## Archetypoid algorithm with the functional robust Frobenius norm

### Description

Archetypoid algorithm with the functional robust Frobenius norm to be used with functional data.

### Usage

```archetypoids_funct_robust(numArchoid, data, huge = 200, ArchObj, PM, prob)
```

### Arguments

 `numArchoid` Number of archetypoids. `data` Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. `huge` Penalization added to solve the convex least squares problems. `ArchObj` The list object returned by the `stepArchetypesRawData_funct_robust` function. `PM` Penalty matrix obtained with `eval.penalty`. `prob` Probability with values in [0,1].

### Value

A list with the following elements:

• cases: Final vector of archetypoids.

• rss: Residual sum of squares corresponding to the final vector of archetypoids.

• archet_ini: Vector of initial archetypoids.

• alphas: Alpha coefficients for the final vector of archetypoids.

• resid: Matrix with the residuals.

Irene Epifanio

### References

Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036

`archetypoids`

### Examples

```## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth\$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth\$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd\$coefs)

lass <- stepArchetypesRawData_funct_robust(data = data_archs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM, prob = 0.8)

afr <- archetypoids_funct_robust(3, data_archs, huge = 200, ArchObj = lass, PM, 0.8)
str(afr)

## End(Not run)

```