  Feature subset selection, as a special case of the general subset selection
problem, has been the topic of a considerable number of studies due to the
growing importance of data-mining applications. In the feature subset selection
problem there are two main issues that need to be addressed: (i) Finding an
appropriate measure function than can be fairly fast and robustly computed for
high-dimensional data. (ii) A search strategy to optimize the measure over the
subset space in a reasonable amount of time. In this article mutual information
between features and class labels is considered to be the measure function. Two
series expansions for mutual information are proposed, and it is shown that
most heuristic criteria suggested in the literature are truncated
approximations of these expansions. It is well-known that searching the whole
subset space is an NP-hard problem. Here, instead of the conventional
sequential search algorithms, we suggest a parallel search strategy based on
semidefinite programming (SDP) that can search through the subset space in
polynomial time. By exploiting the similarities between the proposed algorithm
and an instance of the maximum-cut problem in graph theory, the approximation
ratio of this algorithm is derived and is compared with the approximation ratio
of the backward elimination method. The experiments show that it can be
misleading to judge the quality of a measure solely based on the classification
accuracy, without taking the effect of the non-optimum search strategy into
account.
