Self-Organizing Maps: Batch Algorithm

Description

Kohonen's Self-Organizing Maps are a crude form of multidimensional scaling.

Usage

batchSOM(data, grid = somgrid(), radii, init)

Arguments

Details

The batch SOM algorithm of Kohonen(1995, section 3.14) is used.

Value

An object of class "SOM" with components

References

Kohonen, T. (1995) Self-Organizing Maps. Springer-Verlag.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

somgrid, SOM

Examples

require(graphics)
data(crabs, package = "MASS")

lcrabs <- log(crabs[, 4:8])
crabs.grp <- factor(c("B", "b", "O", "o")[rep(1:4, rep(50,4))])
gr <- somgrid(topo = "hexagonal")
crabs.som <- batchSOM(lcrabs, gr, c(4, 4, 2, 2, 1, 1, 1, 0, 0))
plot(crabs.som)

bins <- as.numeric(knn1(crabs.som$codes, lcrabs, 0:47))
plot(crabs.som$grid, type = "n")
symbols(crabs.som$grid$pts[, 1], crabs.som$grid$pts[, 2],
        circles = rep(0.4, 48), inches = FALSE, add = TRUE)
text(crabs.som$grid$pts[bins, ] + rnorm(400, 0, 0.1),
     as.character(crabs.grp))

Condense training set for k-NN classifier

Description

Condense training set for k-NN classifier

Usage

condense(train, class, store, trace = TRUE)

Arguments

Details

The store set is used to 1-NN classify the rest, and misclassified patterns are added to the store set. The whole set is checked until no additions occur.

Value

Index vector of cases to be retained (the final store set).

References

P. A. Devijver and J. Kittler (1982) Pattern Recognition. A Statistical Approach. Prentice-Hall, pp. 119–121.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

reduce.nn, multiedit

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
keep <- condense(train, cl)
knn(train[keep, , drop=FALSE], test, cl[keep])
keep2 <- reduce.nn(train, keep, cl)
knn(train[keep2, , drop=FALSE], test, cl[keep2])

k-Nearest Neighbour Classification

Description

k-nearest neighbour classification for test set from training set. For each row of the test set, the k nearest (in Euclidean distance) training set vectors are found, and the classification is decided by majority vote, with ties broken at random. If there are ties for the kth nearest vector, all candidates are included in the vote.

Usage

knn(train, test, cl, k = 1, l = 0, prob = FALSE, use.all = TRUE)

Arguments

Value

Factor of classifications of test set. doubt will be returned as NA.

References

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

knn1, knn.cv

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
knn(train, test, cl, k = 3, prob=TRUE)
attributes(.Last.value)

k-Nearest Neighbour Cross-Validatory Classification

Description

k-nearest neighbour cross-validatory classification from training set.

Usage

knn.cv(train, cl, k = 1, l = 0, prob = FALSE, use.all = TRUE)

Arguments

Details

This uses leave-one-out cross validation. For each row of the training set train, the k nearest (in Euclidean distance) other training set vectors are found, and the classification is decided by majority vote, with ties broken at random. If there are ties for the kth nearest vector, all candidates are included in the vote.

Value

Factor of classifications of training set. doubt will be returned as NA.

References

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

knn

Examples

train <- rbind(iris3[,,1], iris3[,,2], iris3[,,3])
cl <- factor(c(rep("s",50), rep("c",50), rep("v",50)))
knn.cv(train, cl, k = 3, prob = TRUE)
attributes(.Last.value)

1-Nearest Neighbour Classification

Description

Nearest neighbour classification for test set from training set. For each row of the test set, the nearest (by Euclidean distance) training set vector is found, and its classification used. If there is more than one nearest, a majority vote is used with ties broken at random.

Usage

knn1(train, test, cl)

Arguments

Value

Factor of classifications of test set.

References

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

knn

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
knn1(train, test, cl)

Learning Vector Quantization 1

Description

Moves examples in a codebook to better represent the training set.

Usage

lvq1(x, cl, codebk, niter = 100 * nrow(codebk$x), alpha = 0.03)

Arguments

Details

Selects niter examples at random with replacement, and adjusts the nearest example in the codebook for each.

Value

A codebook, represented as a list with components x and cl giving the examples and classes.

References

Kohonen, T. (1990) The self-organizing map. Proc. IEEE 78, 1464–1480.

Kohonen, T. (1995) Self-Organizing Maps. Springer, Berlin.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvqinit, olvq1, lvq2, lvq3, lvqtest

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
cd <- lvqinit(train, cl, 10)
lvqtest(cd, train)
cd0 <- olvq1(train, cl, cd)
lvqtest(cd0, train)
cd1 <- lvq1(train, cl, cd0)
lvqtest(cd1, train)

Learning Vector Quantization 2.1

Description

Moves examples in a codebook to better represent the training set.

Usage

lvq2(x, cl, codebk, niter = 100 * nrow(codebk$x), alpha = 0.03,
     win = 0.3)

Arguments

Details

Selects niter examples at random with replacement, and adjusts the nearest two examples in the codebook if one is correct and the other incorrect.

Value

A codebook, represented as a list with components x and cl giving the examples and classes.

References

Kohonen, T. (1990) The self-organizing map. Proc. IEEE 78, 1464–1480.

Kohonen, T. (1995) Self-Organizing Maps. Springer, Berlin.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvqinit, lvq1, olvq1, lvq3, lvqtest

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
cd <- lvqinit(train, cl, 10)
lvqtest(cd, train)
cd0 <- olvq1(train, cl, cd)
lvqtest(cd0, train)
cd2 <- lvq2(train, cl, cd0)
lvqtest(cd2, train)

Learning Vector Quantization 3

Description

Moves examples in a codebook to better represent the training set.

Usage

lvq3(x, cl, codebk, niter = 100*nrow(codebk$x), alpha = 0.03,
     win = 0.3, epsilon = 0.1)

Arguments

Details

Selects niter examples at random with replacement, and adjusts the nearest two examples in the codebook for each.

Value

A codebook, represented as a list with components x and cl giving the examples and classes.

References

Kohonen, T. (1990) The self-organizing map. Proc. IEEE 78, 1464–1480.

Kohonen, T. (1995) Self-Organizing Maps. Springer, Berlin.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvqinit, lvq1, olvq1, lvq2, lvqtest

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
cd <- lvqinit(train, cl, 10)
lvqtest(cd, train)
cd0 <- olvq1(train, cl, cd)
lvqtest(cd0, train)
cd3 <- lvq3(train, cl, cd0)
lvqtest(cd3, train)

Initialize a LVQ Codebook

Description

Construct an initial codebook for LVQ methods.

Usage

lvqinit(x, cl, size, prior, k = 5)

Arguments

Details

Selects size examples from the training set without replacement with proportions proportional to the prior or the original proportions.

Value

A codebook, represented as a list with components x and cl giving the examples and classes.

References

Kohonen, T. (1990) The self-organizing map. Proc. IEEE 78, 1464–1480.

Kohonen, T. (1995) Self-Organizing Maps. Springer, Berlin.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvq1, lvq2, lvq3, olvq1, lvqtest

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
cd <- lvqinit(train, cl, 10)
lvqtest(cd, train)
cd1 <- olvq1(train, cl, cd)
lvqtest(cd1, train)

Classify Test Set from LVQ Codebook

Description

Classify a test set by 1-NN from a specified LVQ codebook.

Usage

lvqtest(codebk, test)

Arguments

Details

Uses 1-NN to classify each test example against the codebook.

Value

Factor of classification for each row of x

References

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvqinit, olvq1

Examples

# The function is currently defined as
function(codebk, test) knn1(codebk$x, test, codebk$cl)

Multiedit for k-NN Classifier

Description

Multiedit for k-NN classifier

Usage

multiedit(x, class, k = 1, V = 3, I = 5, trace = TRUE)

Arguments

Value

Index vector of cases to be retained.

References

P. A. Devijver and J. Kittler (1982) Pattern Recognition. A Statistical Approach. Prentice-Hall, p. 115.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

condense, reduce.nn

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep(1,25),rep(2,25), rep(3,25)), labels=c("s", "c", "v"))
table(cl, knn(train, test, cl, 3))
ind1 <- multiedit(train, cl, 3)
length(ind1)
table(cl, knn(train[ind1, , drop=FALSE], test, cl[ind1], 1))
ntrain <- train[ind1,]; ncl <- cl[ind1]
ind2 <- condense(ntrain, ncl)
length(ind2)
table(cl, knn(ntrain[ind2, , drop=FALSE], test, ncl[ind2], 1))

Optimized Learning Vector Quantization 1

Description

Moves examples in a codebook to better represent the training set.

Usage

olvq1(x, cl, codebk, niter = 40 * nrow(codebk$x), alpha = 0.3)

Arguments

Details

Selects niter examples at random with replacement, and adjusts the nearest example in the codebook for each.

Value

A codebook, represented as a list with components x and cl giving the examples and classes.

References

Kohonen, T. (1990) The self-organizing map. Proc. IEEE 78, 1464–1480.

Kohonen, T. (1995) Self-Organizing Maps. Springer, Berlin.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

lvqinit, lvqtest, lvq1, lvq2, lvq3

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
cd <- lvqinit(train, cl, 10)
lvqtest(cd, train)
cd1 <- olvq1(train, cl, cd)
lvqtest(cd1, train)

Reduce Training Set for a k-NN Classifier

Description

Reduce training set for a k-NN classifier. Used after condense.

Usage

reduce.nn(train, ind, class)

Arguments

Details

All the members of the training set are tried in random order. Any which when dropped do not cause any members of the training set to be wrongly classified are dropped.

Value

Index vector of cases to be retained.

References

Gates, G.W. (1972) The reduced nearest neighbor rule. IEEE Trans. Information Theory IT-18, 431–432.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

condense, multiedit

Examples

train <- rbind(iris3[1:25,,1], iris3[1:25,,2], iris3[1:25,,3])
test <- rbind(iris3[26:50,,1], iris3[26:50,,2], iris3[26:50,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
keep <- condense(train, cl)
knn(train[keep,], test, cl[keep])
keep2 <- reduce.nn(train, keep, cl)
knn(train[keep2,], test, cl[keep2])

Self-Organizing Maps: Online Algorithm

Description

Kohonen's Self-Organizing Maps are a crude form of multidimensional scaling.

Usage

SOM(data, grid = somgrid(), rlen = 10000, alpha, radii, init)

Arguments

Details

alpha and radii can also be lists, in which case each component is used in turn, allowing two- or more phase training.

Value

An object of class "SOM" with components

References

Kohonen, T. (1995) Self-Organizing Maps. Springer-Verlag

Kohonen, T., Hynninen, J., Kangas, J. and Laaksonen, J. (1996) SOM PAK: The self-organizing map program package. Laboratory of Computer and Information Science, Helsinki University of Technology, Technical Report A31.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

somgrid, batchSOM

Examples

require(graphics)
data(crabs, package = "MASS")

lcrabs <- log(crabs[, 4:8])
crabs.grp <- factor(c("B", "b", "O", "o")[rep(1:4, rep(50,4))])
gr <- somgrid(topo = "hexagonal")
crabs.som <- SOM(lcrabs, gr)
plot(crabs.som)

## 2-phase training
crabs.som2 <- SOM(lcrabs, gr,
    alpha = list(seq(0.05, 0, length.out = 1e4), seq(0.02, 0, length.out = 1e5)),
    radii = list(seq(8, 1, length.out = 1e4), seq(4, 1, length.out = 1e5)))
plot(crabs.som2)

Plot SOM Fits

Description

Plotting functions for SOM results.

Usage

somgrid(xdim = 8, ydim = 6, topo = c("rectangular", "hexagonal"))

## S3 method for class 'somgrid'
plot(x, type = "p", ...)

## S3 method for class 'SOM'
plot(x, ...)

Arguments

Details

The class "somgrid" records the coordinates of the grid to be used for (batch or on-line) SOM: this has a plot method.

The plot method for class "SOM" plots a stars plot of the representative at each grid point.

Value

For somgrid, an object of class "somgrid", a list with components

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

batchSOM, SOM