Package ‘e1071’
August 5, 2015
Version 1.6-7
Title Misc Functions of the Department of Statistics, Probability
Theory Group (Formerly: E1071), TU Wien
Imports graphics, grDevices, class, stats, methods, utils
Suggests cluster, mlbench, nnet, randomForest, rpart, SparseM, xtable,
Matrix, MASS
Description Functions for latent class analysis, short time Fourier
transform, fuzzy clustering, support vector machines,
shortest path computation, bagged clustering, naive Bayes
classifier, …
License GPL-2
LazyLoad yes
NeedsCompilation yes
Author David Meyer [aut, cre],
Evgenia Dimitriadou [aut, cph],
Kurt Hornik [aut],
Andreas Weingessel [aut],
Friedrich Leisch [aut],
Chih-Chung Chang [ctb, cph] (libsvm C++-code),
Chih-Chen Lin [ctb, cph] (libsvm C++-code)
Maintainer David Meyer
Repository CRAN
Date/Publication 2015-08-05 18:51:12
R topics documented:
allShortestPaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
bclust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
bincombinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
bootstrap.lca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
boxplot.bclust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
classAgreement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1
2 R topics documented:
cmeans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
countpattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
cshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Discrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
e1071-deprecated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
fclustIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
hamming.distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
hamming.window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
hanning.window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
hsv_palette . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
ica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
impute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
interpolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
lca . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
matchClasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
matchControls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
naiveBayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
plot.stft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
plot.svm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
plot.tune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
predict.svm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
probplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
rbridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
read.matrix.csr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
rectangle.window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
rwiener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
sigmoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
stft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
svm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
tune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
tune.control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
tune.wrapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
write.svm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Index 60
allShortestPaths 3
allShortestPaths Find Shortest Paths Between All Nodes in a Directed Graph
Description
allShortestPaths finds all shortest paths in a directed (or undirected) graph using Floyd’s algo-
rithm. extractPath can be used to actually extract the path between a given pair of nodes.
Usage
allShortestPaths(x)
extractPath(obj, start, end)
Arguments
x matrix or distance object
obj return value of allShortestPaths
start integer, starting point of path
end integer, end point of path
Details
If x is a matrix, then x[i,j] has to be the length of the direct path from point i to point j. If no
direct connection from point i to point j exist, then x[i,j] should be either NA or Inf. Note that
the graph can be directed, hence x[i,j] need not be the same as x[j,i]. The main diagonal of
x is ignored. Alternatively, x can be a distance object as returned by dist (corresponding to an
undirected graph).
Value
allShortestPaths returns a list with components
length A matrix with the total lengths of the shortest path between each pair of points.
middlePoints A matrix giving a point in the middle of each shortest path (or 0 if the direct
connection is the shortest path), this is mainly used as input for extractPath.
extractPath returns a vector of node numbers giving with the shortest path between two points.
Author(s)
Friedrich Leisch
References
Kumar, V., Grama, A., Gupta, A. and Karypis, G. Introduction to Parallel Programming – Design
and Analysis of Algorithms, Benjamin Cummings Publishing, 1994, ISBN 0-8053-3170-0
4 bclust
Examples
## build a graph with 5 nodes
x <- matrix(NA, 5, 5)
diag(x) <- 0
x[1,2] <- 30; x[1,3] <- 10
x[2,4] <- 70; x[2,5] <- 40
x[3,4] <- 50; x[3,5] <- 20
x[4,5] <- 60
x[5,4] <- 10
print(x)
## compute all path lengths
z <- allShortestPaths(x)
print(z)
## the following should give 1 -> 3 -> 5 -> 4
extractPath(z, 1, 4)
bclust Bagged Clustering
Description
Cluster the data in x using the bagged clustering algorithm. A partitioning cluster algorithm such as
kmeans is run repeatedly on bootstrap samples from the original data. The resulting cluster centers
are then combined using the hierarchical cluster algorithm hclust.
Usage
bclust(x, centers=2, iter.base=10, minsize=0,
dist.method=”euclidian”,
hclust.method=”average”, base.method=”kmeans”,
base.centers=20, verbose=TRUE,
final.kmeans=FALSE, docmdscale=FALSE,
resample=TRUE, weights=NULL, maxcluster=base.centers, …)
hclust.bclust(object, x, centers, dist.method=object$dist.method,
hclust.method=object$hclust.method, final.kmeans=FALSE,
docmdscale = FALSE, maxcluster=object$maxcluster)
## S3 method for class ‘bclust’
plot(x, maxcluster=x$maxcluster, main, …)
centers.bclust(object, k)
clusters.bclust(object, k, x=NULL)
Arguments
x Matrix of inputs (or object of class “bclust” for plot).
centers, k Number of clusters.
bclust 5
iter.base Number of runs of the base cluster algorithm.
minsize Minimum number of points in a base cluster.
dist.method Distance method used for the hierarchical clustering, see dist for available dis-
tances.
hclust.method Linkage method used for the hierarchical clustering, see hclust for available
methods.
base.method Partitioning cluster method used as base algorithm.
base.centers Number of centers used in each repetition of the base method.
verbose Output status messages.
final.kmeans If TRUE, a final kmeans step is performed using the output of the bagged cluster-
ing as initialization.
docmdscale Logical, if TRUE a cmdscale result is included in the return value.
resample Logical, if TRUE the base method is run on bootstrap samples of x, else directly
on x.
weights Vector of length nrow(x), weights for the resampling. By default all observa-
tions have equal weight.
maxcluster Maximum number of clusters memberships are to be computed for.
object Object of class “bclust”.
main Main title of the plot.
… Optional arguments top be passed to the base method in bclust, ignored in
plot.
Details
First, iter.base bootstrap samples of the original data in x are created by drawing with replace-
ment. The base cluster method is run on each of these samples with base.centers centers. The
base.method must be the name of a partitioning cluster function returning a list with the same
components as the return value of kmeans.
This results in a collection of iter.base * base.centers centers, which are subsequently clus-
tered using the hierarchical method hclust. Base centers with less than minsize points in there
respective partitions are removed before the hierarchical clustering.
The resulting dendrogram is then cut to produce centers clusters. Hence, the name of the argument
centers is a little bit misleading as the resulting clusters need not be convex, e.g., when single
linkage is used. The name was chosen for compatibility with standard partitioning cluster methods
such as kmeans.
A new hierarchical clustering (e.g., using another hclust.method) re-using previous base runs can
be performed by running hclust.bclust on the return value of bclust.
Value
bclust and hclust.bclust return objects of class “bclust” including the components
hclust Return value of the hierarchical clustering of the collection of base centers (Ob-
ject of class “hclust”).
6 bincombinations
cluster Vector with indices of the clusters the inputs are assigned to.
centers Matrix of centers of the final clusters. Only useful, if the hierarchical clustering
method produces convex clusters.
allcenters Matrix of all iter.base * base.centers centers found in the base runs.
Author(s)
Friedrich Leisch
References
Friedrich Leisch. Bagged clustering. Working Paper 51, SFB “Adaptive Information Systems and
Modeling in Economics and Management Science”, August 1999. http://epub.wu.ac.at/1272/
1/document.pdf
See Also
hclust, kmeans, boxplot.bclust
Examples
data(iris)
bc1 <- bclust(iris[,1:4], 3, base.centers=5)
plot(bc1)
table(clusters.bclust(bc1, 3))
centers.bclust(bc1, 3)
bincombinations Binary Combinations
Description
Returns a matrix containing the 2p vectors of length p.
Usage
bincombinations(p)
Arguments
p Length of binary vectors
Author(s)
Friedrich Leisch
http://epub.wu.ac.at/1272/1/document.pdf
http://epub.wu.ac.at/1272/1/document.pdf
bootstrap.lca 7
Examples
bincombinations(2)
bincombinations(3)
bootstrap.lca Bootstrap Samples of LCA Results
Description
This function draws bootstrap samples from a given LCA model and refits a new LCA model for
each sample. The quality of fit of these models is compared to the original model.
Usage
bootstrap.lca(l, nsamples=10, lcaiter=30, verbose=FALSE)
Arguments
l An LCA model as created by lca
nsamples Number of bootstrap samples
lcaiter Number of LCA iterations
verbose If TRUE some output is printed during the computations.
Details
From a given LCA model l, nsamples bootstrap samples are drawn. For each sample a new LCA
model is fitted. The goodness of fit for each model is computed via Likelihood Ratio and Pearson’s
Chisquare. The values for the fitted models are compared with the values of the original model l.
By this method it can be tested whether the data to which l was originally fitted come from an LCA
model.
Value
An object of class bootstrap.lca is returned, containing
logl, loglsat The LogLikelihood of the models and of the corresponding saturated models
lratio Likelihood quotient of the models and the corresponding saturated models
lratiomean, lratiosd
Mean and Standard deviation of lratio
lratioorg Likelihood quotient of the original model and the corresponding saturated model
zratio Z-Statistics of lratioorg
pvalzratio, pvalratio
P-Values for zratio, computed via normal distribution and empirical distribu-
tion
chisq Pearson’s Chisq of the models
8 boxplot.bclust
chisqmean, chisqsd
Mean and Standard deviation of chisq
chisqorg Pearson’s Chisq of the original model
zchisq Z-Statistics of chisqorg
pvalzchisq, pvalchisq
P-Values for zchisq, computed via normal distribution and empirical distribu-
tion
nsamples Number of bootstrap samples
lcaiter Number of LCA Iterations
Author(s)
Andreas Weingessel
References
Anton K. Formann: “Die Latent-Class-Analysis”, Beltz Verlag 1984
See Also
lca
Examples
## Generate a 4-dim. sample with 2 latent classes of 500 data points each.
## The probabilities for the 2 classes are given by type1 and type2.
type1 <- c(0.8,0.8,0.2,0.2)
type2 <- c(0.2,0.2,0.8,0.8)
x <- matrix(runif(4000),nr=1000)
x[1:500,] <- t(t(x[1:500,])
N
=
||U ||2
N
• F (U ; k) shows the fuzziness or the overlap of the partition and depends on kN elements.
• 1/k ≤ F (U ; k) ≤ 1, where if F (U ; k) = 1 then U is a hard partition and if F (U ; k) =
1/k then U = [1/k] is the centroid of the fuzzy partion space Pfk. The converse is also
valid.
partition.entropy: It is a measure that provides information about the membership matrix without
also considering the data itself. The minimum values imply a good partition in the meaning of
a more crisp partition. H(U ; k) =
∑N
i=1 h(ui)/N , where h(u) = −
∑k
j=1 uj loga(uj) the
Shannon’s entropy.
• H(U ; k) shows the uncertainty of a fuzzy partition and depends also on kN elements.
Specifically, h(ui) is interpreted as the amount of fuzzy information about the member-
ship of xi in k classes that is retained by column uj . Thus, at U = [1/k] the most
information is withheld since the membership is the fuzziest possible.
• 0 ≤ H(U ; k) ≤ loga(k), where forH(U ; k) = 0 U is a hard partition and forH(U ; k) =
loga(k) U = [1/k].
proportion.exponent: It is a measure P (U ; k) of fuzziness adept to detect structural variations in
the partition matrix as it becomes more fuzzier. A crisp cluster in the partition matrix can
drive it to infinity when the partition coefficient and the partition entropy are more sensitive
to small changes when approaching a hard partition. Its evaluation does not also involve the
data or the algorithm used to partition them and its maximum implies the optimal partition but
without knowing what maximum is a statistically significant maximum.
• 0 ≤ P (U ; k) <∞, since the [0, 1] values explode to [0,∞) due to the natural logarithm. Specifically, P = 0 when and only when U = [1/k], while P →∞ when any column of U is crisp. • P (U ; k) can easily explode and it is good for partitions with large column maximums and at detecting structural variations. separation.index (known as CS Index): This index identifies unique cluster structure with well- defined properties that depend on the data and a measure of distance. It answers the question if the clusters are compact and separated, but it rather seems computationally infeasible for big data sets since a distance matrix between all the data membership values has to be calculated. It also presupposes that a hard partition is derived from the fuzzy one. D1(U ; k;X, d) = mini+1≤ l≤ k−1 { min1≤ j≤ k { dis(uj ,ul) max1≤m≤k{dia(um)} }} , where dia is the diameter of the subset, dis the distance of two subsets, and d a metric. U is a CS partition of X ⇔ D1 > 1. When this holds then U is unique.
20 hamming.distance
Value
Returns a vector with the validity measures values.
Author(s)
Evgenia Dimitriadou
References
James C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press,
1981, NY.
L. X. Xie and G. Beni, Validity measure for fuzzy clustering, IEEE Transactions on Pattern Analysis
and Machine Intelligence, vol. 3, n. 8, p. 841-847, 1991.
I. Gath and A. B. Geva, Unsupervised Optimal Fuzzy Clustering, IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 11, n. 7, p. 773-781, 1989.
Y. Fukuyama and M. Sugeno, A new method of choosing the number of clusters for the fuzzy $c$-
means method, Proc. 5th Fuzzy Syst. Symp., p. 247-250, 1989 (in japanese).
See Also
cmeans
Examples
# a 2-dimensional example
x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
matrix(rnorm(100,mean=1,sd=0.3),ncol=2))
cl<-cmeans(x,2,20,verbose=TRUE,method="cmeans")
resultindexes <- fclustIndex(cl,x, index="all")
resultindexes
hamming.distance Hamming Distances of Vectors
Description
If both x and y are vectors, hamming.distance returns the Hamming distance (number of different
elements) between this two vectors. If x is a matrix, the Hamming distances between the rows of x
are computed and y is ignored.
Usage
hamming.distance(x, y)
Arguments
x a vector or matrix.
y an optional vector.
hamming.window 21
Examples
x <- c(1, 0, 0)
y <- c(1, 0, 1)
hamming.distance(x, y)
z <- rbind(x,y)
rownames(z) <- c("Fred", "Tom")
hamming.distance(z)
hamming.distance(1:3, 3:1)
hamming.window Computes the Coefficients of a Hamming Window.
Description
The filter coefficients wi of a Hamming window of length n are computed according to the formula
wi = 0.54− 0.46 cos
2πi
n− 1
Usage
hamming.window(n)
Arguments
n The length of the window.
Value
A vector containing the filter coefficients.
Author(s)
Andreas Weingessel
References
For a definition of the Hamming window, see for example
Alan V. Oppenheim and Roland W. Schafer: "Discrete-Time Signal Processing", Prentice-Hall,
1989.
See Also
stft, hanning.window
22 hanning.window
Examples
hamming.window(10)
x<-rnorm(500)
y<-stft(x, wtype="hamming.window")
plot(y)
hanning.window Computes the Coefficients of a Hanning Window.
Description
The filter coefficients wi of a Hanning window of length n are computed according to the formula
wi = 0.5− 0.5 cos
2πi
n− 1
Usage
hanning.window(n)
Arguments
n The length of the window.
Value
A vector containing the filter coefficients.
Author(s)
Andreas Weingessel
References
For a definition of the Hanning window, see for example
Alan V. Oppenheim and Roland W. Schafer: "Discrete-Time Signal Processing", Prentice-Hall,
1989.
See Also
stft, hamming.window
Examples
hanning.window(10)
x<-rnorm(500)
y<-stft(x, wtype="hanning.window")
plot(y)
hsv_palette 23
hsv_palette Sequential color palette based on HSV colors
Description
Computes a sequential color palette based on HSV colors by varying the saturation, given hue and
value.
Usage
hsv_palette(h = 2/3, from = 0.7, to = 0.2, v = 1)
Arguments
h hue
from lower bound for saturation
to upper bound for saturation
v value
Value
A function with one argument: the size of the palette, i.e., the number of colors.
Author(s)
David Meyer
See Also
hsv
Examples
pie(rep(1, 10), col = hsv_palette()(10))
pie(rep(1, 10), col = hsv_palette(h = 0)(10))
24 ica
ica Independent Component Analysis
Description
This is an R-implementation of the Matlab-Function of Petteri.Pajunen@hut.fi.
For a data matrix X independent components are extracted by applying a nonlinear PCA algorithm.
The parameter fun determines which nonlinearity is used. fun can either be a function or one of the
following strings “negative kurtosis”, “positive kurtosis”, “4th moment” which can be abbreviated to
uniqueness. If fun equals “negative (positive) kurtosis” the function tanh (x-tanh(x)) is used which
provides ICA for sources with negative (positive) kurtosis. For fun == “4th moments” the signed
square function is used.
Usage
ica(X, lrate, epochs=100, ncomp=dim(X)[2], fun=”negative”)
Arguments
X The matrix for which the ICA is to be computed
lrate learning rate
epochs number of iterations
ncomp number of independent components
fun function used for the nonlinear computation part
Value
An object of class “ica” which is a list with components
weights ICA weight matrix
projection Projected data
epochs Number of iterations
fun Name of the used function
lrate Learning rate used
initweights Initial weight matrix
Note
Currently, there is no reconstruction from the ICA subspace to the original input space.
Author(s)
Andreas Weingessel
impute 25
References
Oja et al., “Learning in Nonlinear Constrained Hebbian Networks”, in Proc. ICANN-91, pp. 385–
390.
Karhunen and Joutsensalo, “Generalizations of Principal Component Analysis, Optimization Prob-
lems, and Neural Networks”, Neural Networks, v. 8, no. 4, pp. 549–562, 1995.
impute Replace Missing Values
Description
Replaces missing values of a matrix or dataframe with the medians (what=”median”) or means
(what=”mean”) of the respective columns.
Usage
impute(x, what = c(“median”, “mean”))
Arguments
x A matrix or dataframe.
what What to impute.
Value
A matrix or dataframe.
Author(s)
Friedrich Leisch
Examples
x<- matrix(1:10, ncol=2)
x[c(1,3,7)] <- NA
print(x)
print(impute(x))
26 interpolate
interpolate Interpolate Values of Array
Description
For each row in matrix x, the hypercube of a containing this point is searched. The corners of the
hypercube are linearly interpolated. By default, dimnames(a) is taken to contain the coordinate
values for each point in a. This can be overridden using adims. If method=="constant", the value
of the “lower left” corner of the hypercube is returned.
Usage
interpolate(x, a, adims=lapply(dimnames(a), as.numeric),
method="linear")
Arguments
x Matrix of values at which interpolation shall take place.
a Array of arbitrary dimension.
adims List of the same structure as dimnames(a).
method Interpolation method, one of "linear" or "constant".
Author(s)
Friedrich Leisch
See Also
approx, spline
Examples
x <- seq(0,3,0.2)
z <- outer(x,x, function(x,y) sin(x*y))
dimnames(z) <- list(x,x)
sin(1.1*2.1)
interpolate(c(1.1, 2.1),z)
kurtosis 27
kurtosis Kurtosis
Description
Computes the kurtosis.
Usage
kurtosis(x, na.rm = FALSE, type = 3)
Arguments
x a numeric vector containing the values whose kurtosis is to be computed.
na.rm a logical value indicating whether NA values should be stripped before the com-
putation proceeds.
type an integer between 1 and 3 selecting one of the algorithms for computing skew-
ness detailed below.
Details
If x contains missings and these are not removed, the skewness is NA.
Otherwise, write xi for the non-missing elements of x, n for their number, µ for their mean, s for
their standard deviation, and mr =
∑
i(xi − µ)
r/n for the sample moments of order r.
Joanes and Gill (1998) discuss three methods for estimating kurtosis:
Type 1: g2 = m4/m22 − 3. This is the typical definition used in many older textbooks.
Type 2: G2 = ((n+ 1)g2 + 6) ∗ (n− 1)/((n− 2)(n− 3)). Used in SAS and SPSS.
Type 3: b2 = m4/s4 − 3 = (g2 + 3)(1− 1/n)2 − 3. Used in MINITAB and BMDP.
Only G2 (corresponding to type = 2) is unbiased under normality.
Value
The estimated kurtosis of x.
References
D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The
Statistician, 47, 183–189.
Examples
x <- rnorm(100)
kurtosis(x)
28 lca
lca Latent Class Analysis (LCA)
Description
A latent class analysis with k classes is performed on the data given by x.
Usage
lca(x, k, niter=100, matchdata=FALSE, verbose=FALSE)
Arguments
x Either a data matrix of binary observations or a list of patterns as created by
countpattern
k Number of classes used for LCA
niter Number of Iterations
matchdata If TRUE and x is a data matrix, the class membership of every data point is
returned, otherwise the class membership of every pattern is returned.
verbose If TRUE some output is printed during the computations.
Value
An object of class "lca" is returned, containing
w Probabilities to belong to each class
p Probabilities of a ‘1’ for each variable in each class
matching Depending on matchdata either the class membership of each pattern or of each
data point
logl, loglsat The LogLikelihood of the model and of the saturated model
bic, bicsat The BIC of the model and of the saturated model
chisq Pearson’s Chisq
lhquot Likelihood quotient of the model and the saturated model
n Number of data points.
np Number of free parameters.
Author(s)
Andreas Weingessel
References
Anton K. Formann: “Die Latent-Class-Analysis”, Beltz Verlag 1984
matchClasses 29
See Also
countpattern, bootstrap.lca
Examples
## Generate a 4-dim. sample with 2 latent classes of 500 data points each.
## The probabilities for the 2 classes are given by type1 and type2.
type1 <- c(0.8,0.8,0.2,0.2)
type2 <- c(0.2,0.2,0.8,0.8)
x <- matrix(runif(4000),nr=1000)
x[1:500,] <- t(t(x[1:500,])
Examples
## Categorical data only:
data(HouseVotes84, package = “mlbench”)
model <- naiveBayes(Class ~ ., data = HouseVotes84)
predict(model, HouseVotes84[1:10,])
predict(model, HouseVotes84[1:10,], type = "raw")
pred <- predict(model, HouseVotes84)
table(pred, HouseVotes84$Class)
## using laplace smoothing:
model <- naiveBayes(Class ~ ., data = HouseVotes84, laplace = 3)
pred <- predict(model, HouseVotes84[,-1])
table(pred, HouseVotes84$Class)
## Example of using a contingency table:
data(Titanic)
m <- naiveBayes(Survived ~ ., data = Titanic)
m
predict(m, as.data.frame(Titanic))
## Example with metric predictors:
data(iris)
m <- naiveBayes(Species ~ ., data = iris)
## alternatively:
m <- naiveBayes(iris[,-5], iris[,5])
m
table(predict(m, iris), iris[,5])
permutations All Permutations of Integers 1:n
Description
Returns a matrix containing all permutations of the integers 1:n (one permutation per row).
36 plot.stft
Usage
permutations(n)
Arguments
n Number of element to permute.
Author(s)
Friedrich Leisch
Examples
permutations(3)
plot.stft Plot Short Time Fourier Transforms
Description
An object of class "stft" is plotted as a gray scale image. The x-axis corresponds to time, the
y-axis to frequency. If the default colormap is used, dark regions in the plot correspond to high
values at the particular time/frequency location.
Usage
## S3 method for class 'stft'
plot(x, col = gray(63:0/63), ...)
Arguments
x An object of class "stft" as obtained by the function stft.
col An optional colormap. By default 64 gray values are used, where white corre-
sponds to the minimum value and black to the maximum.
... further arguments to be passed to or from methods.
Value
No return value. This function is only for plotting.
Author(s)
Andreas Weingessel
See Also
stft
plot.svm 37
Examples
x<-rnorm(500)
y<-stft(x)
plot(y)
plot.svm Plot SVM Objects
Description
Generates a scatter plot of the input data of a svm fit for classification models by highlighting the
classes and support vectors. Optionally, draws a filled contour plot of the class regions.
Usage
## S3 method for class 'svm'
plot(x, data, formula, fill = TRUE, grid = 50, slice = list(),
symbolPalette = palette(), svSymbol = "x", dataSymbol = "o", ...)
Arguments
x An object of class svm
data data to visualize. Should be the same used for fitting.
formula formula selecting the visualized two dimensions. Only needed if more than two
input variables are used.
fill switch indicating whether a contour plot for the class regions should be added.
grid granularity for the contour plot.
slice a list of named values for the dimensions held constant (only needed if more
than two variables are used). The defaults for unspecified dimensions are 0 (for
numeric variables) and the first level (for factors). Factor levels can either be
specified as factors or character vectors of length 1.
symbolPalette Color palette used for the class the data points and support vectors belong to.
svSymbol Symbol used for support vectors.
dataSymbol Symbol used for data points (other than support vectors).
... additional graphics parameters passed to filled.contour and plot.
Author(s)
David Meyer
See Also
svm
38 plot.tune
Examples
## a simple example
data(cats, package = “MASS”)
m <- svm(Sex~., data = cats)
plot(m, cats)
## more than two variables: fix 2 dimensions
data(iris)
m2 <- svm(Species~., data = iris)
plot(m2, iris, Petal.Width ~ Petal.Length,
slice = list(Sepal.Width = 3, Sepal.Length = 4))
## plot with custom symbols and colors
plot(m, cats, svSymbol = 1, dataSymbol = 2, symbolPalette = rainbow(4),
color.palette = terrain.colors)
plot.tune Plot Tuning Object
Description
Visualizes the results of parameter tuning.
Usage
## S3 method for class 'tune'
plot(x, type = c("contour", "perspective"), theta = 60,
col = "lightblue", main = NULL, xlab = NULL, ylab = NULL,
swapxy = FALSE, transform.x = NULL, transform.y = NULL,
transform.z = NULL, color.palette = hsv_palette(),
nlevels = 20, ...)
Arguments
x an object of class tune
type choose whether a contour plot or a perspective plot is used if two parameters are
to be visualized. Ignored if only one parameter has been tuned.
theta angle of azimuthal direction.
col the color(s) of the surface facets. Transparent colors are ignored.
main main title
xlab, ylab titles for the axes. N.B. These must be character strings; expressions are not
accepted. Numbers will be coerced to character strings.
swapxy if TRUE, the parameter axes are swaped (only used in case of two parameters).
predict.svm 39
transform.x, transform.y, transform.z
functions to transform the parameters (x and y) and the error measures (z). Ig-
nored if NULL.
color.palette color palette used in contour plot.
nlevels number of levels used in contour plot.
... Further graphics parameters.
Author(s)
David Meyer (based on C/C++-code by Chih-Chung Chang and Chih-Jen Lin)
See Also
tune
Examples
data(iris)
obj <- tune.svm(Species~., data = iris, sampling = "fix",
gamma = 2^c(-8,-4,0,4), cost = 2^c(-8,-4,-2,0))
plot(obj, transform.x = log2, transform.y = log2)
plot(obj, type = "perspective", theta = 120, phi = 45)
predict.svm Predict Method for Support Vector Machines
Description
This function predicts values based upon a model trained by svm.
Usage
## S3 method for class 'svm'
predict(object, newdata, decision.values = FALSE,
probability = FALSE, ..., na.action = na.omit)
Arguments
object Object of class "svm", created by svm.
newdata An object containing the new input data: either a matrix or a sparse matrix (ob-
ject of class Matrix provided by the Matrix package, or of class matrix.csr
provided by the SparseM package, or of class simple_triplet_matrix pro-
vided by the slam package). A vector will be transformed to a n x 1 matrix.
decision.values
Logical controlling whether the decision values of all binary classifiers com-
puted in multiclass classification shall be computed and returned.
40 predict.svm
probability Logical indicating whether class probabilities should be computed and returned.
Only possible if the model was fitted with the probability option enabled.
na.action A function to specify the action to be taken if ‘NA’s are found. The default
action is na.omit, which leads to rejection of cases with missing values on any
required variable. An alternative is na.fail, which causes an error if NA cases
are found. (NOTE: If given, this argument must be named.)
... Currently not used.
Value
A vector of predicted values (for classification: a vector of labels, for density estimation: a logical
vector). If decision.value is TRUE, the vector gets a "decision.values" attribute containing a n
x c matrix (n number of predicted values, c number of classifiers) of all c binary classifiers’ decision
values. There are k * (k - 1) / 2 classifiers (k number of classes). The colnames of the matrix
indicate the labels of the two classes. If probability is TRUE, the vector gets a "probabilities"
attribute containing a n x k matrix (n number of predicted values, k number of classes) of the class
probabilities.
Note
If the training set was scaled by svm (done by default), the new data is scaled accordingly using
scale and center of the training data.
Author(s)
David Meyer (based on C++-code by Chih-Chung Chang and Chih-Jen Lin)
See Also
svm
Examples
data(iris)
attach(iris)
## classification mode
# default with factor response:
model <- svm(Species ~ ., data = iris)
# alternatively the traditional interface:
x <- subset(iris, select = -Species)
y <- Species
model <- svm(x, y, probability = TRUE)
print(model)
summary(model)
# test with train data
probplot 41
pred <- predict(model, x)
# (same as:)
pred <- fitted(model)
# compute decision values and probabilites
pred <- predict(model, x, decision.values = TRUE, probability = TRUE)
attr(pred, "decision.values")[1:4,]
attr(pred, "probabilities")[1:4,]
## try regression mode on two dimensions
# create data
x <- seq(0.1, 5, by = 0.05)
y <- log(x) + rnorm(x, sd = 0.2)
# estimate model and predict input values
m <- svm(x, y)
new <- predict(m, x)
# visualize
plot (x, y)
points (x, log(x), col = 2)
points (x, new, col = 4)
## density-estimation
# create 2-dim. normal with rho=0:
X <- data.frame(a = rnorm(1000), b = rnorm(1000))
attach(X)
# traditional way:
m <- svm(X, gamma = 0.1)
# formula interface:
m <- svm(~., data = X, gamma = 0.1)
# or:
m <- svm(~ a + b, gamma = 0.1)
# test:
newdata <- data.frame(a = c(0, 4), b = c(0, 4))
predict (m, newdata)
# visualize:
plot(X, col = 1:1000 %in% m$index + 1, xlim = c(-5,5), ylim=c(-5,5))
points(newdata, pch = "+", col = 2, cex = 5)
probplot Probability Plot
42 probplot
Description
Generates a probability plot for a specified theoretical distribution, i.e., basically a qqplot where
the y-axis is labeled with probabilities instead of quantiles. The function is mainly intended for
teaching the concept of quantile plots.
Usage
probplot(x, qdist=qnorm, probs=NULL, line=TRUE,
xlab=NULL, ylab="Probability in %", ...)
## S3 method for class 'probplot'
lines(x, h=NULL, v=NULL, bend=FALSE, ...)
Arguments
x A data vector for probplot, an object of class probplot for the lines method.
qdist A character string or a function for the quantiles of the target distribution.
probs Vector of probabilities at which horizontal lines should be drawn.
line Add a line passing through the quartiles to the plot?
xlab, ylab Graphical parameters.
h The y-value for a horizontal line.
v The x-value for a vertical line.
bend If TRUE, lines are “bent” at the quartile line, else regular ablines are added. See
examples.
... Further arguments for qdist and graphical parameters for lines.
Author(s)
Friedrich Leisch
See Also
qqplot
Examples
## a simple example
x <- rnorm(100, mean=5)
probplot(x)
## the same with horizontal tickmarks at the y-axis
opar <- par("las")
par(las=1)
probplot(x)
## this should show the lack of fit at the tails
probplot(x, "qunif")
## for increasing degrees of freedom the t-distribution converges to
rbridge 43
## normal
probplot(x, qt, df=1)
probplot(x, qt, df=3)
probplot(x, qt, df=10)
probplot(x, qt, df=100)
## manually add the line through the quartiles
p <- probplot(x, line=FALSE)
lines(p, col="green", lty=2, lwd=2)
## Make the line at prob=0.5 red
lines(p, h=0.5, col="red")
### The following use the estimted distribution given by the green
### line:
## What is the probability that x is smaller than 7?
lines(p, v=7, bend=TRUE, col="blue")
## Median and 90% confidence interval
lines(p, h=.5, col="red", lwd=3, bend=TRUE)
lines(p, h=c(.05, .95), col="red", lwd=2, lty=3, bend=TRUE)
par(opar)
rbridge Simulation of Brownian Bridge
Description
rwiener returns a time series containing a simulated realization of the Brownian bridge on the
interval [0,end]. If W(t) is a Wiener process, then the Brownian bridge is defined as W(t) - t W(1).
Usage
rbridge(end = 1, frequency = 1000)
Arguments
end the time of the last observation.
frequency the number of observations per unit of time.
See Also
rwiener
44 read.matrix.csr
Examples
# simulate a Brownian bridge on [0,1] and plot it
x <- rbridge()
plot(x,type="l")
read.matrix.csr Read/Write Sparse Data
Description
reads and writes a file in sparse data format.
Usage
read.matrix.csr(file, fac = TRUE, ncol = NULL)
write.matrix.csr(x, file = "out.dat", y = NULL, fac = TRUE)
Arguments
x An object of class matrix.csr
y A vector (either numeric or a factor)
file The filename.
fac If TRUE, the y-values (if any) are interpreted as factor levels.
ncol Number of columns, detected automatically. Can be used to add empty columns
(possibly not stored in the sparse format).
Value
If the data file includes no y variable, read.matrix.csr returns an object of class matrix.csr,
else a list with components:
x object of class matrix.csr
y vector of numeric values or factor levels, depending on fac.
Author(s)
David Meyer
See Also
matrix.csr
rectangle.window 45
Examples
## Not run:
library(methods)
if (require(SparseM)) {
data(iris)
x <- as.matrix(iris[,1:4])
y <- iris[,5]
xs <- as.matrix.csr(x)
write.matrix.csr(xs, y = y, file = "iris.dat")
xs2 <- read.matrix.csr("iris.dat")$x
if (!all(as.matrix(xs) == as.matrix(xs2)))
stop("Error: objects are not equal!")
}
## End(Not run)
rectangle.window Computes the Coefficients of a Rectangle Window.
Description
Returns the filter coefficients of a rectangle window. That is a vector of n 1.
The purpose of this function is just to have a name for the R command rep (1, n).
Usage
rectangle.window(n)
Arguments
n The length of the window.
Value
A vector of length n filled with 1.
Author(s)
Andreas Weingessel
See Also
stft
Examples
x<-rnorm(500)
y<-stft(x, wtype="rectangle.window")
plot(y)
46 sigmoid
rwiener Simulation of Wiener Process
Description
rwiener returns a time series containing a simulated realization of the Wiener process on the inter-
val [0,end]
Usage
rwiener(end = 1, frequency = 1000)
Arguments
end the time of the last observation.
frequency the number of observations per unit of time.
Examples
# simulate a Wiener process on [0,1] and plot it
x <- rwiener()
plot(x,type="l")
sigmoid The Logistic Function and Derivatives
Description
Sigmoid 1/(1 + exp(−x)), first and second derivative.
Usage
sigmoid(x)
dsigmoid(x)
d2sigmoid(x)
Arguments
x a numeric vector
Author(s)
Friedrich Leisch
skewness 47
Examples
plot(sigmoid, -5, 5, ylim = c(-.2, 1))
plot(dsigmoid, -5, 5, add = TRUE, col = 2)
plot(d2sigmoid, -5, 5, add = TRUE, col = 3)
skewness Skewness
Description
Computes the skewness.
Usage
skewness(x, na.rm = FALSE, type = 3)
Arguments
x a numeric vector containing the values whose skewness is to be computed.
na.rm a logical value indicating whether NA values should be stripped before the com-
putation proceeds.
type an integer between 1 and 3 selecting one of the algorithms for computing skew-
ness detailed below.
Details
If x contains missings and these are not removed, the skewness is NA.
Otherwise, write xi for the non-missing elements of x, n for their number, µ for their mean, s for
their standard deviation, and mr =
∑
i(xi − µ)
r/n for the sample moments of order r.
Joanes and Gill (1998) discuss three methods for estimating skewness:
Type 1: g1 = m3/m
3/2
2 . This is the typical definition used in many older textbooks.
Type 2: G1 = g1
√
n(n− 1)/(n− 2). Used in SAS and SPSS.
Type 3: b1 = m3/s3 = g1((n− 1)/n)3/2. Used in MINITAB and BMDP.
All three skewness measures are unbiased under normality.
Value
The estimated skewness of x.
References
D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The
Statistician, 47, 183–189.
48 stft
Examples
x <- rnorm(100)
skewness(x)
stft Computes the Short Time Fourier Transform of a Vector
Description
This function computes the Short Time Fourier Transform of a given vector X.
First, time-slices of length win are extracted from the vector. The shift of one time-slice to the
next one is given by inc. The values of these time-slices are smoothed by mulitplying them with a
window function specified in wtype. For the thus obtained windows, the Fast Fourier Transform is
computed.
Usage
stft(X, win=min(80,floor(length(X)/10)), inc=min(24,
floor(length(X)/30)), coef=64, wtype="hanning.window")
Arguments
X The vector from which the stft is computed.
win Length of the window. For long vectors the default window size is 80, for short
vectors the window size is chosen so that 10 windows fit in the vector.
inc Increment by which the window is shifted. For long vectors the default incre-
ment is 24, for short vectors the increment is chosen so that 30 increments fit in
the vector.
coef Number of Fourier coefficients
wtype Type of window used
Value
Object of type stft. Contains the values of the stft and information about the parameters.
values A matrix containing the results of the stft. Each row of the matrix contains the
coef Fourier coefficients of one window.
windowsize The value of the parameter win
increment The value of the parameter inc
windowtype The value of the parameter wtype
Author(s)
Andreas Weingessel
svm 49
See Also
plot.stft
Examples
x<-rnorm(500)
y<-stft(x)
plot(y)
svm Support Vector Machines
Description
svm is used to train a support vector machine. It can be used to carry out general regression and
classification (of nu and epsilon-type), as well as density-estimation. A formula interface is pro-
vided.
Usage
## S3 method for class 'formula'
svm(formula, data = NULL, ..., subset, na.action =
na.omit, scale = TRUE)
## Default S3 method:
svm(x, y = NULL, scale = TRUE, type = NULL, kernel =
"radial", degree = 3, gamma = if (is.vector(x)) 1 else 1 / ncol(x),
coef0 = 0, cost = 1, nu = 0.5,
class.weights = NULL, cachesize = 40, tolerance = 0.001, epsilon = 0.1,
shrinking = TRUE, cross = 0, probability = FALSE, fitted = TRUE,
..., subset, na.action = na.omit)
Arguments
formula a symbolic description of the model to be fit.
data an optional data frame containing the variables in the model. By default the
variables are taken from the environment which ‘svm’ is called from.
x a data matrix, a vector, or a sparse matrix (object of class Matrix provided by
the Matrix package, or of class matrix.csr provided by the SparseM package,
or of class simple_triplet_matrix provided by the slam package).
y a response vector with one label for each row/component of x. Can be either a
factor (for classification tasks) or a numeric vector (for regression).
scale A logical vector indicating the variables to be scaled. If scale is of length 1, the
value is recycled as many times as needed. Per default, data are scaled internally
(both x and y variables) to zero mean and unit variance. The center and scale
values are returned and used for later predictions.
50 svm
type svm can be used as a classification machine, as a regression machine, or for
novelty detection. Depending of whether y is a factor or not, the default setting
for type is C-classification or eps-regression, respectively, but may be
overwritten by setting an explicit value.
Valid options are:
• C-classification
• nu-classification
• one-classification (for novelty detection)
• eps-regression
• nu-regression
kernel the kernel used in training and predicting. You might consider changing some
of the following parameters, depending on the kernel type.
linear: u′v
polynomial: (γu′v + coef0)degree
radial basis: e( − γ|u− v|2)
sigmoid: tanh(γu′v + coef0)
degree parameter needed for kernel of type polynomial (default: 3)
gamma parameter needed for all kernels except linear (default: 1/(data dimension))
coef0 parameter needed for kernels of type polynomial and sigmoid (default: 0)
cost cost of constraints violation (default: 1)—it is the ‘C’-constant of the regular-
ization term in the Lagrange formulation.
nu parameter needed for nu-classification, nu-regression, and one-classification
class.weights a named vector of weights for the different classes, used for asymmetric class
sizes. Not all factor levels have to be supplied (default weight: 1). All compo-
nents have to be named.
cachesize cache memory in MB (default 40)
tolerance tolerance of termination criterion (default: 0.001)
epsilon epsilon in the insensitive-loss function (default: 0.1)
shrinking option whether to use the shrinking-heuristics (default: TRUE)
cross if a integer value k>0 is specified, a k-fold cross validation on the training data is
performed to assess the quality of the model: the accuracy rate for classification
and the Mean Squared Error for regression
fitted logical indicating whether the fitted values should be computed and included in
the model or not (default: TRUE)
probability logical indicating whether the model should allow for probability predictions.
… additional parameters for the low level fitting function svm.default
subset An index vector specifying the cases to be used in the training sample. (NOTE:
If given, this argument must be named.)
na.action A function to specify the action to be taken if NAs are found. The default action is
na.omit, which leads to rejection of cases with missing values on any required
variable. An alternative is na.fail, which causes an error if NA cases are found.
(NOTE: If given, this argument must be named.)
svm 51
Details
For multiclass-classification with k levels, k>2, libsvm uses the ‘one-against-one’-approach, in
which k(k-1)/2 binary classifiers are trained; the appropriate class is found by a voting scheme.
libsvm internally uses a sparse data representation, which is also high-level supported by the pack-
age SparseM.
If the predictor variables include factors, the formula interface must be used to get a correct model
matrix.
plot.svm allows a simple graphical visualization of classification models.
The probability model for classification fits a logistic distribution using maximum likelihood to
the decision values of all binary classifiers, and computes the a-posteriori class probabilities for
the multi-class problem using quadratic optimization. The probabilistic regression model assumes
(zero-mean) laplace-distributed errors for the predictions, and estimates the scale parameter using
maximum likelihood.
Value
An object of class “svm” containing the fitted model, including:
SV The resulting support vectors (possibly scaled).
index The index of the resulting support vectors in the data matrix. Note that this index
refers to the preprocessed data (after the possible effect of na.omit and subset)
coefs The corresponding coefficients times the training labels.
rho The negative intercept.
sigma In case of a probabilistic regression model, the scale parameter of the hypothe-
sized (zero-mean) laplace distribution estimated by maximum likelihood.
probA, probB numeric vectors of length k(k-1)/2, k number of classes, containing the parame-
ters of the logistic distributions fitted to the decision values of the binary classi-
fiers (1 / (1 + exp(a x + b))).
Note
Data are scaled internally, usually yielding better results.
Parameters of SVM-models usually must be tuned to yield sensible results!
Author(s)
David Meyer (based on C/C++-code by Chih-Chung Chang and Chih-Jen Lin)
References
• Chang, Chih-Chung and Lin, Chih-Jen:
LIBSVM: a library for Support Vector Machines
http://www.csie.ntu.edu.tw/~cjlin/libsvm
http://www.csie.ntu.edu.tw/~cjlin/libsvm
52 svm
• Exact formulations of models, algorithms, etc. can be found in the document:
Chang, Chih-Chung and Lin, Chih-Jen:
LIBSVM: a library for Support Vector Machines
http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.ps.gz
• More implementation details and speed benchmarks can be found on: Rong-En Fan and Pai-
Hsune Chen and Chih-Jen Lin:
Working Set Selection Using the Second Order Information for Training SVM
http://www.csie.ntu.edu.tw/~cjlin/papers/quadworkset.pdf
See Also
predict.svm plot.svm tune.svm matrix.csr (in package SparseM)
Examples
data(iris)
attach(iris)
## classification mode
# default with factor response:
model <- svm(Species ~ ., data = iris)
# alternatively the traditional interface:
x <- subset(iris, select = -Species)
y <- Species
model <- svm(x, y)
print(model)
summary(model)
# test with train data
pred <- predict(model, x)
# (same as:)
pred <- fitted(model)
# Check accuracy:
table(pred, y)
# compute decision values and probabilities:
pred <- predict(model, x, decision.values = TRUE)
attr(pred, "decision.values")[1:4,]
# visualize (classes by color, SV by crosses):
plot(cmdscale(dist(iris[,-5])),
col = as.integer(iris[,5]),
pch = c("o","+")[1:150 %in% model$index + 1])
## try regression mode on two dimensions
# create data
x <- seq(0.1, 5, by = 0.05)
y <- log(x) + rnorm(x, sd = 0.2)
http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.ps.gz
http://www.csie.ntu.edu.tw/~cjlin/papers/quadworkset.pdf
tune 53
# estimate model and predict input values
m <- svm(x, y)
new <- predict(m, x)
# visualize
plot(x, y)
points(x, log(x), col = 2)
points(x, new, col = 4)
## density-estimation
# create 2-dim. normal with rho=0:
X <- data.frame(a = rnorm(1000), b = rnorm(1000))
attach(X)
# traditional way:
m <- svm(X, gamma = 0.1)
# formula interface:
m <- svm(~., data = X, gamma = 0.1)
# or:
m <- svm(~ a + b, gamma = 0.1)
# test:
newdata <- data.frame(a = c(0, 4), b = c(0, 4))
predict (m, newdata)
# visualize:
plot(X, col = 1:1000 %in% m$index + 1, xlim = c(-5,5), ylim=c(-5,5))
points(newdata, pch = "+", col = 2, cex = 5)
# weights: (example not particularly sensible)
i2 <- iris
levels(i2$Species)[3] <- "versicolor"
summary(i2$Species)
wts <- 100 / table(i2$Species)
wts
m <- svm(Species ~ ., data = i2, class.weights = wts)
tune Parameter Tuning of Functions Using Grid Search
Description
This generic function tunes hyperparameters of statistical methods using a grid search over supplied
parameter ranges.
54 tune
Usage
tune(method, train.x, train.y = NULL, data = list(), validation.x =
NULL, validation.y = NULL, ranges = NULL, predict.func = predict,
tunecontrol = tune.control(), ...)
best.tune(...)
Arguments
method either the function to be tuned, or a character string naming such a function.
train.x either a formula or a matrix of predictors.
train.y the response variable if train.x is a predictor matrix. Ignored if train.x is a
formula.
data data, if a formula interface is used. Ignored, if predictor matrix and response are
supplied directly.
validation.x an optional validation set. Depending on whether a formula interface is used or
not, the response can be included in validation.x or separately specified using
validation.y.
validation.y if no formula interface is used, the response of the (optional) validation set.
ranges a named list of parameter vectors spanning the sampling space. The vectors will
usually be created by seq.
predict.func optional predict function, if the standard predict behavior is inadequate.
tunecontrol object of class "tune.control", as created by the function tune.control().
If omitted, tune.control() gives the defaults.
... Further parameters passed to the training functions.
Details
As performance measure, the classification error is used for classification, and the mean squared
error for regression. It is possible to specify only one parameter combination (i.e., vectors of length
1) to obtain an error estimation of the specified type (bootstrap, cross-classification, etc.) on the
given data set. For convenience, there are several tune.foo() wrappers defined, e.g., for nnet(),
randomForest(), rpart(), svm(), and knn().
Cross-validation randomizes the data set before building the splits which—once created—remain
constant during the training process. The splits can be recovered through the train.ind component
of the returned object.
Value
For tune, an object of class tune, including the components:
best.parameters
a 1 x k data frame, k number of parameters.
best.performance
best achieved performance.
performances if requested, a data frame of all parameter combinations along with the corre-
sponding performance results.
tune 55
train.ind list of index vectors used for splits into training and validation sets.
best.model if requested, the model trained on the complete training data using the best pa-
rameter combination.
best.tune() returns the best model detected by tune.
Author(s)
David Meyer
See Also
tune.control, plot.tune, tune.svm, tune.wrapper
Examples
data(iris)
## tune `svm’ for classification with RBF-kernel (default in svm),
## using one split for training/validation set
obj <- tune(svm, Species~., data = iris,
ranges = list(gamma = 2^(-1:1), cost = 2^(2:4)),
tunecontrol = tune.control(sampling = "fix")
)
## alternatively:
## obj <- tune.svm(Species~., data = iris, gamma = 2^(-1:1), cost = 2^(2:4))
summary(obj)
plot(obj)
## tune `knn' using a convenience function; this time with the
## conventional interface and bootstrap sampling:
x <- iris[,-5]
y <- iris[,5]
obj2 <- tune.knn(x, y, k = 1:5, tunecontrol = tune.control(sampling = "boot"))
summary(obj2)
plot(obj2)
## tune `rpart' for regression, using 10-fold cross validation (default)
data(mtcars)
obj3 <- tune.rpart(mpg~., data = mtcars, minsplit = c(5,10,15))
summary(obj3)
plot(obj3)
## simple error estimation for lm using 10-fold cross validation
tune(lm, mpg~., data = mtcars)
56 tune.control
tune.control Control Parameters for the Tune Function
Description
Creates an object of class tune.control to be used with the tune function, containing various
control parameters.
Usage
tune.control(random = FALSE, nrepeat = 1, repeat.aggregate = mean,
sampling = c("cross", "fix", "bootstrap"), sampling.aggregate = mean,
sampling.dispersion = sd,
cross = 10, fix = 2/3, nboot = 10, boot.size = 9/10, best.model = TRUE,
performances = TRUE, error.fun = NULL)
Arguments
random if an integer value is specified, random parameter vectors are drawn from the
parameter space.
nrepeat specifies how often training shall be repeated.
repeat.aggregate
function for aggregating the repeated training results.
sampling sampling scheme. If sampling = "cross", a cross-times cross validation
is performed. If sampling = "boot", nboot training sets of size
boot.size (part) are sampled (with replacement) from the supplied data. If
sampling = "fix", a single split into training/validation set is used,
the training set containing a fix part of the supplied data. Note that a separate
validation set can be supplied via validation.x and validation.y. It is only
used for sampling = "boot" and sampling = "fix"; in the latter case, fix is
set to 1.
sampling.aggregate,sampling.dispersion
functions for aggregating the training results on the generated training samples
(default: mean and standard deviation).
cross number of partitions for cross-validation.
fix part of the data used for training in fixed sampling.
nboot number of bootstrap replications.
boot.size size of the bootstrap samples.
best.model if TRUE, the best model is trained and returned (the best parameter set is used for
training on the complete training set).
performances if TRUE, the performance results for all parameter combinations are returned.
error.fun function returning the error measure to be minimized. It takes two arguments:
a vector of true values and a vector of predicted values. If NULL, the misclassi-
fication error is used for categorical predictions and the mean squared error for
numeric predictions.
tune.wrapper 57
Value
An object of class "tune.control" containing all the above parameters (either the defaults or the
user specified values).
Author(s)
David Meyer
See Also
tune
tune.wrapper Convenience Tuning Wrapper Functions
Description
Convenience tuning wrapper functions, using tune.
Usage
tune.svm(x, y = NULL, data = NULL, degree = NULL, gamma = NULL, coef0 = NULL,
cost = NULL, nu = NULL, class.weights = NULL, epsilon = NULL, …)
best.svm(x, tunecontrol = tune.control(), …)
tune.nnet(x, y = NULL, data = NULL, size = NULL, decay = NULL,
trace = FALSE, tunecontrol = tune.control(nrepeat = 5),
…)
best.nnet(x, tunecontrol = tune.control(nrepeat = 5), …)
tune.rpart(formula, data, na.action = na.omit, minsplit = NULL,
minbucket = NULL, cp = NULL, maxcompete = NULL, maxsurrogate = NULL,
usesurrogate = NULL, xval = NULL, surrogatestyle = NULL, maxdepth =
NULL, predict.func = NULL, …)
best.rpart(formula, tunecontrol = tune.control(), …)
tune.randomForest(x, y = NULL, data = NULL, nodesize = NULL,
mtry = NULL, ntree = NULL, …)
best.randomForest(x, tunecontrol = tune.control(), …)
tune.knn(x, y, k = NULL, l = NULL, …)
58 write.svm
Arguments
formula, x, y, data
formula and data arguments of function to be tuned.
predict.func predicting function.
na.action function handling missingness.
minsplit, minbucket, cp, maxcompete, maxsurrogate, usesurrogate, xval, surrogatestyle, maxdepth
rpart parameters.
degree, gamma, coef0, cost, nu, class.weights, epsilon
svm parameters.
k, l knn parameters.
mtry, nodesize, ntree
randomForest parameters.
size, decay, trace
parameters passed to nnet.
tunecontrol object of class “tune.control” containing tuning parameters.
… Further parameters passed to tune.
Details
For examples, see the help page of tune().
Value
tune.foo() returns a tuning object including the best parameter set obtained by optimizing over
the specified parameter vectors. best.foo() directly returns the best model, i.e. the fit of a new
model using the optimal parameters found by tune.foo.
Author(s)
David Meyer
See Also
tune
write.svm Write SVM Object to File
Description
This function exports an SVM object (trained by svm) to two specified files. One is in the format
that the function ’svm\_load\_model’ of libsvm can read. The other is for scaling data, containing a
data with centers and scales for all variables.
write.svm 59
Usage
write.svm(object, svm.file = “Rdata.svm”,
scale.file = “Rdata.scale”, yscale.file = “Rdata.yscale”)
Arguments
object Object of class “svm”, created by svm.
svm.file filename to export the svm object to.
scale.file filename to export the scaling data of the explanatory variables to.
yscale.file filename to export the scaling data of the dependent variable to, if any.
Details
This function is useful when SVM models trained in R shall be used in other environments. The
SVM model is saved in the standard format of libsvm. The scaling data are written to a separate
file because scaling data are not included in the standard format of libsvm. The format of the
scaling data file is a n times 2 matrix: the n-th row corresponds to the n-th dimension of the data,
the columns being formed of the corresponding mean and scale. If scaling information for the
dependent variable exists (in case of regression models), it is stored in yet another file (1 times 2
matrix).
Author(s)
Tomomi TAKASHINA (based on ’predict.svm’ by David Meyer)
See Also
svm
Examples
data(iris)
attach(iris)
## classification mode
# default with factor response:
model <- svm (Species~., data=iris)
# export SVM object to file
write.svm(model, svm.file = "iris-classifier.svm", scale.file = "iris-classifier.scale")
# read scale file
# the n-th row is corresponding to n-th dimension. The 1st column contains the
# center value, the 2nd column is the scale value.
read.table("iris-classifier.scale")
Index
∗Topic IO
read.matrix.csr, 44
∗Topic arith
interpolate, 26
∗Topic array
element, 17
∗Topic category
classAgreement, 9
matchClasses, 29
naiveBayes, 33
∗Topic classif
naiveBayes, 33
plot.svm, 37
predict.svm, 39
svm, 49
write.svm, 58
∗Topic cluster
bclust, 4
cmeans, 11
cshell, 14
fclustIndex, 18
lca, 28
∗Topic datagen
permutations, 35
∗Topic distribution
Discrete, 16
rbridge, 43
rwiener, 46
∗Topic hplot
boxplot.bclust, 8
hsv_palette, 23
probplot, 41
∗Topic manip
impute, 25
matchControls, 31
∗Topic math
sigmoid, 46
∗Topic misc
e1071-deprecated, 17
∗Topic models
plot.tune, 38
tune, 53
tune.control, 56
tune.wrapper, 57
∗Topic multivariate
bclust, 4
bootstrap.lca, 7
countpattern, 13
hamming.distance, 20
ica, 24
interpolate, 26
lca, 28
∗Topic neural
plot.svm, 37
predict.svm, 39
svm, 49
write.svm, 58
∗Topic nonlinear
plot.svm, 37
predict.svm, 39
svm, 49
write.svm, 58
∗Topic optimize
allShortestPaths, 3
∗Topic ts
hamming.window, 21
hanning.window, 22
plot.stft, 36
rectangle.window, 45
stft, 48
∗Topic univar
kurtosis, 27
moment, 32
skewness, 47
∗Topic utilities
bincombinations, 6
allShortestPaths, 3
approx, 26
60
INDEX 61
bclust, 4, 9
best.nnet (tune.wrapper), 57
best.randomForest (tune.wrapper), 57
best.rpart (tune.wrapper), 57
best.svm (tune.wrapper), 57
best.tune (tune), 53
bincombinations, 6
bootstrap.lca, 7, 29
boxplot, 9
boxplot.bclust, 6, 8
centers.bclust (bclust), 4
classAgreement, 9, 30
clusters.bclust (bclust), 4
cmdscale, 5
cmeans, 11, 20
compareMatchedClasses (matchClasses), 29
countpattern, 13, 28, 29
cshell, 14
d2sigmoid (sigmoid), 46
daisy, 31
ddiscrete (Discrete), 16
Deprecated, 17
Discrete, 16
dist, 3, 5
dsigmoid (sigmoid), 46
e1071-deprecated, 17
element, 17
Extract, 17
extractPath (allShortestPaths), 3
fclustIndex, 18
grep, 31
hamming.distance, 20
hamming.window, 21
hanning.window, 22
hclust, 4–6
hclust.bclust (bclust), 4
hsv, 23
hsv_palette, 23
ica, 24
impute, 25
interpolate, 26
kmeans, 4–6
kurtosis, 27
lca, 7, 8, 28
lines.probplot (probplot), 41
matchClasses, 10, 29
matchControls, 31
Matrix, 39, 49
matrix.csr, 39, 44, 49, 52
mean, 33
moment, 32
naiveBayes, 33
pdiscrete (Discrete), 16
permutations, 35
plot.bclust (bclust), 4
plot.ica (ica), 24
plot.stft, 36
plot.svm, 37, 52
plot.tune, 38, 55
predict.lca (lca), 28
predict.naiveBayes (naiveBayes), 33
predict.svm, 39, 52
print.bootstrap.lca (bootstrap.lca), 7
print.fclust (cmeans), 11
print.ica (ica), 24
print.lca (lca), 28
print.naiveBayes (naiveBayes), 33
print.summary.lca (lca), 28
print.summary.svm (svm), 49
print.summary.tune (tune), 53
print.svm (svm), 49
print.tune (tune), 53
probplot, 41
qdiscrete (Discrete), 16
qqplot, 42
rbridge, 43
rdiscrete (Discrete), 16
read.matrix.csr, 44
rectangle.window, 45
rwiener, 46
sample, 16
sigmoid, 46
simple_triplet_matrix, 39, 49
skewness, 47
spline, 26
62 INDEX
stft, 48
summary.lca (lca), 28
summary.svm (svm), 49
summary.tune (tune), 53
svm, 37, 40, 49, 59
tune, 39, 53, 57, 58
tune.control, 55, 56
tune.knn (tune.wrapper), 57
tune.nnet (tune.wrapper), 57
tune.randomForest (tune.wrapper), 57
tune.rpart (tune.wrapper), 57
tune.svm, 52, 55
tune.svm (tune.wrapper), 57
tune.wrapper, 55, 57
var, 33
write.matrix.csr (read.matrix.csr), 44
write.svm, 58
allShortestPaths
bclust
bincombinations
bootstrap.lca
boxplot.bclust
classAgreement
cmeans
countpattern
cshell
Discrete
e1071-deprecated
element
fclustIndex
hamming.distance
hamming.window
hanning.window
hsv_palette
ica
impute
interpolate
kurtosis
lca
matchClasses
matchControls
moment
naiveBayes
permutations
plot.stft
plot.svm
plot.tune
predict.svm
probplot
rbridge
read.matrix.csr
rectangle.window
rwiener
sigmoid
skewness
stft
svm
tune
tune.control
tune.wrapper
write.svm
Index