ManiFeSt: Manifold-based Feature Selection for Small Data Sets
This addresses the challenge of feature selection in small datasets, which is crucial for domains with limited data, but it appears incremental as it builds on existing manifold and kernel techniques.
The paper tackles the problem of few-sample supervised feature selection by introducing a manifold-based method that learns feature associations via kernels and uses Riemannian geometry to compute a composite kernel for feature scoring. The method demonstrates higher accuracy in selecting informative features and leads to improved classification and generalization on benchmarks.
In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian geometry, a composite kernel is computed, extracting the differences between the learned feature associations. Finally, a FS score based on spectral analysis is proposed. Considering multi-feature associations makes our method multivariate by design. This in turn allows for the extraction of the hidden manifold underlying the features and avoids overfitting, facilitating few-sample FS. We showcase the efficacy of our method on illustrative examples and several benchmarks, where our method demonstrates higher accuracy in selecting the informative features compared to competing methods. In addition, we show that our FS leads to improved classification and better generalization when applied to test data.