| Title: | Automatic Estimation of Number of Principal Components in PCA |
|---|---|
| Description: | Automatic estimation of number of principal components in PCA with PEnalized SEmi-integrated Likelihood (PESEL). See Piotr Sobczyk, Malgorzata Bogdan, Julie Josse 'Bayesian dimensionality reduction with PCA using penalized semi-integrated likelihood' (2017) <doi:10.1080/10618600.2017.1340302>. |
| Authors: | Piotr Sobczyk, Julie Josse, Malgorzata Bogdan |
| Maintainer: | Piotr Sobczyk <[email protected]> |
| License: | GPL-3 |
| Version: | 0.7.4 |
| Built: | 2024-10-27 05:49:23 UTC |
| Source: | https://github.com/psobczyk/pesel |
Automatic estimation of number of principal components in PCA with PEnalized SEmi-integrated Likelihood (PESEL).
Version: 0.7.4
Piotr Sobczyk, Julie Josse, Malgorzata Bogdan
Maintainer: Piotr Sobczyk [email protected]
Piotr Sobczyk, Malgorzata Bogdan, Julie Josse Bayesian dimensionality reduction with PCA using penalized semi-integrated likelihood, Journal of Computational and Graphical Statistics 2017
# EXAMPLE 1 - noise with(set.seed(23), pesel(matrix(rnorm(10000), ncol = 100), npc.min = 0)) # EXAMPLE 2 - fixed effects PCA model sigma <- 0.5 k <- 5 n <- 100 numb.vars <- 10 # factors are drawn from normal distribution factors <- replicate(k, rnorm(n, 0, 1)) # coefficients are drawn from uniform distribution coeff <- replicate(numb.vars, rnorm(k, 0, 1)) SIGNAL <- scale(factors %*% coeff) X <- SIGNAL + replicate(numb.vars, sigma * rnorm(n)) pesel(X)# EXAMPLE 1 - noise with(set.seed(23), pesel(matrix(rnorm(10000), ncol = 100), npc.min = 0)) # EXAMPLE 2 - fixed effects PCA model sigma <- 0.5 k <- 5 n <- 100 numb.vars <- 10 # factors are drawn from normal distribution factors <- replicate(k, rnorm(n, 0, 1)) # coefficients are drawn from uniform distribution coeff <- replicate(numb.vars, rnorm(k, 0, 1)) SIGNAL <- scale(factors %*% coeff) X <- SIGNAL + replicate(numb.vars, sigma * rnorm(n)) pesel(X)
Underlying assumption is that only small number of principal components, associated with largest singular values, is relevent, while the rest of them is noise. For a given numeric data set, function estimates the number of PCs according to penalized likelihood criterion. Function adjusts the model used to the case when number of variables is larger than the number of observations.
pesel( X, npc.min = 0, npc.max = 10, prior = NULL, scale = TRUE, method = c("heterogenous", "homogenous"), asymptotics = NULL )pesel( X, npc.min = 0, npc.max = 10, prior = NULL, scale = TRUE, method = c("heterogenous", "homogenous"), asymptotics = NULL )
X |
a data frame or a matrix contatining only continuous variables |
npc.min |
minimal number of principal components, for all the possible number of PCs between npc.min and npc.max criterion is computed |
npc.max |
maximal number of principal components, if greater than dimensions of X, min(ncol(X), nrow(X))-1 is used, for all the possible number of PCs between npc.min and npc.max criterion is computed |
prior |
a numeric positive vector of length npc.max-ncp.min+1. Prior distribution on number of principal components. Defaults to uniform distibution |
scale |
a boolean, if TRUE (default value) then data is scaled before applying criterion |
method |
name of criterion to be used |
asymptotics |
a character, asymptotics ('n' or 'p') to be used. Default is NULL for which asymptotics is selected based on dimensions of X |
Please note that no categorical variables and missing values are allowed.
number of components
# EXAMPLE 1 - noise with(set.seed(23), pesel(matrix(rnorm(10000), ncol = 100), npc.min = 0)) # EXAMPLE 2 - fixed effects PCA model sigma <- 0.5 k <- 5 n <- 100 numb.vars <- 10 # factors are drawn from normal distribution factors <- replicate(k, rnorm(n, 0, 1)) # coefficients are drawn from uniform distribution coeff <- replicate(numb.vars, rnorm(k, 0, 1)) SIGNAL <- scale(factors %*% coeff) X <- SIGNAL + replicate(numb.vars, sigma * rnorm(n)) pesel(X)# EXAMPLE 1 - noise with(set.seed(23), pesel(matrix(rnorm(10000), ncol = 100), npc.min = 0)) # EXAMPLE 2 - fixed effects PCA model sigma <- 0.5 k <- 5 n <- 100 numb.vars <- 10 # factors are drawn from normal distribution factors <- replicate(k, rnorm(n, 0, 1)) # coefficients are drawn from uniform distribution coeff <- replicate(numb.vars, rnorm(k, 0, 1)) SIGNAL <- scale(factors %*% coeff) X <- SIGNAL + replicate(numb.vars, sigma * rnorm(n)) pesel(X)
Derived under assumption that number of variables tends to infinity while number of observations is limited.
pesel_heterogeneous(X, minK, maxK)pesel_heterogeneous(X, minK, maxK)
X |
a matrix containing only continuous variables |
minK |
minimal number of principal components fitted |
maxK |
maximal number of principal components fitted |
numeric vector, PESEL criterion for each k in range [minK, maxK]
Derived under assumption that number of variables tends to infinity while number of observations is limited.
pesel_homogeneous(X, minK, maxK)pesel_homogeneous(X, minK, maxK)
X |
a matrix containing only continuous variables |
minK |
minimal number of principal components fitted |
maxK |
maximal number of principal components fitted |
numeric vector, PESEL criterion for each k in range [minK, maxK]