Exploring Variable Clustering and Importance in JMP

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This presentation was given live at JMP Discovery Summit 2013 in San Antonio, Texas, USA. To sign up to attend this year's conference, visit http://jmp.com/summit

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Exploring Variable Clustering and Importance in JMP

  1. 1. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. EXPLORING VARIABLE CLUSTERING AND IMPORTANCE IN JMP CHRIS GOTWALT AND RYAN PARKER
  2. 2. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING INTRODUCTION • Variable clustering is a method that performs dimension reduction on the number of input variables to be used in a predictive model. • Reduces inputs by finding groups of similar variables so that a single variable can represent each group. • Helps reduce effects of collinearity on the input variables. • Developed by SAS/STAT Development Director Warren Sarle.
  3. 3. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING AN ITERATIVE ALGORITHM • Iteratively splits and assigns variables to clusters. • Sample iterations for variables in Wine Quality data set: Iteration 1 Alcohol, Citric Acid, pH, Sugar, Sulfur Dioxide Alcohol, Citric Acid, Sulfur Dioxide Alcohol, Sugar pH, Sulfur Dioxide pH, Sugar Citric Acid Iteration 2 Iteration 3
  4. 4. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING ALGORITHM DETAILS • At each iteration the cluster with the largest second eigenvalue is split. • Variables within this cluster are assigned to two new clusters based on each variable’s correlation with the first two orthoblique rotated principal components. • After the split, variables from other clusters are reassigned to one of the new clusters if they have a higher correlation with the new cluster. • Ends when the second eigenvalue of all clusters is less than one.
  5. 5. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING REDUCING EACH CLUSTER TO A SINGLE VARIABLE pH Sugar pH Citric Acid • Each cluster can be reduced to a single variable for modeling. • There are two ways to do this: 1. We can use the most representative variable from each cluster. 2. Alternatively, the cluster component from each cluster can be used.
  6. 6. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING MOST REPRESENTATIVE VARIABLES • These are variables that best represent each cluster. • They have the highest correlation with the variables in its cluster. • Most representative variables provide a clear interpretation when used.
  7. 7. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING CLUSTER COMPONENTS • New variables created using the first principal component of each cluster. • Provide a way to combine variables in each cluster into a single variable. • Similar to traditional principal components analysis (PCA) except that each cluster component only uses variables from that cluster. • Interpretation not as clear when compared to most representative variables.
  8. 8. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE CLUSTERING DEMO: IMPORTANT TERMS • RSquare with Own Cluster • The RSquare a variable has with variables in its cluster. • RSquare with Next Closest • The RSquare a variable has with variables in the next most similar cluster. • 1-RSquare Ratio • Relative similarity between a variable’s own cluster and the next closest cluster. • Values should always be less than 1. • Values greater than 1 indicate variable should be moved to the next closest cluster.
  9. 9. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE INTRODUCTION • Provides a general way to assess the importance of variables for predictive models in JMP. • Insight is in terms of practical significance of input variables. • Based on functional decomposition ideas of I. M. Sobol.
  10. 10. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE FUNCTIONAL DECOMPOSITION • I. M. Sobol showed that we can decompose a function 𝑓(𝑋1, … , 𝑋 𝑝) into the sum of lower dimensional inputs: • 𝑓 𝑋1, … , 𝑋 𝑝 = 𝑓0 + 𝑓1 𝑋1 + ⋯ + 𝑓𝑝 𝑋 𝑝 + 𝑓12 𝑋1, 𝑋2 + ⋯ • Decomposition has a function for each 𝑋𝑖, each pair (𝑋𝑖, 𝑋𝑗), etc. • The variability of these lower dimensional functions assess the importance of the input variables.
  11. 11. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE IMPORTANCE EFFECTS • Assessment of variable importance is in terms of effect indices. • These indices are numbers between 0 and 1 indicating relative importance. • Main effect indices measure variability of predictions due to a single input. • They do not account for interaction effects. • Total effect indices measure the total variability of predictions due the input. • Combines all main and higher order interaction effects.
  12. 12. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE DISTRIBUTION OF INPUT VARIABLES • Variability in predictions is due to the distribution of input variables • JMP 11 provides three input variable distribution options: 1. Independent Uniform 2. Independent Resampled 3. Dependent Resampled • Monte Carlo estimation procedure used for independent cases. • 𝐾-nearest neighbors estimation used for dependent case.
  13. 13. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE USE RESAMPLED INPUTS? Uniform Acceptable Resampled Needed
  14. 14. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE MARGINAL INFERENCE Main Effects0.16 0.03
  15. 15. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. VARIABLE IMPORTANCE DEMO

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