Projection of a Vector to a Sparse Vector

Description

projFunc: R implementation of projFunc.

Usage

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projFunc(s, k1, k2)

Arguments

s

data vector.

k1

sparseness, l1 norm constraint.

k2

l2 norm constraint.

Details

The projection is done according to Hoyer, 2004: given an l_1-norm and an l_2-norm minimize the Euclidean distance to the original vector. The projection is a convex quadratic problem which is solved iteratively where at each iteration at least one component is set to zero.

In the applications, instead of the l_1-norm a sparseness measurement is used which relates the l_1-norm to the l_2-norm.

Implementation in R.

Value

v

sparse projected vector.

Author(s)

Sepp Hochreiter

References

Patrik O. Hoyer, ‘Non-negative Matrix Factorization with Sparseness Constraints’, Journal of Machine Learning Research 5:1457-1469, 2004.

See Also

fabia, fabias, fabiap, fabi, fabiasp, mfsc, nmfdiv, nmfeu, nmfsc, extractPlot, extractBic, plotBicluster, Factorization, projFuncPos, projFunc, estimateMode, makeFabiaData, makeFabiaDataBlocks, makeFabiaDataPos, makeFabiaDataBlocksPos, matrixImagePlot, fabiaDemo, fabiaVersion

Examples

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#---------------
# DEMO
#---------------

size <- 30
sparseness <- 0.7

s <- as.vector(rnorm(size))
sp <- sqrt(1.0*size)-(sqrt(1.0*size)-1.0)*sparseness

ss <- projFunc(s,k1=sp,k2=1)

s
ss

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