R: Scale Invariant Probabilistic Neural Networks

spnn-package {spnn}

R Documentation

Scale Invariant Probabilistic Neural Networks

Description

Scale invariant version of the original PNN proposed by Specht (1990) <doi:10.1016/0893-6080(90)90049-q> with the added functionality of allowing for smoothing along multiple dimensions while accounting for covariances within the data set. It is written in the R statistical programming language. Given a data set with categorical variables, we use this algorithm to estimate the probabilities of a new observation vector belonging to a specific category. This type of neural network provides the benefits of fast training time relative to backpropagation and statistical generalization with only a small set of known observations.

Details

The package exports 4 main functions:

spnn.learn Create or update a Scale Invariant Probabilistic Neural Network.
spnn.predict Estimates the category probabilities of new observations using a fitted SPNN.
cspnn.learn Create or update a Condensed Scale Invariant Probabilistic Neural Network.
cspnn.predict Estimates the category probabilities of new observations using a fitted CSPNN.

Author(s)

Romin Ebrahimi <romin.ebrahimi@utexas.edu>

References

[1] Specht, Donald F. "Probabilistic neural networks." Neural networks 3.1 (1990): 109-118.

[2] Specht, Donald F. "Enhancements to probabilistic neural networks." Neural Networks, 1992.IJCNN., International Joint Conference on. Vol. 1. IEEE, 1992.

[3] Ebrahimi, Romin "Scale Invariant Probabilistic Neural Networks." The University of Texas, 2018 https://repositories.lib.utexas.edu/handle/2152/65166

Examples

library(spnn)
library(datasets)

data(iris)

# shuffle the iris data set
indexRandom <- sample(1:nrow(iris), size = nrow(iris), replace = FALSE)

# use 100 observations for training set
trainData <- iris[indexRandom[1:100],]

# use remaining observations for testing
testData <- iris[indexRandom[101:length(indexRandom)],]

# fit spnn
spnn <- spnn.learn(set = trainData, category.column = 5)

# estimate probabilities
predictions <- spnn.predict(nn = spnn, newData = testData[,1:4])

# reference matrix must be supplied
# this is not the optimal reference matrix
# this matrix is provided as a simple example
xr <- matrix(c(c(5.00, 3.41, 1.44, 0.24),
               c(5.88, 2.75, 4.23, 1.30),
               c(6.61, 2.97, 5.59, 2.01)),
             nrow = length(unique(trainData$Species)),
             ncol = ncol(trainData) - 1,
             byrow = TRUE)

# fit cspnn
cspnn <- cspnn.learn(set = trainData, xr = xr, category.column = 5)

# estimate probabilities
predictions <- cspnn.predict(nn = cspnn, newData = testData[,1:4])