Locality and Similarity Preserving Embedding

Locality and Similarity Preserving Embedding (LSPE) is a feature selection method based on Neighborhood Preserving Embedding (do.npe) and Sparsity Preserving Projection (do.spp) by first building a neighborhood graph and then mapping the locality structure to reconstruct coefficients such that data similarity is preserved. Use of \(\ell_{2,1}\) norm boosts to impose column-sparsity that enables feature selection procedure.

do.lspe(
  X,
  ndim = 2,
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  alpha = 1,
  beta = 1,
  bandwidth = 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.
preprocess: an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.
alpha: nonnegative number to control \(\ell_{2,1}\) norm of projection.
beta: nonnegative number to control the degree of local similarity.
bandwidth: positive number for Gaussian kernel bandwidth to define similarity.

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

Fang X, Xu Y, Li X, Fan Z, Liu H, Chen Y (2014). “Locality and Similarity Preserving Embedding for Feature Selection.” Neurocomputing, 128, 304--315.

Author

Kisung You

Examples

# \donttest{
#### generate R12in72 dataset
set.seed(100)
X = aux.gensamples(n=50, dname="R12in72")

#### try different bandwidth values
out1 = do.lspe(X, bandwidth=0.1)
out2 = do.lspe(X, bandwidth=1)
out3 = do.lspe(X, bandwidth=10)

#### visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="LSPE::bandwidth=0.1")
plot(out2$Y, main="LSPE::bandwidth=1")
plot(out3$Y, main="LSPE::bandwidth=10")

par(opar)
# }