The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem.

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Real-time applications of spike sorting, e.g., neural decoding, generally require high numbers of channels, and manual spike sorting methods are extremely time consuming, subjective and, generally, do not perform well for low signalto-noise ratio (SNR) signals. Hence, an automatic method is sought which is efficient and robust in both detecting neural spikes and constructing a classification model of spikes arriving with underlying statistics that are time-varying.We present such a system under study for application with a microelectrode array of 96 channels with typically three or four units (i.e., neurons) per channel. There are several novel elements of the system including filtering the neural signal to a frequency band having better SNR for spike detection, a fixed feature space for simple implementation yet adequate resolving capabilities, a Gaussian statistics model also for simple implementation as a log-likelihood classifier, a systematic approach to determining the number of clusters in a pattern recognition problem, and a robust linear discriminant, histogram-based technique for determining boundaries between feature space clusters.

Abstract-An algorithm for multi-input multi-output (MIMO) adaptive filtering is introduced that distributes the adaptive computation over a set of linearly connected computational modules. Each module has an input and an output and transmits data to and receives data from its nearest neighbor.A gradient-based algorithm for adapting the parameters in each module to minimize the global mean-squared error is derived using principles of back propagation. The performance surface is explored to understand the characteristics of the adaptive algorithm. The minimum mean-squared error is a many to one function of the parameters; therefore, upper bounds on each parameter are used to prevent excessive parameter drift and insure stability with fixed step sizes. Guidelines for choosing the LMS algorithm step sizes and initial conditions are developed. Several examples illustrate the performance of the algorithm.