random.subspace: Random Subspace (RS) projections

In clusterv: Assessment of Cluster Stability by Randomized Maps

Random Subspace (RS) projections

Description

Random projections to a lower dimension subspace (random subspace method) The projection is performed randomly selecting a subset of variables (components) and then projecting the data onto the selected components. It is the projection used by Ho for her Random subspace ensemble algorithm.

Usage

random.subspace(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

Random Subspace (RS) are randomized maps represented by d' \times d matrices R =\sqrt{d/d'} (r_{ij}), where r_{ij} are uniformly chosen with entries in \{0,1\}, and with exactly one 1 per row and at most one 1 per column (d' is the dimension of the projected space and d the dimension of the original space). It is worth noting that, in this case, the "compressed" data set D_R = R D can be quickly computed in time \mathcal{O}(n d'), independently from d.

Value

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

Author(s)

Giorgio Valentini [e-mail]

References

T.Ho, The random subspace method for constructing decision forests, IEEE Transactions on Pattern Analysis and Machine Intelligence 20 (8) (1998) 832-844.

See Also

Plus.Minus.One.random.projection, norm.random.projection,

Achlioptas.random.projection

Examples

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

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