  Feature selection can efficiently identify the most informative features with
respect to the target feature used in training. However, state-of-the-art
vector-based methods are unable to encapsulate the relationships between
feature samples into the feature selection process, thus leading to significant
information loss. To address this problem, we propose a new graph-based
structurally interacting elastic net method for feature selection.
Specifically, we commence by constructing feature graphs that can incorporate
pairwise relationship between samples. With the feature graphs to hand, we
propose a new information theoretic criterion to measure the joint relevance of
different pairwise feature combinations with respect to the target feature
graph representation. This measure is used to obtain a structural interaction
matrix where the elements represent the proposed information theoretic measure
between feature pairs. We then formulate a new optimization model through the
combination of the structural interaction matrix and an elastic net regression
model for the feature subset selection problem. This allows us to a) preserve
the information of the original vectorial space, b) remedy the information loss
of the original feature space caused by using graph representation, and c)
promote a sparse solution and also encourage correlated features to be
selected. Because the proposed optimization problem is non-convex, we develop
an efficient alternating direction multiplier method (ADMM) to locate the
optimal solutions. Extensive experiments on various datasets demonstrate the
effectiveness of the proposed methods.
