Generalized guard-zone algorithm (GGA) for learning: automatic selection of threshold

Absrract-This work IS a continuation of our earlier work on the Generalized Guard-zones Algorithm (GGA) for self-supervised parameter learning. An atlempt is made here for the automatic determination of the guard-zone parameter i' N (i.e. the threshold used for discarding doubtful or mislabeled samples) at every instant of learning, for the general m-elass N-featu re pattern recognition problem. This is done by minimizing the mean squared error (MSE) of the estimate, under a simple probabilistic model which takes into consideration the presence of mislabeled training samples. Under the assumptions of normality, it is found that Ihe estimates for i," so obtained are distribution-free, that is, they do not depend on the parameters of the distribution. They are functions of N, the iteration number n and certain percentage points or the beta distribution with parameters Nand TIN. The effectiveness of the automatic selection of guard-zone dimension is further demonstrated on a bivariate three-class data set to show the improvement in performance of the GGA. GGA Learning Optimum dimension/threshold 1. INTRODUCTION automatically based on mean squared error (MSE). The explicit expressions for the MSE are obtained for A Generalized Guard-lOne Algorithm (GGA) was both the GGA and the non-GGA (i.e. the usual described by Pathak and Pal(l) for learning class unsupervised stochastic approximation learning parameters using a restricted updating program, algorithm not based on guard-zone) using the model together with investigation of its stochastic conver­ ofChittineni,16l involving mislabeled training samples. gence for optimum learning. Basically, the aim of the An approximation for the guard-zone parameter An GGA is to detect mislabeled training samples and was obtained for which the MSE for the GGA is outliers and to reject them from the parameter updat­ smaller than that for the non-GGA. In other words, ing procedure. The algorithm is a generalization of the value of i'N selected automatically by the system some existing ones(2.J) which were found to be useful makes the GGA discard the doubtful (mislabeled) for practical data but without mathematical formu­ samples from the training procedure, thus improving lation of their various features (e.g. con vergence, its performance visit -vis the non-GGA for self-super­ optimum dimension for guard zone/threshold, per­ vised learning. formance in presence of mislabeling, etc.) This feature is further exemplified with the help of Recently, it was reported(4) that the guard zone a two-feature three-class normally distributed data parameter (An) of GGA lies between certain bounds set. and …