In the standard, convex RSR problem (do.rsr), row-sparsity for self-representation is acquired using matrix $$\ell_{2,1}$$ norm, i.e, $$\|W\|_{2,1} = \sum \|W_{i:}\|_2$$. 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.

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.

## References

Zhu P, Zhu W, Wang W, Zuo W, Hu Q (2017). “Non-Convex Regularized Self-Representation for Unsupervised Feature Selection.” Image and Vision Computing, 60, 22--29.

do.rsr

Kisung You

## Examples

# \donttest{
## 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")