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# 6.5 `cao` - Determine minimum embedding dimension by Cao's method

This mex-file applies Cao's method [38] to the input data set. If the data set contains points of dimension `D`, it computes E and E* for a data set of dimension 1 (taken from the first column of the input data set), then for a data set of dimension 2 (taken from the first two columns) up to a dimension of D. Optionally, this algorithm extends Cao's method in a straightforward manner to use more than one nearest neighbors.

Syntax:

- `[E, E*] = cao(pointset, query_indices, k)`

Input arguments:

- `pointset` - a `N` by `D` double matrix containing the coordinates of the point set, organized as `N` points of dimension `D`
- `query_indices` - query points are taken out of the pointset, query_indices is a vector of length `R` which contains the indices of the query points (indices may vary from 1 to N)
- `k` - number of nearest neighbors to compute. Cao's method can be extended to use more than only the first nearest neighbor (k=1).

Output arguments:

- `E` and `E*` are vectors of size `D`. Please refer the Cao's article [38] for a precise description of their meaning.

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