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Principal Component Analysis and Clustering
- 1. Principal Component Analysis and Clustering Professor Daymond 27-Nov-2016
- 2. UNDERSTANDING BORROWER SEGMENTS Majority of the accounts are of credit based borrowers whose revolving utilization with the most revolving accounts and bankcards Credit based accounts The accounts are mostly with fixed instalments like car loans, student loans etc., Most instalment accounts and instalment utilization are the major factors of this segment Fixed Instalment accounts These are borrowers with past due records and most of the late fees of credit and loan amount. Also with the recent history of delinquency this segment is medium risk Past due accounts These are borrowers who are highly inquired for loans which exhibits the most credit card purchase behaviour and attempt to try all possible loans for one Highly Inquired accounts Debt to collection accounts holds the most number of public records like tax liens etc., Collections money owed and tax liens are the major factors of this segment With highest delinquency, exceeded usage of credit limit and multiple accounts in the recent times makes this segment as high risk Debt Collections accounts High risk delinquent accounts
- 3. IDENTIFYINGTHEPRINCIPALCOMPONENTS With the given dataset(N=27000) and 77 variables, it is important to reduce the data set to a smaller set of variables to derive a feasible conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the principal components The variance of each principal component is implied Eigen values of the component. The greater the Eigen values, the better the variance is explained by each component. Hence the break point criteria for components is that the Eigen values must be greater than 1 and the cumulative variance should be at least 75%. From the results(Appendix 1), it is observed that there are 18 components with Eigen values greater than 1 and contribute to approximately 76% of the total variance. The coefficients of the principal components are the Eigen vectors(Appendix 2) generally the linear combination of the inputs which implies the axis length and the direction of each principal components .From figure 1, scree plot it is observed that curve is almost flat after Eigen value 1 implying that the further components contribute very small to the variance. Hence there are total of 18 principal components that provides a significant variance of data Figure 1 Figure 2
- 4. INTERPRETINGTHEPRINCIPALCOMPONENTS In order to interpret the principal components, the correlation matrix of the Eigen Vectors is observed for highest correlation with the original variables. The data is standardized by PRINCOMP and hence the correlation matrix has values lesser than 1. The values closer to an absolute 1 i.e. either positive or negative are said to be highly correlated with the original variables. PRINCIPAL COMPONENT 1 From Figure 4, it is observed that the highest coefficients are correlated with the various number of accounts i.e. how valuable are the customers in terms of usage and the least correlated with the duration since the recent account i.e. how credible the customers are? Similarly, each of the principal component is analysed for the highest and the lowest coefficients and tabulated for reference. Figure 3 Figure 4
- 5. IDENTIFYINGTHECLUSTERS Once the principal components are identified, the next step is to feed the principal components in to a cluster and run the FASTCLUS procedure with various MAXCLUSTERS size ranging from 3 to 20 after PROC STDIZE. FASTCLUS uses k-means clustering, an iterative approach helps to identify the approximately equal sized clusters with a decent spread. A set of values are selected as Initial Seeds for reference i.e. mean and then the nearest values are formed as temporary clusters and replaced with the mean of new clusters and this is repeated iteratively until there is no change in clusters. ‘Complete convergence is satisfied’ implies that the final SEEDS is equal to the cluster mean. Summary The summary of statistics of clusters displays the frequency of observations in each cluster and the root mean square deviation. The next column displays the largest distance from the seed to the observation i.e. the total spread of the cluster approximately. The last column displays the distance from the centre of the cluster to the centre of the nearest cluster. Six appropriate sized clusters are obtained with 14 clusters and at 35th iteration. Cluster 1, 4, 6, 9, 12, 14 are the identified clusters and Cluster 1 is observed to be the nearest cluster for all the clusters Goodness-of-fit metrics The higher values of Pseudo F Statistic are preferred to attain good number of clusters R-square accounts for the variance accounted by the clusters The higher CCC values are indicate good clustering generally expected to be more than 2 or 3. Higher F Statistic and CCC implies that the clustering solution is good
- 6. IDENTIFYINGTHECLUSTERS Cluster means and standard deviation of variables are displayed as part of FASTCLUS. Similar to identifying the principal components, each of the cluster is analysed for higher and lower coefficients and understand the relation between the principal components and the cluster segments. Figure 4 The clusters are analysed and derived with respect to the loan data variables. Figure 4, displays the customer segment identified after the analysis of the coefficient matrix. These are the major segments of the loan data • Credit based – revolving accounts • Fixed instalment based loan accounts • accounts who are mostly past due of credit and late fees • accounts who are highly inquired • accounts who more than 75% and creates many new accounts Further PROC UNIVARIATE is executed with the new cluster dataset and the output are approximately same with respect to the box plot. Hence it is ensured that the segments are almost correct Figure 6 Boxplot of Percentage greater than 75 over all clustersFigure 5 Boxplot of instalment accounts over all clusters
- 7. SCORINGTHENEWDATA The new data is then scored with the old statistics and the segments are identified. The scoring of new data set consists of the following steps: • The outputs stats from the PRINCOMP is used to score the new dataset • The output from STDIZE is used as input to standardize the new scored dataset • The output stat from the FASTCLUS is used as input stat for the new dataset Figure 7 displays the frequency distribution of mean across the new and old dataset for comparison. It is observed that the clusters are approximately the same and the segments have been identified correctly. OLD DATA NEW DATA
- 8. LEARNINGS Identifying the principal components is complex and after clustering the same gives a much more clear picture With very less business knowledge, identifying the clusters and the segment verification was difficult Learnt how to write a macro to run the clusters from 3 to 20 and then identify the best one from the batch Use of UNIVARIATE was a revelation when my segments matched with the box plot even though I am not sure if the segments are correct as such.