The MetricType policy in mlpack

Many machine learning methods operate with some sort of metric, and often, this metric can be any arbitrary metric. For instance, consider the problem of nearest neighbor search; one can find the nearest neighbor of a point with respect to the standard Euclidean distance, or the Manhattan (city-block) distance. The actual search techniques, though, remain the same. And this is true of many machine learning methods: the specific metric that is used can be any valid metric.

mlpack algorithms, when possible, allow the use of an arbitrary metric via the use of the MetricType template parameter. Any metric passed as a MetricType template parameter will need to have

• an Evaluate function
• a default constructor.

The signature of the Evaluate function is straightforward:

template<typename VecTypeA, typename VecTypeB>
double Evaluate(const VecTypeA& a, const VecTypeB& b);

The function takes two vector arguments, a and b, and returns a double that is the evaluation of the metric between the two arguments. So, for a particular metric , the Evaluate() function should return .

The arguments a and b, of types VecTypeA and VecTypeB, respectively, will be an Armadillo-like vector type (usually arma::vec, arma::sp_vec, or similar). In general it should be valid to assume that VecTypeA is a class with the same API as arma::vec.

Note that for metrics that do not hold any state, the Evaluate() method can be marked as static.

Overall, the MetricType template policy is quite simple (much like the The KernelType policy in mlpack KernelType policy). Below is an example metric class, which implements the L2 distance:

class ExampleMetric
{
  // Default constructor is required.
  ExampleMetric() { }

  // The example metric holds no state, so we can mark Evaluate() as static.
  template<typename VecTypeA, typename VecTypeB>
  static double Evaluate(const VecTypeA& a, const VecTypeB& b)
  {
    // Return the L2 norm of the difference between the points, which is the
    // same as the L2 distance.
    return arma::norm(a - b);
  }
};

Then, this metric can easily be used inside of other mlpack algorithms. For example, the code below runs range search on a random dataset with the ExampleKernel, by instantiating a mlpack::range::RangeSearch object that uses the ExampleKernel. Then, the number of results are printed. The RangeSearch class takes three template parameters: MetricType, MatType, and TreeType. (All three have defaults, so we will just leave MatType and TreeType to their defaults.)

#include <mlpack/core.hpp>
#include <mlpack/methods/range_search/range_search.hpp>
#include "example_metric.hpp" // A file that contains ExampleKernel.

using namespace mlpack;
using namespace mlpack::range;
using namespace std;

int main()
{
  // Create a random dataset with 10 dimensions and 5000 points.
  arma::mat data = arma::randu<arma::mat>(10, 5000);

  // Instantiate the RangeSearch object with the ExampleKernel.
  RangeSearch<ExampleKernel> rs(data);

  // These vectors will store the results.
  vector<vector<size_t>> neighbors;
  vector<vector<double>> distances;

  // Create a random 10-dimensional query point.
  arma::vec query = arma::randu<arma::vec>(10);

  // Find those points with distance (according to ExampleMetric) between 1 and
  // 2 from the query point.
  rs.Search(query, math::Range(1.0, 2.0), neighbors, distances);

  // Now, print the number of points inside the desired range.  We know that
  // neighbors and distances will have length 1, since there was only one query
  // point.
  cout << neighbors[0].size() << " points within the range [1.0, 2.0] of the "
      << "query point!" << endl;
}

mlpack comes with a number of pre-written metrics that satisfy the MetricType policy:

• mlpack::metric::ManhattanDistance
• mlpack::metric::EuclideanDistance
• mlpack::metric::ChebyshevDistance
• mlpack::metric::MahalanobisDistance
• mlpack::metric::LMetric (for arbitrary L-metrics)
• mlpack::metric::IPMetric (requires a The KernelType policy in mlpack KernelType parameter)