Improved Design Of A Piecewise Linear Network

Abstract

An efficient design of the Piecewise Linear Network (PLN) which maps the N dimensional input vector space into an M dimensional output vector space is presented. Several clusters are formed in the given datasets and a linear mapping is fitted for each cluster using regression and the total mapping error is calculated. We have designed this network using Self Organizing Map (SOM) clustering which uses the Euclidean distance measure. Again the same has been designed by using various weighted distance measures whose results are compared. It is observed that there is a decrease in Mean Square Error (MSE) of the PLN, when it is finally re-designed with the optimum version of the weighted distance measure. Design of the PLN using Sequential Leader Algorithm (SLA) has also been implemented in this thesis and the results are compared with the one designed using SOM. It is shown that the SLA outperforms the Self-organizing map clustering. In SLA a threshold to optimize the number of clusters formed is also computed and the PLN is designed accordingly. On deleting of several clusters formed by the Sequential leader algorithm to match the number used in SOM using several heuristics, and on designing the PLN with the final number of clusters, the Mean square error(MSE) of the designed PLN decreases. A pruning algorithm for pruning the insignificant clusters in designing the PLN is demonstrated. This algorithm designs the network by pruning one cluster at a time, without significantly decreasing the MSE and hence the design becomes more compact. A second version of the pruning method which makes the design more efficient is also implemented.