dimension: Function to determine the required number of dimension for...
In RandPro: Random Projection with Classification

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/dimension.R

Johnson-Lindenstrauss (JL) lemma is the heart of random projection. The lemma states that a small set of points in a high-dimensional space can be embedded into low dimensional space in such a way that distances between the points are nearly preserved. The lemma has been used in dimensionality reduction, compressed sensing, manifold learning and graph embedding. The epsilon is the error tolerant parameter and it is inversely proportional to the accuracy of the result. The higher error tolerant level decreases the number of dimension and also the computation complexity with the marginal loss of accuracy.

1	dimension(sample, epsilon = 0.1)

`sample`	- number of samples
`epsilon`	- error tolerance level with default value 0.1

The function dimension() is used to find the minimum dimension required to project the data from high dimensional space to low dimensional space. The number of sample and error tolerant level has been passed as an input argument to the function dimension() . It will return the size of the random subspace to guarantee a bounded distortion introduced by the random projection.

minimum number of dimension required to maintain the pair wise distance between any two points with the controlled amount of error(eps)

Aghila G

Siddharth R

[1] William B.Johnson, Joram Lindenstrauss, "Extension of Lipschitz mappings into a Hilbert space (1984)"

[2] Sanjoy Dasgupta , Anupam Gupta "An elementary proof of a theorem of Johnson and Lindenstrauss (2003)"

Johnson-Lindenstrauss Elementary Proof

#load library
library(RandPro)

#Calculate minimum dimension using eps =0.5 for 1000000 sample
y <- dimension(1000000,0.5)

#Calculating minimum dimension using different epsilon value for 1000000 sample
d <-  c(0.5,0.1)
x<- dimension(103260,d)