Visual Methods for Examining SVM Classifiers Doina Caragea, Dianne Cook, Hadley Wickham and Vasant Honavar  This chapter focuses on two topics studied empirically using graphics:

1)   Ways to ﬁnd the role different variables play in a classiﬁer, to learn more about the

data and go beyond predictive accuracy alone.

1. 2)  The variation in the support vector machine ﬁtting when the inputs change.

This web page contains color copies of the figures in the chapter the the R code that was used to generate these figures.

Reference: Caragea, D., Cook, D., Wickham, H., and Honavar, V. (2007). Invited Chapter. Visual Methods for Examining SVM Classifiers. In: Visual Data Mining: Theory, Techniques, and Tools for Visual Analytics. Springer, LNCS Volume 4404. To appear.

Fig. 1. Two projections from a tour of a 5-dimensional data set (variables V5, V6, V7, V8, V9), where the two groups are separable. The left plot shows a projection where the groups are well-separated, and the right plot shows a projection where they are not separated. The magnitude of the projection coefficients indicate the variable importance, the larger the coefficient - in the direction of separation - the more important the variable.

Fig. 2. SVM results for a 4-dim data set. (Left) A projection where the linear separation found by SVM can be seen. (Right) A grid over the data colored according to the class colors. The grid points that have predicted values close to 0, deﬁne a nice linear boundary between the two groups.

Fig. 3. A subset of the data (2/3 from each class) is used for training and the rest of the data is used for test. (Top left) A projection showing the separation for the training set. Support vectors are shown as larger solid circles. (Top Right) Bounded support vectors are also shown as open circles. (Bottom) The test set is shown with respect to the separating hyperplane found by the algorithm. We can see the errors. They belong entirely to one group (colored purple).

Fig. 6. Variation of the margin with the cost C . Plots corresponding to values C=1, C=0.7, C=0.5, C=0.1 are shown, from top left to bottom right. As C decreases the margin increases, as seen by the increasing distance between support vectors shown as larger solid circles.

Fig. 5. Visualization of SVM results using three diﬀerent subsets of the data, corresponding to three diﬀerent sets of 4 variables. (Top left) Gene subset S1 = {V800, V403, V535, V596}. (Top right) Gene subset S2 = {V390, V389, V4, V596}. (Bottom left) Gene subset S3 = {V800, V721, V357, V596}. Note that the subset S2 presents the largest separation margin, suggesting that S2 may be a better choice than S1 and S3.

Fig. 7. We examine the variation of the separating hyperplane when sub-sampling the data. We ﬁnd the projection that shows the linear separation for the ﬁrst data set and we keep this projection ﬁxed for the subsequent views. There is some variation in the separating hyperplane from sample to sample. In some samples the separating hyperplane rotated substantially from that of the ﬁrst sample, as seen by the thick band of grid points.                  Fig. 8. Two diﬀerent runs of the SVM with slightly diﬀerent training data sets (9/10 points of the whole data set are selected at each run). The projection is kept ﬁxed in the (Left) and (Middle) plots. A small rotation of the data shows the clear separation found by the second run of the SVM.   