Tracking Independent Sources
In this paper, we review an Artiicial Neural Network we have previously used for extraction of independent signals from a mixture of signals. The network, called the Extended Exploratory Projection Pursuit Network, is shown to be superior to Exploratory Projection Pursuit because of its ability to track time-dependence in its inputs. We give results on artiicial and real data. One of the most interesting problems to which Arti-cial Neural Networks is being applied is the blind separation of independent sources from a (linear) mixture of sources 2, 9]. The problem is blind in that we assume no prior information about either the mixing matrix or the sources other than that the sources should be independent and at most one should be drawn from a Gaussian distribution. have been mixed linearly to get a set of values (in practice, liable to be sensor readings), x 1 ; x 2 ; :::; x n using a mixing matrix A. x = As (1) We assume no prior knowledge of the input signals nor of the mixing matrix A. However, the unknown signals, s i must be independent from each other and at most one of them may be drawn from a Gaussian distribution. The task is to nd an un-mixing matrix W such that y = Wx (2) is such that the individual elements of y are the original signals (up to a permutation and scaling factor). Some of the methods used to solve this problem have been based on the statistical method of Exploratory Projection Pursuit (EPP). We have previously used an EPP network ((5]) to search for lters which identify the independent sources but have found better results with an extension of the network which we have called an Extended Exploratory Projection Pursuit (EEPP) network((8]). We have, however, continued to justify our method by referring to the theoretical results of the EPP network, though this leaves open the question as to why the EEPP network should perform better than the EPP network which has been analytically derived for this exact purpose. In this paper, we show that the EEPP network has superior capabilities in tracking the locally time-dependent statistics of the data. We will use artiicial data to make an empirical investigation of the separation properties. Our arti-cial data will be drawn from a number of diierent time-dependent distributions and we will conclude with results from real speech data. 2 …