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Feature selection can efficiently identify the most informative features withrespect to the target feature used in training. However, state-of-the-artvector-based methods are unable to encapsulate the relationships betweenfeature samples into the feature selection process, thus leading to significantinformation loss. To address this problem, we propose a new graph-basedstructurally interacting elastic net method for feature selection.Specifically, we commence by constructing feature graphs that can incorporatepairwise relationship between samples. With the feature graphs to hand, wepropose a new information theoretic criterion to measure the joint relevance ofdifferent pairwise feature combinations with respect to the target featuregraph representation. This measure is used to obtain a structural interactionmatrix where the elements represent the proposed information theoretic measurebetween feature pairs. We then formulate a new optimization model through thecombination of the structural interaction matrix and an elastic net regressionmodel for the feature subset selection problem. This allows us to a) preservethe information of the original vectorial space, b) remedy the information lossof the original feature space caused by using graph representation, and c)promote a sparse solution and also encourage correlated features to beselected. Because the proposed optimization problem is non-convex, we developan efficient alternating direction multiplier method (ADMM) to locate theoptimal solutions. Extensive experiments on various datasets demonstrate theeffectiveness of the proposed methods.

Identifying The Most Informative Features Using A Structurally Interacting Elastic Net