  The demand for extracting rules from high dimensional real world data is
increasing in various fields. However, the possible redundancy of such data
sometimes makes it difficult to obtain a good generalization ability for novel
samples. To resolve this problem, we provide a scheme that reduces the
effective dimensions of data by pruning redundant components for bicategorical
classification based on the Bayesian framework. First, the potential of the
proposed method is confirmed in ideal situations using the replica method.
Unfortunately, performing the scheme exactly is computationally difficult. So,
we next develop a tractable approximation algorithm, which turns out to offer
nearly optimal performance in ideal cases when the system size is large.
Finally, the efficacy of the developed classifier is experimentally examined
for a real world problem of colon cancer classification, which shows that the
developed method can be practically useful.
