# feature_NRSR: Non-convex Regularized Self-Representation In Rdimtools: Dimension Reduction and Estimation Methods

 do.nrsr R Documentation

## Non-convex Regularized Self-Representation

### Description

In the standard, convex RSR problem (do.rsr), row-sparsity for self-representation is acquired using matrix \ell_{2,1} norm, i.e, \|W\|_{2,1} = ∑ \|W_{i:}\|_2. Its non-convex extension aims at achieving higher-level of sparsity using arbitrarily chosen \|W\|_{2,l} norm for l\in (0,1) and this exploits Iteratively Reweighted Least Squares (IRLS) algorithm for computation.

### Usage

do.nrsr(
X,
ndim = 2,
expl = 0.5,
preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
lbd = 1
)


### Arguments

 X an (n\times p) matrix or data frame whose rows are observations and columns represent independent variables. ndim an integer-valued target dimension. expl an exponent in \ell_{2,l} norm for sparsity. Must be in (0,1), or l=1 reduces to RSR problem. preprocess an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details. lbd nonnegative number to control the degree of self-representation by imposing row-sparsity.

### Value

a named list containing

Y

an (n\times ndim) matrix whose rows are embedded observations.

featidx

a length-ndim vector of indices with highest scores.

trfinfo

a list containing information for out-of-sample prediction.

projection

a (p\times ndim) whose columns are basis for projection.

Kisung You

### References

\insertRef

zhu_nonconvex_2017Rdimtools

do.rsr

### Examples


## use iris data
data(iris)
set.seed(100)
subid = sample(1:150, 50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

#### try different exponents for regularization
out1 = do.nrsr(X, expl=0.01)
out2 = do.nrsr(X, expl=0.1)
out3 = do.nrsr(X, expl=0.5)

#### visualize
plot(out1$Y, pch=19, col=label, main="NRSR::expl=0.01") plot(out2$Y, pch=19, col=label, main="NRSR::expl=0.1")