Feature selection via sensitivity analysis of SVM probabilistic outputs
Feature selection is an important aspect of solving data-mining and machine-learning problems. This paper proposes a feature-selection method for the Support Vector Machine (SVM) learning. Like most feature-selection methods, the proposed method ranks all features in decreasing order of importance so that more relevant features can be identified. It uses a novel criterion based on the probabilistic outputs of SVM. This criterion, termed Feature-based Sensitivity of Posterior Probabilities (FSPP), evaluates the importance of a specific feature by computing the aggregate value, over the feature space, of the absolute difference of the probabilistic outputs of SVM with and without the feature. The exact form of this criterion is not easily computable and approximation is needed. Four approximations, FSPP1-FSPP4, are proposed for this purpose. The first two approximations evaluate the criterion by randomly permuting the values of the feature among samples of the training data. They differ in their choices of the mapping function from standard SVM output to its probabilistic output: FSPP1 uses a simple threshold function while FSPP2 uses a sigmoid function. The second two directly approximate the criterion but differ in the smoothness assumptions of criterion with respect to the features. The performance of these approximations, used in an overall feature-selection scheme, is then evaluated on various artificial problems and real-world problems, including datasets from the recent Neural Information Processing Systems (NIPS) feature selection competition. FSPP1-3 show good performance consistently with FSPP2 being the best overall by a slight margin. The performance of FSPP2 is competitive with some of the best performing feature-selection methods in the literature on the datasets that we have tested. Its associated computations are modest and hence it is suitable as a feature-selection method for SVM applications.
feature selection sensitivity support vector machines feature ranking