| Title: | 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. |
| Authors: | Romin Ebrahimi |
| Maintainer: | Romin Ebrahimi <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.2.1 |
| Built: | 2024-10-26 04:25:26 UTC |
| Source: | https://github.com/romin-ebrahimi/spnn |
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.
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.
Romin Ebrahimi <[email protected]>
[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
spnn.learn,
spnn.predict,
cspnn.learn,
cspnn.predict
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$Species)), ncol = ncol(trainData) - 1, byrow = TRUE) # fit cspnn cspnn <- cspnn.learn(set = trainData, xr = xr, category.column = 5) # estimate probabilities predictions <- cspnn.predict(nn = cspnn, newData = testData[,1:4])library(spnn) library(datasets) data(iris) # shuffle the iris data set indexRandom <- sample(1:nrow(iris), size = nrow(iris), replace = FALSE) # use 100 observations for training set trainData <- iris[indexRandom[1:100],] # use remaining observations for testing testData <- iris[indexRandom[101:length(indexRandom)],] # fit spnn spnn <- spnn.learn(set = trainData, category.column = 5) # estimate probabilities predictions <- spnn.predict(nn = spnn, newData = testData[,1:4]) # reference matrix must be supplied # this is not the optimal reference matrix # this matrix is provided as a simple example xr <- matrix(c(c(5.00, 3.41, 1.44, 0.24), c(5.88, 2.75, 4.23, 1.30), c(6.61, 2.97, 5.59, 2.01)), nrow = length(unique(trainData$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])
Create or update a Condensed Scale Invariant Probabilistic Neural Network.
cspnn.learn(set, nn, xr, sigma, category.column = 1)cspnn.learn(set, nn, xr, sigma, category.column = 1)
set |
data.frame or matrix representing the training set. The first column (default category.column = 1) is used to define the category or class of each observation. |
nn |
(optional) A Condensed Scale Invariant Probabilistic Neural Network object. If provided, the training data set input is concatenated to the current training data set of the neural network. If not provided, a new CSPNN object is created. |
xr |
The m by n reference matrix containing optimal parameters for probability estimation. Where m is the number of unique categories and n is the number of input factors used. This matrix must be provided. |
sigma |
An n by n square matrix of smoothing parameters where n is the number of input factors. Defaults to using the covariance matrix of the training data set excluding the category.column. |
category.column |
The column number of category data. Default is 1. |
The function cspnn.learn creates a new Condensed Scale Invariant Probabilistic Neural Network with a given training data set or updates the training data of an existing CSPNN. It sets the parameters: model, set, xr, category.column, categories, sigma, sigmaInverse, k, and n for the CSPNN.
A trained Condensed Scale Invariant Probabilistic Neural Network (CSPNN)
spnn-package, cspnn.predict, iris
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)],] # 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$Species)), ncol = ncol(trainData) - 1, byrow = TRUE) # fit cspnn cspnn <- cspnn.learn(set = trainData, xr = xr, category.column = 5) # estimate probabilities predictions <- cspnn.predict(nn = cspnn, newData = testData[,1:4])library(spnn) library(datasets) data(iris) # shuffle the iris data set indexRandom <- sample(1:nrow(iris), size = nrow(iris), replace = FALSE) # use 100 observations for training set trainData <- iris[indexRandom[1:100],] # use remaining observations for testing testData <- iris[indexRandom[101:length(indexRandom)],] # reference matrix must be supplied # this is not the optimal reference matrix # this matrix is provided as a simple example xr <- matrix(c(c(5.00, 3.41, 1.44, 0.24), c(5.88, 2.75, 4.23, 1.30), c(6.61, 2.97, 5.59, 2.01)), nrow = length(unique(trainData$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])
Estimates the category probabilities of new observations using a fitted CSPNN.
cspnn.predict(nn, newData)cspnn.predict(nn, newData)
nn |
A trained Condensed Scaled Invariant Probabilistic Neural Network. |
newData |
A matrix of new observations where each row represents a single observation vector. |
Given a trained Condensed Scale Invariant Probabilistic Neural Network and new data, the function cspnn.predict returns the category with the highest probability and the probability estimates for each category.
A list of the guessed categories and the probability estimates of each category.
spnn-package, cspnn.learn, iris
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)],] # 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$Species)), ncol = ncol(trainData) - 1, byrow = TRUE) # fit cspnn cspnn <- cspnn.learn(set = trainData, xr = xr, category.column = 5) # estimate probabilities predictions <- cspnn.predict(nn = cspnn, newData = testData[,1:4])library(spnn) library(datasets) data(iris) # shuffle the iris data set indexRandom <- sample(1:nrow(iris), size = nrow(iris), replace = FALSE) # use 100 observations for training set trainData <- iris[indexRandom[1:100],] # use remaining observations for testing testData <- iris[indexRandom[101:length(indexRandom)],] # reference matrix must be supplied # this is not the optimal reference matrix # this matrix is provided as a simple example xr <- matrix(c(c(5.00, 3.41, 1.44, 0.24), c(5.88, 2.75, 4.23, 1.30), c(6.61, 2.97, 5.59, 2.01)), nrow = length(unique(trainData$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])
Create or update a Scale Invariant Probabilistic Neural Network.
spnn.learn(set, nn, sigma, category.column = 1)spnn.learn(set, nn, sigma, category.column = 1)
set |
data.frame or matrix representing the training set. The first column (default category.column = 1) is used to define the category or class of each observation. |
nn |
(optional) A Scale Invariant Probabilistic Neural Network object. If provided, the training data set input is concatenated to the current training data set of the neural network. If not provided, a new SPNN object is created. |
sigma |
An n by n square matrix of smoothing parameters where n is the number of input factors. Defaults to using the covariance matrix of the training data set excluding the category.column. |
category.column |
The column number of category data. Default is 1. |
The function spnn.learn creates a new Scale Invariant Probabilistic Neural Network with a given training data set or updates the training data of an existing SPNN. It sets the parameters: model, set, category.column, categories, sigma, sigmaInverse, k, and n for the SPNN.
A trained Scale Invariant Probabilistic Neural Network (SPNN)
spnn-package, spnn.predict, iris
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])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])
Estimates the category probabilities of new observations using a fitted SPNN.
spnn.predict(nn, newData)spnn.predict(nn, newData)
nn |
A trained Scaled Invariant Probabilistic Neural Network. |
newData |
A matrix of new observations where each row represents a single observation vector. |
Given a trained Scale Invariant Probabilistic Neural Network and new data, the function spnn.predict returns the category with the highest probability and the probability estimates for each category.
A list of the guessed categories and the probability estimates of each category.
spnn-package, spnn.learn, iris
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])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])