Bounded Component Analysis of the Training Error

This paper addresses the problem of the supervised signal extraction of a desired signal in a linear mixture. The main assumption is the bounded support of the sources, property that allows to propose a loss function based on the convex perimeter of the training error. This work reviews our recent results on the Bounded Component Analysis of the training error with special emphasis on the harder case where the mixture is underdetermined, that is, there are more sources than sensors. In this scenario, due to the lack of degrees of freedom, one cannot extract perfectly the desired source even in the noiseless case. However, the Bounded Component Analysis of the error can be used to obtain a linear estimate of the target signal while cancelling as many as possible of the interfering sources, what it will be referred as a Partial Zero Forcing criterion. An application of the technique is presented in wireless communications scenarios dominated by the interference. The Bounded Component Analysis of the error is used as a preprocessing for the received observations which simplifies the structure of the interference and noise in the linear estimate. This estimate is then passed through a Support Vector Machine classifier with Radial Basis Function kernels, which detects the transmitted symbols. We illustrate with simulations the superior performance of the method with respect to other criteria for a complex and noisy mixture of 10 sources and 8 sensors.