# ridgeSIR: ridge SIR In SISIR: Sparse Interval Sliced Inverse Regression

## Description

`ridgeSIR` performs the first step of the method (ridge regularization of SIR)

## Usage

 `1` ```ridgeSIR(x, y, H, d, mu2 = NULL) ```

## Arguments

 `x` explanatory variables (numeric matrix or data frame) `y` target variable (numeric vector) `H` number of slices (integer) `d` number of dimensions to be kept `mu2` ridge regularization parameter (numeric, positive)

SI-SIR

## Value

S3 object of class `ridgeRes`: a list consisting of

• `EDR` the estimated EDR space (a p x d matrix)

• `condC` the estimated slice projection on EDR (a d x H matrix)

• `eigenvalues` the eigenvalues obtained during the generalized eigendecomposition performed by SIR

• `parameters` a list of hyper-parameters for the method:

• `H` number of slices

• `d` dimension of the EDR space

• `mu2` regularization parameter for the ridge penalty

• `utils` useful outputs for further computations:

• `Sigma` covariance matrix for x

• `slices` slice number for all observations

• `invsqrtS` value of the inverse square root of the regularized covariance matrix for x

## Author(s)

Victor Picheny, [email protected]

Remi Servien, [email protected]

Nathalie Villa-Vialaneix, [email protected]

## References

Picheny, V., Servien, R. and Villa-Vialaneix, N. (2016) Interpretable sparse SIR for digitized functional data. Preprint.

`sparseSIR`, `SISIR`, `tune.ridgeSIR`
 ```1 2 3 4 5 6 7 8 9``` ```set.seed(1140) tsteps <- seq(0, 1, length = 50) simulate_bm <- function() return(c(0, cumsum(rnorm(length(tsteps)-1, sd=1)))) x <- t(replicate(50, simulate_bm())) beta <- cbind(sin(tsteps*3*pi/2), sin(tsteps*5*pi/2)) y <- log(abs(x %*% beta[ ,1])) + sqrt(abs(x %*% beta[ ,2])) y <- y + rnorm(50, sd = 0.1) res_ridge <- ridgeSIR(x, y, H = 10, d = 2, mu2 = 10^8) ## Not run: print(res_ridge) ```