adamethods: do_alphas_rss_multiv – R documentation

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do_alphas_rss_multiv

Alphas and RSS of every set of multivariate archetypoids

Description

In the ADALARA algorithm, every time that a set of archetypoids is computed using a sample of the data, the alpha coefficients and the associated residual sum of squares (RSS) for the entire data set must be computed.

Usage

do_alphas_rss_multiv(data, subset, huge, k_subset, rand_obs, alphas_subset, 
                  type_alg = "ada", PM, prob, nbasis, nvars)

Arguments

`data`	Data matrix with all the observations.
`subset`	Data matrix with a sample of the `data` observations.
`huge`	Penalization added to solve the convex least squares problems.
`k_subset`	Archetypoids obtained from `subset`.
`rand_obs`	Sample observations that form `subset`.
`alphas_subset`	Alpha coefficients related to `k_subset`.
`type_alg`	String. Options are 'ada' for the non-robust multivariate adalara algorithm, 'ada_rob' for the robust multivariate adalara algorithm, 'fada' for the non-robust fda fadalara algorithm and 'fada_rob' for the robust fda fadalara algorithm.
`PM`	Penalty matrix obtained with `eval.penalty`. Needed when `type_alg = 'fada'` or `type_alg = 'fada_rob'`.
`prob`	Probability with values in [0,1]. Needed when `type_alg = 'ada_rob'` or `type_alg = 'fada_rob'`.
`nbasis`	Number of basis.
`nvars`	Number of variables.

Value

A list with the following elements:

rss Real number of the residual sum of squares.
resid_rss Matrix with the residuals.
alphas Matrix with the alpha values.

Author(s)

Guillermo Vinue

Examples

## Not run: 
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]

# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)

# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)

X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1]) 
X[,,2] <- t(temp_fd$coef[,,2])

# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
# We have to give names to the dimensions to know the 
# observations that were identified as archetypoids.
dimnames(Xs) <- list(paste("Obs", 1:dim(hgtm)[2], sep = ""), 
                     1:nbasis,
                     c("boys", "girls"))

n <- dim(Xs)[1] 
# Number of archetypoids:
k <- 3 
numRep <- 20
huge <- 200

# Size of the random sample of observations:
m <- 15
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
data_alg <- Xs

nbasis <- dim(data_alg)[2] # number of basis.
nvars <- dim(data_alg)[3] # number of variables.
n <- nrow(data_alg)

suppressWarnings(RNGversion("3.5.0"))
set.seed(1) 
rand_obs_si <- sample(1:n, size = m)  
si <- apply(data_alg, 2:3, function(x) x[rand_obs_si])  

fada_si <- do_fada_multiv_robust(si, k, numRep, huge, 0.8, FALSE, PM)

k_si <- fada_si$cases
alphas_si <- fada_si$alphas
colnames(alphas_si) <- rownames(si)

rss_si <- do_alphas_rss_multiv(data_alg, si, huge, k_si, rand_obs_si, alphas_si, 
                               "fada_rob", PM, 0.8, nbasis, nvars)
str(rss_si)                                

## End(Not run)

adamethods

Archetypoid Algorithms and Anomaly Detection

v1.2.1

GPL (>= 2)

Authors

Guillermo Vinue, Irene Epifanio

Initial release

2020-08-04