[mlpack-git] [mlpack/mlpack] Modeling LSH For Performance Tuning (#749)

[Ryan Curtin]

> +
> +    // Reference set for kNN
> +    arma::mat refMat = sampleSet.cols(refSetStart, refSetEnd);
> +    referenceSizes(i) = refMat.n_cols;
> +
> +    arma::Mat<size_t> neighbors; // Not going to be used but required.
> +    arma::mat kNNDistances; // What we need.
> +    KNN naive(refMat, true); // true: train and use naive kNN.
> +    naive.Search(queryMat, k, neighbors, kNNDistances);
> +
> +    // Store the squared distances (what we need).
> +    kNNDistances = arma::pow(kNNDistances, 2);
> +
> +    // Compute Arithmetic and Geometric mean of the distances.
> +    Ek.row(i) = arma::mean(kNNDistances.t());
> +    Gk.row(i) = arma::exp(arma::mean(arma::log(kNNDistances.t()), 0));

Shouldn't `Gk` be the geometric mean?  What's implemented here doesn't appear to be that.  I think you can calculate the geometric mean as

```
Gk.row(i) = arma::pow(arma::prod(kNNDistances.t()), 1.0 / kNNDistances.n_cols);
```

After making that change, L-BFGS to fit the geometric distribution converges, instead of resulting in a NaN.

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