acpgen(x,h1,h2,center=TRUE,reduce=TRUE,kernel="gaussien")
K(u,kernel="gaussien")
W(x,h,D=NULL,kernel="gaussien")
WsansC(x,h,D=NULL,kernel="gaussien")"loadings": see loadings for its print
method.scores = TRUE, the scores of the supplied
data on the principal components.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: $$\frac{\pi}{4}\cos(\frac{\pi}{2}u) I_{|u|\leq 1}$$
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�user 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.
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"Run the code above in your browser using DataLab