# hilbert.order: Estimate the Hilbert order for a given matrix In hilbertSimilarity: Hilbert Similarity Index for High Dimensional Data

## Description

Estimate the Hilbert order, or the number of bins in each dimension, so that if the matrix was random every row in the matrix would correspond to a single bin.

## Usage

 `1` ```hilbert.order(mat) ```

## Arguments

 `mat` the matrix for which to estimate the Hilbert order

## Details

Assuming the matrix is fully random, there is no need to generate more voxels (the combination of bins over all dimensions) than there are rows in the matrix. The number can be derived from the following formula:

c^d < N

where c is the number of bins, d is the number of dimensions and N is the total number of cells in the dataset. c can be computed easily using the following formula:

c = floor(N^1/d)

The number of cuts for `do.cut` is the number of bins plus 1.

## Value

the suggested number of bins to use for the specified `mat`.

Yann Abraham

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# generate a random 3D matrix with 2 peaks mat <- rbind(matrix(rnorm(300),ncol=3), matrix(rnorm(300,5,1),ncol=3)) dimnames(mat)[] <- LETTERS[1:3] # estimate the Hilbert order hilbert.order(mat) # generate 2 bins with a minimum bin size of 5 cuts <- make.cut(mat,n=3,count.lim=5) show.cut(cuts) # Generate the cuts cut.mat <- do.cut(mat,cuts,type='fixed') head(cut.mat) ```

hilbertSimilarity documentation built on Nov. 12, 2019, 1:06 a.m.