Bounds on number of hidden neurons of multilayer perceptrons in classification and recognition

Abstract

In evaluating learning algorithms, it is often necessary to investigate the capability of the underlying network. This paper investigates multilayer perceptrons(MLP) in the realization of arbitrary functions which map from a finite subset of E" into Em. A least upper bound of hidden neurons needed to solve this problem is derived. It is shown that as long as the number of hidden neurons exceeds this bound, an MLP can realize arbitrary switching functions without needing learning algorithms. In studying classification problems, we also derive an upper bound which is tighter than the ones obtained with the common assumption of the general position condition on the input set. In addition, a lower bound is derived in addressing recognition problems.

Evolutionary Multi-objective Optimization in Uncertain Environments

“…Taking into account the study in [127], the selection criterion adopted in this chapter is based on the Pareto ranking scheme described in [84] and niche count [102] is used in the event of a tie. The algorithm employs a fixed-size population and an archive to store non-dominated solutions found during the evolution process.…”

“…It is assumed that noise has a disruptive influence on the value of each individual in the objective space [13,27,127,128,227], i.e. In this study, noise is implemented as an additive normal distributed perturbation with zero mean.…”

“…Instead of performing the aggregation of objective values, Hughes [126,127] suggested the aggregation of individual performance with respect to a set of predetermined target vectors. In this approach, individuals are ranked according to their relative performance in an ascending order for each target.…”

“…Visualization of the evolved PF A is used in [33,78,127] to demonstrate the effectiveness of the proposed methods. To be precise, we are concerned about how good the PF A truly is and not how it is perceived since it is the true objective values that matters during implementation.…”

“…In an independent study, Hughes [127,128] suggested a multi-objective probabilistic selection evolutionary algorithm (MOPSEA) which also employs probabilistic dominance to account for the effects of noise in the objective space.…”