Package 'amap' reference manual

Package 'amap'

Title:	Another Multidimensional Analysis Package
Description:	Tools for Clustering and Principal Component Analysis (With robust methods, and parallelized functions).
Authors:	Antoine Lucas
Maintainer:	Antoine Lucas <[email protected]>
License:	GPL
Version:	0.8-19
Built:	2024-08-22 06:32:37 UTC
Source:	CRAN

Title:

Another Multidimensional Analysis Package

Description:

Tools for Clustering and Principal Component Analysis (With robust methods, and parallelized functions).

Authors:

Antoine Lucas

Maintainer:

Antoine Lucas <[email protected]>

License:

GPL

Version:

0.8-19

Built:

2024-08-22 06:32:37 UTC

Source:

CRAN

Principal component analysis

Description

Principal component analysis

Usage

acp(x,center=TRUE,reduce=TRUE,wI=rep(1,nrow(x)),wV=rep(1,ncol(x)))
pca(x,center=TRUE,reduce=TRUE,wI=rep(1,nrow(x)),wV=rep(1,ncol(x)))
## S3 method for class 'acp'
print(x, ...) 
acp(x,center=TRUE,reduce=TRUE,wI=rep(1,nrow(x)),wV=rep(1,ncol(x)))
pca(x,center=TRUE,reduce=TRUE,wI=rep(1,nrow(x)),wV=rep(1,ncol(x)))
## S3 method for class 'acp'
print(x, ...)

Arguments

`x`	Matrix / data frame
`center`	a logical value indicating whether we center data
`reduce`	a logical value indicating whether we "reduce" data i.e. divide each column by standard deviation
`wI`, `wV`	weigth vector for individuals / variables
`...`	arguments to be passed to or from other methods.

Details

This function offer a variant of princomp and prcomp functions, with a slightly different graphic representation (see plot.acp).

Value

An object of class acp The object is a list with components:

`sdev`	the standard deviations of the principal components.
`loadings`	the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). This is of class `"loadings"`: see `loadings` for its `print` method.
`scores`	if `scores = TRUE`, the scores of the supplied data on the principal components.
`eig`	Eigen values

Author(s)

Antoine Lucas

Examples

data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acp(lubisch)
plot(p)
data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acp(lubisch)
plot(p)

Generalised principal component analysis

Description

Generalised principal component analysis

Usage

acpgen(x,h1,h2,center=TRUE,reduce=TRUE,kernel="gaussien")
K(u,kernel="gaussien")
W(x,h,D=NULL,kernel="gaussien")
acpgen(x,h1,h2,center=TRUE,reduce=TRUE,kernel="gaussien")
K(u,kernel="gaussien")
W(x,h,D=NULL,kernel="gaussien")

Arguments

`x`	Matrix or data frame
`h`	Scalar: bandwidth of the Kernel
`h1`	Scalar: bandwidth of the Kernel for W
`h2`	Scalar: bandwidth of the Kernel for U
`kernel`	The kernel used. This must be one of '"gaussien"', '"quartic"', '"triweight"', '"epanechikov"' , '"cosinus"' or '"uniform"'
`center`	A logical value indicating whether we center data
`reduce`	A logical value indicating whether we "reduce" data i.e. divide each column by standard deviation
`D`	A product scalar matrix / une matrice de produit scalaire
`u`	Vector

Details

acpgen compute generalised pca. i.e. spectral analysis of $U_n . W_n^{-1}$ , and project $X_i$ with $W_n^{-1}$ on the principal vector sub-spaces.

$X_i$ a column vector of $p$ variables of individu $i$ (input data)

W compute estimation of noise in the variance.

$W_n=\frac{\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}K(||X_i-X_j||_{V_n^{-1}}/h)(X_i-X_j)(X_i-X_j)'}{\sum_{i=1}^{n-1}\sum_{j=i+1}^{n}K(||X_i-X_j||_{V_n^{-1}}/h)}$

with $V_n$ variance estimation;

U compute robust variance. $U_n^{-1} = S_n^{-1} - 1/h V_n^{-1}$

$S_n=\frac{\sum_{i=1}^{n}K(||X_i||_{V_n^{-1}}/h)(X_i-\mu_n)(X_i-\mu_n)'}{\sum_{i=1}^nK(||X_i||_{V_n^{-1}}/h)}$

with $\mu_n$ estimator of the mean.

K compute kernel, i.e.

gaussien:

$\frac{1}{\sqrt{2\pi}} e^{-u^2/2}$

quartic:

$\frac{15}{16}(1-u^2)^2 I_{|u|\leq 1}$

triweight:

$\frac{35}{32}(1-u^2)^3 I_{|u|\leq 1}$

epanechikov:

$\frac{3}{4}(1-u^2) I_{|u|\leq 1}$

cosinus:

$\frac{\pi}{4}\cos(\frac{\pi}{2}u) I_{|u|\leq 1}$

Value

An object of class acp The object is a list with components:

`sdev`	the standard deviations of the principal components.
`loadings`	the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). This is of class `"loadings"`: see `loadings` for its `print` method.
`scores`	if `scores = TRUE`, the scores of the supplied data on the principal components.
`eig`	Eigen values

Author(s)

Antoine Lucas

References

H. Caussinus, M. Fekri, S. Hakam and A. Ruiz-Gazen, A monitoring display of multivariate outliers Computational Statistics & Data Analysis, Volume 44, Issues 1-2, 28 October 2003, Pages 237-252

Caussinus, H and Ruiz-Gazen, A. (1993): Projection Pursuit and Generalized Principal Component Analyses, in New Directions in Statistical Data Analysis and Robustness (eds. Morgenthaler et al.), pp. 35-46. Birk\"auser Verlag Basel.

Caussinus, H. and Ruiz-Gazen, A. (1995). Metrics for Finding Typical Structures by Means of Principal Component Analysis. In Data Science and its Applications (eds Y. Escoufier and C. Hayashi), pp. 177-192. Tokyo: Academic Press.

Antoine Lucas and Sylvain Jasson, Using amap and ctc Packages for Huge Clustering, R News, 2006, vol 6, issue 5 pages 58-60.

Examples

data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acpgen(lubisch,h1=1,h2=1/sqrt(2))
plot(p,main='ACP robuste des individus')

# See difference with acp

p <- princomp(lubisch)
class(p)<- "acp"

data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acpgen(lubisch,h1=1,h2=1/sqrt(2))
plot(p,main='ACP robuste des individus')

# See difference with acp

p <- princomp(lubisch)
class(p)<- "acp"

Robust principal component analysis

Description

Robust principal component analysis

Usage

acprob(x,h,center=TRUE,reduce=TRUE,kernel="gaussien")
acprob(x,h,center=TRUE,reduce=TRUE,kernel="gaussien")

Arguments

`x`	Matrix / data frame
`h`	Scalar: bandwidth of the Kernel
`kernel`	The kernel used. This must be one of '"gaussien"', '"quartic"', '"triweight"', '"epanechikov"' , '"cosinus"' or '"uniform"'
`center`	A logical value indicating whether we center data
`reduce`	A logical value indicating whether we "reduce" data i.e. divide each column by standard deviation

Details

acpgen compute robust pca. i.e. spectral analysis of a robust variance instead of usual variance. Robust variance: see varrob

Value

An object of class acp The object is a list with components:

`sdev`	the standard deviations of the principal components.
`loadings`	the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). This is of class `"loadings"`: see `loadings` for its `print` method.
`scores`	if `scores = TRUE`, the scores of the supplied data on the principal components.
`eig`	Eigen values

Author(s)

Antoine Lucas

References

H. Caussinus, M. Fekri, S. Hakam and A. Ruiz-Gazen, A monitoring display of multivariate outliers Computational Statistics & Data Analysis, Volume 44, Issues 1-2, 28 October 2003, Pages 237-252

Antoine Lucas and Sylvain Jasson, Using amap and ctc Packages for Huge Clustering, R News, 2006, vol 6, issue 5 pages 58-60.

Correspondance factorial analysis.

Description

Compute an acp on a contingency table tacking into account weight of rows and columns

Usage

afc(x)
afc(x)

Arguments

`x`	A contingency table, or a result of function `burt` or `matlogic`

Author(s)

Antoine Lucas

Examples

## Not run: 
color <- as.factor(c('blue','red','red','blue','red'))
size <- as.factor(c('large','large','small','medium','large'))
x <- data.frame(color,size)

afc.1 <- afc(burt(x))
afc.2 <- afc(matlogic(x))

plotAll(afc.1)
plotAll(afc.2)

## End(Not run)
## Not run: 
color <- as.factor(c('blue','red','red','blue','red'))
size <- as.factor(c('large','large','small','medium','large'))
x <- data.frame(color,size)

afc.1 <- afc(burt(x))
afc.2 <- afc(matlogic(x))

plotAll(afc.1)
plotAll(afc.2)

## End(Not run)

Compute burt table from a factor dataframe.

Description

matlogic returns for all variables a matrix of logical values for each levels. burt is defined as t(matlogic).matlogic

Usage

burt(x)
matlogic(x)
burt(x)
matlogic(x)

Arguments

`x`	A dataframe that contents only factors

Author(s)

Antoine Lucas

Examples

color <- as.factor(c('blue','red','red','blue','red'))
size <- as.factor(c('large','large','small','medium','large'))
x <- data.frame(color,size)

matlogic(x)
##  color.blue color.red size.large size.medium size.small
##1          1         0          1           0          0
##2          0         1          1           0          0
##3          0         1          0           0          1
##4          1         0          0           1          0
##5          0         1          1           0          0

burt(x)
##              color.blue color.red size.large size.medium size.small
##  color.blue           2         0          1           1          0
##  color.red            0         3          2           0          1
##  size.large           1         2          3           0          0
##  size.medium          1         0          0           1          0
##  size.small           0         1          0           0          1
color <- as.factor(c('blue','red','red','blue','red'))
size <- as.factor(c('large','large','small','medium','large'))
x <- data.frame(color,size)

matlogic(x)
##  color.blue color.red size.large size.medium size.small
##1          1         0          1           0          0
##2          0         1          1           0          0
##3          0         1          0           0          1
##4          1         0          0           1          0
##5          0         1          1           0          0

burt(x)
##              color.blue color.red size.large size.medium size.small
##  color.blue           2         0          1           1          0
##  color.red            0         3          2           0          1
##  size.large           1         2          3           0          0
##  size.medium          1         0          0           1          0
##  size.small           0         1          0           0          1

Compute a dissimilarity matrix

Description

Compute a dissimilarity matrix from a data set (containing only factors).

Usage

diss(x, w=rep(1,ncol(x)) )
diss(x, w=rep(1,ncol(x)) )

Arguments

`x`	A matrix or data frame containing only factors.
`w`	A vector of weight, by default each variable has got same weight

Details

Case of N individuals described by P categorical variables: each element (i,j) of the signed similarities array is computed by sommation over the P variables of the contributions of each variable, multiplied by the weight of the variable. The contribution of a given categorical variable is +1 if the individual i and j are in the same class, and is -1 if they are not.

Value

A dissimilarity matrix.

Author(s)

Antoine Lucas

Examples

data <-
matrix(c(1,1,1,1,1
        ,1,2,1,2,1
        ,2,3,2,3,2
        ,2,4,3,3,2
        ,1,2,4,2,1
        ,2,3,2,3,1),ncol=5,byrow=TRUE)

diss(data)

## With weights
diss(data,w=c(1,1,2,2,3))

data <-
matrix(c(1,1,1,1,1
        ,1,2,1,2,1
        ,2,3,2,3,2
        ,2,4,3,3,2
        ,1,2,4,2,1
        ,2,3,2,3,1),ncol=5,byrow=TRUE)

diss(data)

## With weights
diss(data,w=c(1,1,2,2,3))

Distance Matrix Computation

Description

This function computes and returns the distance matrix computed by using the specified distance measure to compute the distances between the rows of a data matrix.

Usage

Dist(x, method = "euclidean", nbproc = 2, diag = FALSE, upper = FALSE)
Dist(x, method = "euclidean", nbproc = 2, diag = FALSE, upper = FALSE)

Arguments

`x`	numeric matrix or (data frame) or an object of class "exprSet". Distances between the rows of `x` will be computed.
`method`	the distance measure to be used. This must be one of `"euclidean"`, `"maximum"`, `"manhattan"`, `"canberra"`, `"binary"`, `"pearson"`, `"abspearson"`, `"correlation"`, `"abscorrelation"`, `"spearman"` or `"kendall"`. Any unambiguous substring can be given.
`nbproc`	integer, Number of subprocess for parallelization
`diag`	logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist`.
`upper`	logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist`.

Details

Available distance measures are (written for two vectors $x$ and $y$ ):

euclidean:

Usual square distance between the two vectors (2 norm).

maximum:

Maximum distance between two components of $x$ and $y$ (supremum norm)

manhattan:

Absolute distance between the two vectors (1 norm).

canberra:

$\sum_i |x_i - y_i| / |x_i + y_i|$ . Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.

binary:

(aka asymmetric binary): The vectors are regarded as binary bits, so non-zero elements are ‘on’ and zero elements are ‘off’. The distance is the proportion of bits in which only one is on amongst those in which at least one is on.

pearson:

Also named "not centered Pearson" $1 - \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2 % \sum_i y_i^2}}$ .

abspearson:

Absolute Pearson $1 - \left| \frac{\sum_i x_i y_i}{\sqrt{\sum_i x_i^2 % \sum_i y_i^2}} \right|$ .

correlation:

Also named "Centered Pearson" $1 - corr(x,y)$ .

abscorrelation:

Absolute correlation $1 - | corr(x,y) |$ with

$corr(x,y) = \frac{\sum_i x_i y_i -\frac1n \sum_i x_i \sum_i% y_i}{% frac: 2nd part \sqrt{\left(\sum_i x_i^2 -\frac1n \left( \sum_i x_i \right)^2 % \right)% \left( \sum_i y_i^2 -\frac1n \left( \sum_i y_i \right)^2 % \right)} }$ .

spearman:

Compute a distance based on rank. $\sum(d_i^2)$ where $d_i$ is the difference in rank between $x_i$ and $y_i$ .

Dist(x,method="spearman")[i,j] =

cor.test(x[i,],x[j,],method="spearman")$statistic

kendall:

Compute a distance based on rank. $\sum_{i,j} K_{i,j}(x,y)$ with $K_{i,j}(x,y)$ is 0 if $x_i, x_j$ in same order as $y_i,y_j$ , 1 if not.

Missing values are allowed, and are excluded from all computations involving the rows within which they occur. If some columns are excluded in calculating a Euclidean, Manhattan or Canberra distance, the sum is scaled up proportionally to the number of columns used. If all pairs are excluded when calculating a particular distance, the value is NA.

The functions as.matrix.dist() and as.dist() can be used for conversion between objects of class "dist" and conventional distance matrices and vice versa.

Value

An object of class "dist".

The lower triangle of the distance matrix stored by columns in a vector, say do. If n is the number of observations, i.e., n <- attr(do, "Size"), then for $i < j <= n$ , the dissimilarity between (row) i and j is do[n*(i-1) - i*(i-1)/2 + j-i]. The length of the vector is $n*(n-1)/2$ , i.e., of order $n^2$ .

The object has the following attributes (besides "class" equal to "dist"):

`Size`	integer, the number of observations in the dataset.
`Labels`	optionally, contains the labels, if any, of the observations of the dataset.
`Diag`, `Upper`	logicals corresponding to the arguments `diag` and `upper` above, specifying how the object should be printed.
`call`	optionally, the `call` used to create the object.
`methods`	optionally, the distance method used; resulting form `dist()`, the (`match.arg()`ed) `method` argument.

Note

Multi-thread (parallelisation) is disable on Windows.

References

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. London: Academic Press.

Wikipedia https://en.wikipedia.org/wiki/Kendall_tau_distance

Examples

x <- matrix(rnorm(100), nrow=5)
Dist(x)
Dist(x, diag = TRUE)
Dist(x, upper = TRUE)


## compute dist with 8 threads
Dist(x,nbproc=8)


Dist(x,method="abscorrelation")
Dist(x,method="kendall")

x <- matrix(rnorm(100), nrow=5)
Dist(x)
Dist(x, diag = TRUE)
Dist(x, upper = TRUE)


## compute dist with 8 threads
Dist(x,nbproc=8)


Dist(x,method="abscorrelation")
Dist(x,method="kendall")

Hierarchical Clustering

Description

Hierarchical cluster analysis.

Usage

hcluster(x, method = "euclidean", diag = FALSE, upper = FALSE,
         link = "complete", members = NULL, nbproc = 2,
         doubleprecision = TRUE)
hcluster(x, method = "euclidean", diag = FALSE, upper = FALSE,
         link = "complete", members = NULL, nbproc = 2,
         doubleprecision = TRUE)

Arguments

`x`	A numeric matrix of data, or an object that can be coerced to such a matrix (such as a numeric vector or a data frame with all numeric columns). Or an object of class "exprSet".
`method`	the distance measure to be used. This must be one of `"euclidean"`, `"maximum"`, `"manhattan"`, `"canberra"`, `"binary"`, `"pearson"`, `"abspearson"`, `"correlation"`, `"abscorrelation"`, `"spearman"` or `"kendall"`. Any unambiguous substring can be given.
`diag`	logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist`.
`upper`	logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist`.
`link`	the agglomeration method to be used. This should be (an unambiguous abbreviation of) one of `"ward"`, `"single"`, `"complete"`, `"average"`, `"mcquitty"`, `"median"` or `"centroid"`,`"centroid2"`.
`members`	`NULL` or a vector with length size of `d`.
`nbproc`	integer, number of subprocess for parallelization [Linux & Mac only]
`doubleprecision`	True: use of double precision for distance matrix computation; False: use simple precision

Details

This function is a mix of function hclust and function dist. hcluster(x, method = "euclidean",link = "complete") = hclust(dist(x, method = "euclidean"),method = "complete")) It use twice less memory, as it doesn't store distance matrix.

For more details, see documentation of hclust and Dist.

Value

An object of class hclust which describes the tree produced by the clustering process. The object is a list with components:

`merge`	an $n-1$ by 2 matrix. Row $i$ of `merge` describes the merging of clusters at step $i$ of the clustering. If an element $j$ in the row is negative, then observation $-j$ was merged at this stage. If $j$ is positive then the merge was with the cluster formed at the (earlier) stage $j$ of the algorithm. Thus negative entries in `merge` indicate agglomerations of singletons, and positive entries indicate agglomerations of non-singletons.
`height`	a set of $n-1$ non-decreasing real values. The clustering height: that is, the value of the criterion associated with the clustering `method` for the particular agglomeration.
`order`	a vector giving the permutation of the original observations suitable for plotting, in the sense that a cluster plot using this ordering and matrix `merge` will not have crossings of the branches.
`labels`	labels for each of the objects being clustered.
`call`	the call which produced the result.
`method`	the cluster method that has been used.
`dist.method`	the distance that has been used to create `d` (only returned if the distance object has a `"method"` attribute).

There is a print and a plot method for hclust objects. The plclust() function is basically the same as the plot method, plot.hclust, primarily for back compatibility with S-plus. Its extra arguments are not yet implemented.

Note

Multi-thread (parallelisation) is disable on Windows.

Author(s)

The hcluster function is based on C code adapted from Cran Fortran routine by Antoine Lucas.

References

Antoine Lucas and Sylvain Jasson, Using amap and ctc Packages for Huge Clustering, R News, 2006, vol 6, issue 5 pages 58-60.

Examples


data(USArrests)
hc <- hcluster(USArrests,link = "ave")
plot(hc)
plot(hc, hang = -1)

## Do the same with centroid clustering and squared Euclidean distance,
## cut the tree into ten clusters and reconstruct the upper part of the
## tree from the cluster centers.
hc <- hclust(dist(USArrests)^2, "cen")
memb <- cutree(hc, k = 10)
cent <- NULL
for(k in 1:10){
  cent <- rbind(cent, colMeans(USArrests[memb == k, , drop = FALSE]))
}
hc1 <- hclust(dist(cent)^2, method = "cen", members = table(memb))
opar <- par(mfrow = c(1, 2))
plot(hc,  labels = FALSE, hang = -1, main = "Original Tree")
plot(hc1, labels = FALSE, hang = -1, main = "Re-start from 10 clusters")
par(opar)


## other combinaison are possible

hc <- hcluster(USArrests,method = "euc",link = "ward", nbproc= 1,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "max",link = "single", nbproc= 2,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "man",link = "complete", nbproc= 1,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "can",link = "average", nbproc= 2,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "bin",link = "mcquitty", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "pea",link = "median", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "abspea",link = "median", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "cor",link = "centroid", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "abscor",link = "centroid", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "spe",link = "complete", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "ken",link = "complete", nbproc= 2,
doubleprecision = FALSE)



data(USArrests)
hc <- hcluster(USArrests,link = "ave")
plot(hc)
plot(hc, hang = -1)

## Do the same with centroid clustering and squared Euclidean distance,
## cut the tree into ten clusters and reconstruct the upper part of the
## tree from the cluster centers.
hc <- hclust(dist(USArrests)^2, "cen")
memb <- cutree(hc, k = 10)
cent <- NULL
for(k in 1:10){
  cent <- rbind(cent, colMeans(USArrests[memb == k, , drop = FALSE]))
}
hc1 <- hclust(dist(cent)^2, method = "cen", members = table(memb))
opar <- par(mfrow = c(1, 2))
plot(hc,  labels = FALSE, hang = -1, main = "Original Tree")
plot(hc1, labels = FALSE, hang = -1, main = "Re-start from 10 clusters")
par(opar)


## other combinaison are possible

hc <- hcluster(USArrests,method = "euc",link = "ward", nbproc= 1,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "max",link = "single", nbproc= 2,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "man",link = "complete", nbproc= 1,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "can",link = "average", nbproc= 2,
doubleprecision = TRUE)
hc <- hcluster(USArrests,method = "bin",link = "mcquitty", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "pea",link = "median", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "abspea",link = "median", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "cor",link = "centroid", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "abscor",link = "centroid", nbproc= 1,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "spe",link = "complete", nbproc= 2,
doubleprecision = FALSE)
hc <- hcluster(USArrests,method = "ken",link = "complete", nbproc= 2,
doubleprecision = FALSE)

K-Means Clustering

Description

Perform k-means clustering on a data matrix.

Usage

Kmeans(x, centers, iter.max = 10, nstart = 1,
         method = "euclidean")
Kmeans(x, centers, iter.max = 10, nstart = 1,
         method = "euclidean")

Arguments

`x`	A numeric matrix of data, or an object that can be coerced to such a matrix (such as a numeric vector or a data frame with all numeric columns). Or an object of class "exprSet".
`centers`	Either the number of clusters or a set of initial cluster centers. If the first, a random set of rows in `x` are chosen as the initial centers.
`iter.max`	The maximum number of iterations allowed.
`nstart`	If `centers` is a number, how many random sets should be chosen?
`method`	the distance measure to be used. This must be one of `"euclidean"`, `"maximum"`, `"manhattan"`, `"canberra"`, `"binary"`, `"pearson"` , `"abspearson"` , `"abscorrelation"`, `"correlation"`, `"spearman"` or `"kendall"`. Any unambiguous substring can be given.

Details

The data given by x is clustered by the k-means algorithm. When this terminates, all cluster centres are at the mean of their Voronoi sets (the set of data points which are nearest to the cluster centre).

The algorithm of Lloyd–Forgy is used; method="euclidean" should return same result as with function kmeans.

Value

A list with components:

`cluster`	A vector of integers indicating the cluster to which each point is allocated.
`centers`	A matrix of cluster centres.
`withinss`	The within-cluster sum of square distances for each cluster.
`size`	The number of points in each cluster.

Note

An objective: to allow NA values.

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))
colnames(x) <- c("x", "y")
(cl <- Kmeans(x, 2))
plot(x, col = cl$cluster)
points(cl$centers, col = 1:2, pch = 8, cex=2)

## random starts do help here with too many clusters
(cl <- Kmeans(x, 5, nstart = 25))
plot(x, col = cl$cluster)
points(cl$centers, col = 1:5, pch = 8)


Kmeans(x, 5,nstart = 25, method="abscorrelation")


## a 2-dimensional example
x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2),
           matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
(cl <- Kmeans(x, 2))
plot(x, col = cl$cluster)
points(cl$centers, col = 1:2, pch = 8, cex=2)

## random starts do help here with too many clusters
(cl <- Kmeans(x, 5, nstart = 25))
plot(x, col = cl$cluster)
points(cl$centers, col = 1:5, pch = 8)


Kmeans(x, 5,nstart = 25, method="abscorrelation")

Dataset Lubischew

Description

Lubischew data (1962): 74 insects, 6 morphologic size. 3 supposed classes

Usage

data(lubisch)
data(lubisch)

Graphics for Principal component Analysis

Description

Graphics for Principal component Analysis

Usage

## S3 method for class 'acp'
plot(x,i=1,j=2,text=TRUE,label='Composants',col='darkblue',
main='Individuals PCA',variables=TRUE,individual.label=NULL,...)
## S3 method for class 'acp'
biplot(x,i=1,j=2,label='Composants',col='darkblue',length=0.1,
main='Variables PCA',circle=TRUE,...)
plot2(x,pourcent=FALSE,eigen=TRUE,label='Comp.',col='lightgrey',
main='Scree Graph',ylab='Eigen Values')
plotAll(x)
## S3 method for class 'acp'
plot(x,i=1,j=2,text=TRUE,label='Composants',col='darkblue',
main='Individuals PCA',variables=TRUE,individual.label=NULL,...)
## S3 method for class 'acp'
biplot(x,i=1,j=2,label='Composants',col='darkblue',length=0.1,
main='Variables PCA',circle=TRUE,...)
plot2(x,pourcent=FALSE,eigen=TRUE,label='Comp.',col='lightgrey',
main='Scree Graph',ylab='Eigen Values')
plotAll(x)

Arguments

`x`	Result of acp or princomp
`i`	X axis
`j`	Y axis
`text`	a logical value indicating whether we use text or points for plot
`pourcent`	a logical value indicating whether we use pourcentage of values
`eigen`	a logical value indicating whether we use eigen values or standard deviation
`label`	label for X and Y axis
`individual.label`	labels naming individuals
`col`	Color of plot
`main`	Title of graphic
`ylab`	Y label
`length`	length of arrows
`variables`, `circle`	a logical value indicating whether we display circle or variables
`...`	cex, pch, and other options; see points.

Value

Graphics:

plot.acp PCA for lines (individuals)

plot.acp PCA for columns (variables)

plot2 Eigen values diagram (Scree Graph)

plotAll Plot both 3 graphs

Author(s)

Antoine Lucas

Examples

data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acp(lubisch)
plotAll(p)
data(lubisch)
lubisch <- lubisch[,-c(1,8)]
p <- acp(lubisch)
plotAll(p)

Optimal Partition (classification).

Description

Classification: Computing an Optimal Partition from Weighted Categorical Variables or from an Array of Signed Similarities.

Usage

pop(x,fmbvr=TRUE,triabs=TRUE,allsol=TRUE)
pop(x,fmbvr=TRUE,triabs=TRUE,allsol=TRUE)

Arguments

`x`	A dissimilarity matrix
`fmbvr`	Logical, TRUE: look for the exact solution
`triabs`	Logical, TRUE: try to init with absolute values
`allsol`	Logical, TRUE all solutions, FALSE only one solution

Author(s)

Michel Petitjean, http://petitjeanmichel.free.fr/itoweb.petitjean.class.html

R port by Antoine Lucas,

References

Theory is explained at http://petitjeanmichel.free.fr/itoweb.petitjean.class.html

Marcotorchino F. Agr\'egation des similarit\'es en classification automatique. Th\'ese de Doctorat d'Etat en Math\'ematiques, Universit\'e Paris VI, 25 June 1981.

Petitjean M. Agr\'egation des similarit\'es: une solution oubli\'ee. RAIRO Oper. Res. 2002,36[1],101-108.

Examples


## pop from a data matrix
data <-
matrix(c(1,1,1,1,1
        ,1,2,1,2,1
        ,2,3,2,3,2
        ,2,4,3,3,2
        ,1,2,4,2,1
        ,2,3,2,3,1),ncol=5,byrow=TRUE)



pop(diss(data))


## pop from a dissimilarity matrix

d <-2 * matrix(c(9,  8,  5,  7,  7,  2
,  8,  9,  2,  5,  1,  7
,  5,  2,  9,  8,  7,  1
,  7,  5,  8,  9,  3,  2
,  7,  1,  7,  3,  9,  6
,  2,  7,  1,  2,  6,  9),ncol=6,byrow=TRUE) - 9

pop(d)


## Not run: 
d <- 2 * matrix(c(57, 15, 11, 32,  1, 34,  4,  6, 17,  7
, 15, 57, 27, 35, 27, 27, 20, 24, 30, 15
, 11, 27, 57, 25, 25, 20, 34, 25, 17, 15
, 32, 35, 25, 57, 22, 44, 13, 22, 30, 11
,  1, 27, 25, 22, 57, 21, 28, 43, 20, 13
, 34, 27, 20, 44, 21, 57, 18, 27, 21,  8
,  4, 20, 34, 13, 28, 18, 57, 31, 28, 13
,  6, 24, 25, 22, 43, 27, 31, 57, 30, 15
, 17, 30, 17, 30, 20, 21, 28, 30, 57, 12
,  7, 15, 15, 11, 13,  8, 13, 15, 12, 57),ncol=10,byrow=TRUE) - 57

pop(d)



## End(Not run)

## pop from a data matrix
data <-
matrix(c(1,1,1,1,1
        ,1,2,1,2,1
        ,2,3,2,3,2
        ,2,4,3,3,2
        ,1,2,4,2,1
        ,2,3,2,3,1),ncol=5,byrow=TRUE)



pop(diss(data))


## pop from a dissimilarity matrix

d <-2 * matrix(c(9,  8,  5,  7,  7,  2
,  8,  9,  2,  5,  1,  7
,  5,  2,  9,  8,  7,  1
,  7,  5,  8,  9,  3,  2
,  7,  1,  7,  3,  9,  6
,  2,  7,  1,  2,  6,  9),ncol=6,byrow=TRUE) - 9

pop(d)


## Not run: 
d <- 2 * matrix(c(57, 15, 11, 32,  1, 34,  4,  6, 17,  7
, 15, 57, 27, 35, 27, 27, 20, 24, 30, 15
, 11, 27, 57, 25, 25, 20, 34, 25, 17, 15
, 32, 35, 25, 57, 22, 44, 13, 22, 30, 11
,  1, 27, 25, 22, 57, 21, 28, 43, 20, 13
, 34, 27, 20, 44, 21, 57, 18, 27, 21,  8
,  4, 20, 34, 13, 28, 18, 57, 31, 28, 13
,  6, 24, 25, 22, 43, 27, 31, 57, 30, 15
, 17, 30, 17, 30, 20, 21, 28, 30, 57, 12
,  7, 15, 15, 11, 13,  8, 13, 15, 12, 57),ncol=10,byrow=TRUE) - 57

pop(d)



## End(Not run)

Robust variance

Description

Compute a robust variance

Usage

varrob(x,h,D=NULL,kernel="gaussien")
varrob(x,h,D=NULL,kernel="gaussien")

Arguments

`x`	Matrix / data frame
`h`	Scalar: bandwidth of the Kernel
`kernel`	The kernel used. This must be one of '"gaussien"', '"quartic"', '"triweight"', '"epanechikov"' , '"cosinus"' or '"uniform"'
`D`	A product scalar matrix / une matrice de produit scalaire

Details

U compute robust variance. $U_n^{-1} = S_n^{-1} - 1/h V_n^{-1}$

$S_n=\frac{\sum_{i=1}^{n}K(||X_i||_{V_n^{-1}}/h)(X_i-\mu_n)(X_i-\mu_n)'}{\sum_{i=1}^nK(||X_i||_{V_n^{-1}}/h)}$

with $\mu_n$ estimator of the mean.

K compute a kernel.

Value

A matrix

Author(s)

Antoine Lucas

References

H. Caussinus, S. Hakam, A. Ruiz-Gazen Projections revelatrices controlees: groupements et structures diverses. 2002, to appear in Rev. Statist. Appli.

Package 'amap'

Help Index

Principal component analysis

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Generalised principal component analysis

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Robust principal component analysis

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Correspondance factorial analysis.

Description

Usage

Arguments

Author(s)

Examples

Compute burt table from a factor dataframe.

Description

Usage

Arguments

Author(s)

Examples

Compute a dissimilarity matrix

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Distance Matrix Computation

Description

Usage

Arguments

Details

Value

Note

References

See Also

Examples

Hierarchical Clustering

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

K-Means Clustering

Description

Usage

Arguments

Details

Value

Note

See Also