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

[Yannis Mentekidis]

> +
> +    // 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));

Yes, I'm using an alternative way to compute it:
```
pow(prod(x_i)), 1/N) = 
exp(log(pow(prod(x_i)), 1/N))) = 
exp(1/N * [ log(prod(x_i))])  = 
exp(1/N * sum( log(x_i))) = 
exp(mean(log(x_i)))
```

Computing the geometric mean this way allows me to use arma::mean(), which can calculate the row-wise, column-wise or overall mean. In this case we have a `queryMat.n_rows` x `k` matrix, and we want the average of each column - or at least, that's my understanding of the paper.

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