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
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, ...)
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. |
This function offer a variant of princomp
and
prcomp
functions, with a slightly different
graphic representation (see plot.acp
).
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
|
scores |
if |
eig |
Eigen values |
Antoine Lucas
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
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")
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 |
acpgen
compute generalised pca. i.e. spectral analysis of
, and project
with
on the principal vector sub-spaces.
a column vector of
variables of individu
(input data)
W
compute estimation of noise in the variance.
with variance estimation;
U
compute robust variance.
with estimator of the mean.
K
compute kernel, i.e.
gaussien:
quartic:
triweight:
epanechikov:
cosinus:
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
|
scores |
if |
eig |
Eigen values |
Antoine Lucas
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.
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
acprob(x,h,center=TRUE,reduce=TRUE,kernel="gaussien")
acprob(x,h,center=TRUE,reduce=TRUE,kernel="gaussien")
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 |
acpgen
compute robust pca. i.e. spectral analysis of a robust
variance instead of usual variance. Robust variance: see
varrob
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
|
scores |
if |
eig |
Eigen values |
Antoine Lucas
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.
Compute an acp on a contingency table tacking into account weight of rows and columns
afc(x)
afc(x)
x |
A contingency table, or a result of function |
Antoine Lucas
## 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)
matlogic returns for all variables a matrix of logical values for each levels. burt is defined as t(matlogic).matlogic
burt(x) matlogic(x)
burt(x) matlogic(x)
x |
A dataframe that contents only factors |
Antoine Lucas
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 from a data set (containing only factors).
diss(x, w=rep(1,ncol(x)) )
diss(x, w=rep(1,ncol(x)) )
x |
A matrix or data frame containing only factors. |
w |
A vector of weight, by default each variable has got same weight |
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.
A dissimilarity matrix.
Antoine Lucas
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))
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.
Dist(x, method = "euclidean", nbproc = 2, diag = FALSE, upper = FALSE)
Dist(x, method = "euclidean", nbproc = 2, diag = FALSE, upper = FALSE)
x |
numeric matrix or (data frame) or an object of class
"exprSet".
Distances between the rows of
|
method |
the distance measure to be used. This must be one of
|
nbproc |
integer, Number of subprocess for parallelization |
diag |
logical value indicating whether the diagonal of the
distance matrix should be printed by |
upper |
logical value indicating whether the upper triangle of the
distance matrix should be printed by |
Available distance measures are (written for two vectors and
):
euclidean
:Usual square distance between the two vectors (2 norm).
maximum
:Maximum distance between two components of
and
(supremum norm)
manhattan
:Absolute distance between the two vectors (1 norm).
canberra
:. 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"
.
abspearson
:Absolute Pearson
.
correlation
:Also named "Centered Pearson"
.
abscorrelation
:Absolute correlation
with
.
spearman
:Compute a distance based on rank.
where
is the difference
in rank between
and
.
Dist(x,method="spearman")[i,j] =
cor.test(x[i,],x[j,],method="spearman")$statistic
kendall
:Compute a distance based on rank.
with
is 0 if
in same order as
,
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.
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 , the dissimilarity between (row) i and j is
do[n*(i-1) - i*(i-1)/2 + j-i]
.
The length of the vector is , i.e., of order
.
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 |
call |
optionally, the |
methods |
optionally, the distance method used; resulting form
|
Multi-thread (parallelisation) is disable on Windows.
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
daisy
in the ‘cluster’ package with more
possibilities in the case of mixed (contiuous / categorical)
variables.
dist
hcluster
.
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 cluster analysis.
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)
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
|
diag |
logical value indicating whether the diagonal of the
distance matrix should be printed by |
upper |
logical value indicating whether the upper triangle of the
distance matrix should be printed by |
link |
the agglomeration method to be used. This should
be (an unambiguous abbreviation of) one of
|
members |
|
nbproc |
integer, number of subprocess for parallelization [Linux & Mac only] |
doubleprecision |
True: use of double precision for distance matrix computation; False: use simple precision |
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
.
An object of class hclust which describes the tree produced by the clustering process. The object is a list with components:
merge |
an |
height |
a set of |
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 |
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 |
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.
Multi-thread (parallelisation) is disable on Windows.
The hcluster
function is based on C code adapted from Cran
Fortran routine
by Antoine Lucas.
Antoine Lucas and Sylvain Jasson, Using amap and ctc Packages for Huge Clustering, R News, 2006, vol 6, issue 5 pages 58-60.
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)
Perform k-means clustering on a data matrix.
Kmeans(x, centers, iter.max = 10, nstart = 1, method = "euclidean")
Kmeans(x, centers, iter.max = 10, nstart = 1, method = "euclidean")
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 |
iter.max |
The maximum number of iterations allowed. |
nstart |
If |
method |
the distance measure to be used. This must be one of
|
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.
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. |
An objective: to allow NA values.
## 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")
Lubischew data (1962): 74 insects, 6 morphologic size. 3 supposed classes
data(lubisch)
data(lubisch)
Graphics for Principal component Analysis
## 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)
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. |
Graphics:
plot.acp
PCA for lines (individuals)
plot.acp
PCA for columns (variables)
plot2
Eigen values diagram (Scree Graph)
plotAll
Plot both 3 graphs
Antoine Lucas
data(lubisch) lubisch <- lubisch[,-c(1,8)] p <- acp(lubisch) plotAll(p)
data(lubisch) lubisch <- lubisch[,-c(1,8)] p <- acp(lubisch) plotAll(p)
Classification: Computing an Optimal Partition from Weighted Categorical Variables or from an Array of Signed Similarities.
pop(x,fmbvr=TRUE,triabs=TRUE,allsol=TRUE)
pop(x,fmbvr=TRUE,triabs=TRUE,allsol=TRUE)
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 |
Michel Petitjean, http://petitjeanmichel.free.fr/itoweb.petitjean.class.html
R port by Antoine Lucas,
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.
## 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)
Compute a robust variance
varrob(x,h,D=NULL,kernel="gaussien")
varrob(x,h,D=NULL,kernel="gaussien")
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 |
U
compute robust variance.
with estimator of the mean.
K
compute a kernel.
A matrix
Antoine Lucas
H. Caussinus, S. Hakam, A. Ruiz-Gazen Projections revelatrices controlees: groupements et structures diverses. 2002, to appear in Rev. Statist. Appli.