Orthogonal Locality Preserving Projection

Orthogonal Locality Preserving Projection (OLPP) is a variant of do.lpp, which extracts orthogonal basis functions to reconstruct the data in a more intuitive fashion. It adopts PCA as preprocessing step and uses only one eigenvector at each iteration in that it might incur warning messages for solving near-singular system of linear equations. Current implementation may not return an orthogonal projection matrix as of the paper. We plan to fix this issue in the near future.

do.olpp(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect"),
  t = 1
)

Arguments

X: an $(n\times p)$ matrix or data frame whose rows are observations
ndim: an integer-valued target dimension.
type: a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.
symmetric: either "intersect" or "union" is supported. Default is "union". See also aux.graphnbd for more details.
t: bandwidth for heat kernel in $(0,\infty)$

Value

a named Rdimtools S3 object containing

Y: an $(n\times ndim)$ matrix whose rows are embedded observations.
projection: a $(p\times ndim)$ whose columns are basis for projection.
algorithm: name of the algorithm.

References

Cai D, He X, Han J, Zhang H (2006). “Orthogonal Laplacianfaces for Face Recognition.” IEEE Transactions on Image Processing, 15(11), 3608--3614.

Author

Kisung You

Examples

if (FALSE) {
## 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])

##  connecting 10% and 25% of data for graph construction each.
output1 <- do.olpp(X,ndim=2,type=c("proportion",0.10))
output2 <- do.olpp(X,ndim=2,type=c("proportion",0.25))

## Visualize
#  In theory, it should show two separated groups of data
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(output1$Y, col=label, pch=19, main="OLPP::10% connected")
plot(output2$Y, col=label, pch=19, main="OLPP::25% connected")
par(opar)
}