjustment)
plotRisk(eval$Caseload, eval$Precision, eval$Recall, eval$Risk)
title(main="Risk Chart using rpart on the audit dataset", 
      sub=paste("Rattle", Sys.time(), Sys.info()["user"]))

To produce:

The plot can be easily used to tell a story about the tradeoff between recovering all risk cases and the amount of effort expended. The solid black diagonal line can be thought of as the baseline. The so called optimal line (the caseload where the sum of the distances of the Revenue and Adjustments from the baseline is maximal) might be an interesting point to consider. The story says that if our investigators actually only investigated 25% of the cases that they are currently investigating, then they would recover 64% of the cases that were found to be fraudulent, and 72% of the dollars that were recovered. The other 75% of the investigative resources could be better deployed, perhaps to target higher risk populations where the returns are greater. Note that the Strike Rate has increased from 26% in the original dataset to 67% at this optimal point.

Perhaps an even better story is that with half of the resources currently deployed on investigations (i.e., a caseload of 50%), with our model we could recover almost 90% of the frauds and marginally more than 90% of the dollars known to be recoverable.

We do note that here we are assuming the caseload directly reflects the actual workload (i.e., every case takes the same amount of effort).

Such Risk Charts are used to compare the performance of alternative models, where the aim is often to extend the red (Revenue) and green (Recall) lines toward the top left corner of the plot, or to maximise the area under these curves.

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