## Archetypoid algorithm with the robust Frobenius norm

### Description

Robust version of the archetypoid algorithm with the Frobenius form.

### Usage

```archetypoids_robust(numArchoid, data, huge = 200, ArchObj, 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_robust` function. `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_norm_frob`

### Examples

```data(mtcars)
data <- mtcars

k <- 3
numRep <- 2
huge <- 200

lass <- stepArchetypesRawData_robust(data = data, numArch = k,
numRep = numRep, verbose = FALSE,
saveHistory = FALSE, prob = 0.8)

res <- archetypoids_robust(k, data, huge, ArchObj = lass, 0.8)
str(res)
res\$cases