An information theoretic approach to quantify the stability of feature selection and ranking algorithms
Feature selection is a key step when dealing with high dimensional data. In particular, these techniques simplify the process of knowledge discovery from the data by selecting the most relevant features out of the noisy, redundant and irrelevant features. A problem that arises in many of these practical applications is that the outcome of the feature selection algorithm is not stable. Thus, small variations in the data may yield very different feature rankings. Assessing the stability of these methods becomes an important issue in the previously mentioned situations. We propose an information theoretic approach based on the Jensen Shannon divergence to quantify this robustness. Unlike other stability measures, this metric is suitable for different algorithm outcomes: full ranked lists, feature subsets as well as the lesser studied partial ranked lists. This generalized metric quantifies the difference among a whole set of lists with the same size, following a probabilistic approach and being able to give more importance to the disagreements that appear at the top of the list. Moreover, it possesses desirable properties including correction for change, upper lower bounds and conditions for a deterministic selection. We illustrate the use of this stability metric with data generated in a fully controlled way and compare it with popular metrics including the Spearmans rank correlation and the Kunchevas index on feature ranking and selection outcomes, respectively. Additionally, experimental validation of the proposed approach is carried out on a real-world problem of food quality assessment showing its potential to quantify stability from different perspectives.