Relative Karhunen-Loeve operator

The Karhunen-Loeve (K-L) subspace is a subspace which provides the best approximation for a stochastic signal under the condition that its dimension is fixed. The K-L subspace, however, does not consider a noise in communication and a noise and patterns in other categories in pattern recognition. Therefore, its noise suppression is not sufficient in communication. It gives a wrong recognition result for similar patterns but belong to different categories. In order to solve this problem, we propose relative K-L operators. The advantage of the relative K-L operators is illustrated by using a simulation