Plus.Minus.One.random.projection: Plus-Minus-One (PMO) random projections

In clusterv: Assessment of Cluster Stability by Randomized Maps

Plus-Minus-One (PMO) random projections

Description

Random projections to a lower dimensional subspace with a random +1/-1 projection matrix The projection is performed using a projection matrix R s.t. Prob(R[i,j]=1)=Prob(R[i,j]=-1)=1/2.

Usage

Plus.Minus.One.random.projection(d = 2, m, scaling = TRUE)

Arguments

d	subspace dimension
m	data matrix (rows are features and columns are examples)
scaling	if TRUE (default) scaling is performed

Details

Plus-Minus-One (PMO) random projections are represented by d'\times d matrices R = 1/\sqrt{d'} (r_{ij}), where r_{ij} are uniformly chosen in \{-1,1\}, such that Prob(r_{ij} = 1) = Prob(r_{ij} = -1) = 1/2.

Value

data matrix (dimension d X ncol(m)) of the examples projected in a d-dimensional random subspace

Author(s)

Giorgio Valentini [e-mail]

See Also

random.subspace, norm.random.projection, Achlioptas.random.projection

Examples

# PMO projection from a 1000 dimensional space to a 50-dimensional subspace
m <- matrix(runif(10000), nrow=1000)
m.p <- Plus.Minus.One.random.projection(d = 50, m, scaling = TRUE)
# PMO projection from a 10000 dimensional space to a 1000-dimensional subspace
m <- matrix(rnorm(500000), nrow=5000)
m.p <- Plus.Minus.One.random.projection(d = 1000, m, scaling = TRUE)
# The same as above without scaling
m <- matrix(rnorm(500000), nrow=5000)
m.p <- Plus.Minus.One.random.projection(d = 1000, m, scaling = FALSE)

clusterv documentation built on June 8, 2025, 10:21 a.m.