Neurocomputing pp 227-236 | Cite as

Probabilistic Interpretation of Feedforward Classification Network Outputs, with Relationships to Statistical Pattern Recognition

Conference paper
Part of the NATO ASI Series book series (volume 68)


We are concerned with feed-forward non-linear networks (multi-layer perceptrons, or MLPs) with multiple outputs. We wish to treat the outputs of the network as probabilities of alternatives (e.g. pattern classes), conditioned on the inputs. We look for appropriate output non-linearities and for appropriate criteria for adaptation of the parameters of the network (e.g. weights). We explain two modifications: probability scoring, which is an alternative to squared error minimisation, and a normalised exponential (softmax) multi-input generalisation of the logistic non-linearity. The two modifications together result in quite simple arithmetic, and hardware implementation is not difficult either. The use of radial units (squared distance instead of dot product) immediately before the softmax output stage produces a network which computes posterior distributions over class labels based on an assumption of Gaussian within-class distributions. However the training, which uses cross-class information, can result in better performance at class discrimination than the usual within-class training method, unless the within-class distribution assumptions are actually correct.


Hide Markov Model Posterior Distribution Class Label Boltzmann Machine Statistical Pattern Recognition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Speech Research UnitRoyal Signals and Radar EstablishmentGreat MalvernUK

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