hann.R: Method Top-Level Functions

Description

Functions to fit Hopfield artificial neural networks or to access the results.

Usage

hann(xi, sigma, classes, H = NULL, labels = NULL, net = NULL,
     control = control.hann())
# S3 method for hann
print(x, ...)
# S3 method for hann
summary(object, ...)
# S3 method for hann
str(object, ...)
# S3 method for hann
plot(x, y, type = "h", ...)
# S3 method for hann
coef(object, ...)
# S3 method for hann
fitted(object, ...)
# S3 method for hann
labels(object, ...)
# S3 method for hann
predict(object, ...)

Value

hann returns an object of class c("hann", "hann1") or

c("hann", "hann3"); see the links below for their description.

Arguments

xi: a matrix of patterns with K rows and N columns.
sigma: a vector coding the Hopfield network (length N).
classes: the classes of the patterns (vector of length K).
H: the number of neurons in the hidden layer (can be 0).
labels: a vector of labels used for the classes.
net, x, object: an object inheriting class "hann".
control: the control parameters.
y: (unused).
type: the type of plot for vectors of parameters (biases).
...: options passed to other methods.

Details

hann() calls either hann1() or hann3() depending on the value given to the argument H (the number of hidden neurons).

The other functions are (standard) methods for accessing the results.

Examples

Run this code

## function to create 'images' default size is 9x9 pixels,
## with 4 possible shapes ("V"ertical, "H"orizontal, "U"p-diag.
## or "D"own-diag)
rpat <- function(type, nr = 9L, nc = 9L,
                 signal = c(200, 255), noise = c(0, 50))
{
    ij <- switch(type,
                 "V" = cbind(1:nr, ceiling(nc/2)),
                 "H" = cbind(ceiling(nr/2), 1:nc),
                 "U" = cbind(nr:1, 1:nc),
                 "D" = cbind(1:nr, 1:nc))
    x <- matrix(runif(nr * nc, noise[1], noise[2]), nr, nc)
    x[ij] <- runif(nr, signal[1], signal[2])
    round(x)
}

## the 4 types of patterns to simulate:
labs <- c("V", "H", "U", "D")
## repeat them 40 times, this will be used as class-vector:
cl <- rep(labs, each = 40)
## simulate the images:
xi <- t(sapply(cl, rpat))
## binarize the patterns (-1/+1):
xi <- binarize(xi)
## build the sigma vector:
sig <- buildSigma(xi, quiet = TRUE)

## optimize the neural net with 10 hidden neurons:
ctr <- control.hann(quiet = TRUE)
nt <- hann(xi, sig, cl, H = 10, control = ctr)

## convergence depends on the initial parameter values, so it might be
## needed to repeat the previous command a few times so that the next
## one shows only values on the diagonal (which can be reached with
## the default 100 iterations)

table(cl, predict(nt, xi, rawsignal = FALSE))

## now generate 10 new patterns...
new_cl <- rep(labs, each = 10)
new_xi <- binarize(t(sapply(new_cl, rpat)))
## ... and see how well they are predicted:
table(new_cl, predict(nt, new_xi, rawsignal = FALSE))

## visualize the optimized neural net
layout(matrix(1:6, 2, 3, TRUE))
plot(nt)
layout(1)