/*!

@file neighbor_search.txt
@author Ryan Curtin
@brief Tutorial for how to use the NeighborSearch class.

@page nstutorial NeighborSearch tutorial (k-nearest-neighbors)

@section intro_nstut Introduction

Nearest-neighbors search is a common machine learning task.  In this setting, we
have a \b query and a \b reference dataset.  For each point in the \b query
dataset, we wish to know the \f$k\f$ points in the \b reference dataset which
are closest to the given query point.

Alternately, if the query and reference datasets are the same, the problem can
be stated more simply: for each point in the dataset, we wish to know the
\f$k\f$ nearest points to that point.

\b mlpack provides:

 - a \ref cli_nstut "simple command-line executable" to run nearest-neighbors search
   (and furthest-neighbors search)
 - a \ref knn_nstut "simple C++ interface" to perform nearest-neighbors search (and
   furthest-neighbors search)
 - a \ref neighborsearch_nstut "generic, extensible, and powerful C++ class (NeighborSearch)" for complex usage

@section toc_nstut Table of Contents

A list of all the sections this tutorial contains.

 - \ref intro_nstut
 - \ref toc_nstut
 - \ref cli_nstut
   - \ref cli_ex1_nstut
   - \ref cli_ex2_nstut
   - \ref cli_ex3_nstut
 - \ref knn_nstut
   - \ref knn_ex1_nstut
   - \ref knn_ex2_nstut
   - \ref knn_ex3_nstut
 - \ref neighborsearch_nstut
   - \ref sort_policy_doc_nstut
   - \ref metric_type_doc_nstut
   - \ref mat_type_doc_nstut
   - \ref tree_type_doc_nstut
   - \ref traverser_type_doc_nstut
 - \ref further_doc_nstut

@section cli_nstut Command-Line 'mlpack_knn'

The simplest way to perform nearest-neighbors search in \b mlpack is to use the
\c mlpack_knn executable.  This program will perform nearest-neighbors search
and place the resultant neighbors into one file and the resultant distances into
another.  The output files are organized such that the first row corresponds to
the nearest neighbors of the first query point, with the first column
corresponding to the nearest neighbor, and so forth.

Below are several examples of simple usage (and the resultant output).  The
\c -v option is used so that output is given.  Further documentation on each
individual option can be found by typing

@code
$ mlpack_knn --help
@endcode

@subsection cli_ex1_nstut One dataset, 5 nearest neighbors

@code
$ mlpack_knn -r dataset.csv -n neighbors_out.csv -d distances_out.csv -k 5 -v
[INFO ] Loading 'dataset.csv' as CSV data.  Size is 3 x 1000.
[INFO ] Loaded reference data from 'dataset.csv' (3 x 1000).
[INFO ] Building reference tree...
[INFO ] Tree built.
[INFO ] Searching for 5 nearest neighbors with dual-tree kd-tree search...
[INFO ] 18412 node combinations were scored.
[INFO ] 54543 base cases were calculated.
[INFO ] Search complete.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ]   distances_file: distances_out.csv
[INFO ]   help: false
[INFO ]   info: ""
[INFO ]   input_model_file: ""
[INFO ]   k: 5
[INFO ]   leaf_size: 20
[INFO ]   naive: false
[INFO ]   neighbors_file: neighbors_out.csv
[INFO ]   output_model_file: ""
[INFO ]   query_file: ""
[INFO ]   random_basis: false
[INFO ]   reference_file: dataset.csv
[INFO ]   seed: 0
[INFO ]   single_mode: false
[INFO ]   tree_type: kd
[INFO ]   verbose: true
[INFO ]   version: false
[INFO ]
[INFO ] Program timers:
[INFO ]   computing_neighbors: 0.108968s
[INFO ]   loading_data: 0.006495s
[INFO ]   saving_data: 0.003843s
[INFO ]   total_time: 0.126036s
[INFO ]   tree_building: 0.003442s
@endcode

Convenient program timers are given for different parts of the calculation at
the bottom of the output, as well as the parameters the simulation was run with.
Now, if we look at the output files:

@code
$ head neighbors_out.csv
862,344,224,43,885
703,499,805,639,450
867,472,972,380,601
397,319,277,443,323
840,827,865,38,438
732,876,751,492,616
563,222,569,985,940
361,97,928,437,79
547,695,419,961,716
982,113,689,843,634

$ head distances_out.csv
5.986076164057e-02,7.664920518084e-02,1.116050961847e-01,1.155595474371e-01,1.169810085522e-01
7.532635022982e-02,1.012564715841e-01,1.127846944644e-01,1.209584396720e-01,1.216543647014e-01
7.659571546879e-02,1.014588981948e-01,1.025114621511e-01,1.128082429187e-01,1.131659758673e-01
2.079405647909e-02,4.710724516732e-02,7.597622408419e-02,9.171977778898e-02,1.037033340864e-01
7.082206779700e-02,9.002355499742e-02,1.044181406406e-01,1.093149568834e-01,1.139700558608e-01
5.688056488896e-02,9.478072514474e-02,1.085637706630e-01,1.114177921451e-01,1.139370265105e-01
7.882260880455e-02,9.454474078041e-02,9.724494179950e-02,1.023829575445e-01,1.066927013814e-01
7.005321598247e-02,9.131417221561e-02,9.498248889074e-02,9.897964162308e-02,1.121202216165e-01
5.295654132754e-02,5.509877761894e-02,8.108227366619e-02,9.785461174861e-02,1.043968140367e-01
3.992859920333e-02,4.471418646159e-02,7.346053904990e-02,9.181982339584e-02,9.843075910782e-02
@endcode

So, the nearest neighbor to point 0 is point 862, with a distance of
5.986076164057e-02.  The second nearest neighbor to point 0 is point 344, with a
distance of 7.664920518084e-02.  The third nearest neighbor to point 5 is point
751, with a distance of 1.085637706630e-01.

@subsection cli_ex2_nstut Query and reference dataset, 10 nearest neighbors

@code
$ mlpack_knn -q query_dataset.csv -r reference_dataset.csv \
> -n neighbors_out.csv -d distances_out.csv -k 10 -v
[INFO ] Loading 'reference_dataset.csv' as CSV data.  Size is 3 x 1000.
[INFO ] Loaded reference data from 'reference_dataset.csv' (3 x 1000).
[INFO ] Building reference tree...
[INFO ] Tree built.
[INFO ] Loading 'query_dataset.csv' as CSV data.  Size is 3 x 50.
[INFO ] Loaded query data from 'query_dataset.csv' (3x50).
[INFO ] Searching for 10 nearest neighbors with dual-tree kd-tree search...
[INFO ] Building query tree...
[INFO ] Tree built.
[INFO ] Search complete.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ]   distances_file: distances_out.csv
[INFO ]   help: false
[INFO ]   info: ""
[INFO ]   input_model_file: ""
[INFO ]   k: 10
[INFO ]   leaf_size: 20
[INFO ]   naive: false
[INFO ]   neighbors_file: neighbors_out.csv
[INFO ]   output_model_file: ""
[INFO ]   query_file: query_dataset.csv
[INFO ]   random_basis: false
[INFO ]   reference_file: reference_dataset.csv
[INFO ]   seed: 0
[INFO ]   single_mode: false
[INFO ]   tree_type: kd
[INFO ]   verbose: true
[INFO ]   version: false
[INFO ]
[INFO ] Program timers:
[INFO ]   computing_neighbors: 0.022589s
[INFO ]   loading_data: 0.003572s
[INFO ]   saving_data: 0.000755s
[INFO ]   total_time: 0.032197s
[INFO ]   tree_building: 0.002590s
@endcode

@subsection cli_ex3_nstut One dataset, 3 nearest neighbors, leaf size of 15 points

@code
$ mlpack_knn -r dataset.csv -n neighbors_out.csv -d distances_out.csv -k 3 -l 15 -v
[INFO ] Loading 'dataset.csv' as CSV data.  Size is 3 x 1000.
[INFO ] Loaded reference data from 'dataset.csv' (3 x 1000).
[INFO ] Building reference tree...
[INFO ] Tree built.
[INFO ] Searching for 3 nearest neighbors with dual-tree kd-tree search...
[INFO ] 19692 node combinations were scored.
[INFO ] 36263 base cases were calculated.
[INFO ] Search complete.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ]   distances_file: distances_out.csv
[INFO ]   help: false
[INFO ]   info: ""
[INFO ]   input_model_file: ""
[INFO ]   k: 3
[INFO ]   leaf_size: 15
[INFO ]   naive: false
[INFO ]   neighbors_file: neighbors_out.csv
[INFO ]   output_model_file: ""
[INFO ]   query_file: ""
[INFO ]   random_basis: false
[INFO ]   reference_file: dataset.csv
[INFO ]   seed: 0
[INFO ]   single_mode: false
[INFO ]   tree_type: kd
[INFO ]   verbose: true
[INFO ]   version: false
[INFO ]
[INFO ] Program timers:
[INFO ]   computing_neighbors: 0.059020s
[INFO ]   loading_data: 0.002791s
[INFO ]   saving_data: 0.002369s
[INFO ]   total_time: 0.069277s
[INFO ]   tree_building: 0.002713s
@endcode

Further documentation on options should be found by using the --help option.

@section knn_nstut The 'KNN' class

The 'KNN' class is, specifically, a typedef of the more extensible
NeighborSearch class, querying for nearest neighbors using the Euclidean
distance.

@code
typedef NeighborSearch<NearestNeighborSort, metric::EuclideanDistance>
    KNN;
@endcode

Using the KNN class is particularly simple; first, the object must be
constructed and given a dataset.  Then, the method is run, and two matrices are
returned: one which holds the indices of the nearest neighbors, and one which
holds the distances of the nearest neighbors.  These are of the same structure
as the output --neighbors_file and --distances_file for the CLI interface (see
above).  A handful of examples of simple usage of the KNN class are given
below.

@subsection knn_ex1_nstut 5 nearest neighbors on a single dataset

@code
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>

using namespace mlpack::neighbor;

// Our dataset matrix, which is column-major.
extern arma::mat data;

KNN a(data);

// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;

a.Search(5, resultingNeighbors, resultingDistances);
@endcode

The output of the search is stored in resultingNeighbors and resultingDistances.

@subsection knn_ex2_nstut 10 nearest neighbors on a query and reference dataset

@code
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>

using namespace mlpack::neighbor;

// Our dataset matrices, which are column-major.
extern arma::mat queryData, referenceData;

KNN a(referenceData);

// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;

a.Search(queryData, 10, resultingNeighbors, resultingDistances);
@endcode

@subsection knn_ex3_nstut Naive (exhaustive) search for 6 nearest neighbors on one dataset

This example uses the O(n^2) naive search (not the tree-based search).

@code
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>

using namespace mlpack::neighbor;

// Our dataset matrix, which is column-major.
extern arma::mat dataset;

KNN a(dataset, true);

// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;

a.Search(6, resultingNeighbors, resultingDistances);
@endcode

Needless to say, naive search can be very slow...

@section neighborsearch_nstut The extensible 'NeighborSearch' class

The NeighborSearch class is very extensible, having the following template
arguments:

@code
template<
  typename SortPolicy = NearestNeighborSort,
  typename MetricType = mlpack::metric::EuclideanDistance,
  typename MatType = arma::mat,
  template<typename TreeMetricType,
           typename TreeStatType,
           typename TreeMatType> class TreeType = tree::KDTree,
  template<typename RuleType> class TraversalType =
      TreeType<MetricType, NeighborSearchStat<SortPolicy>,
               MatType>::template DualTreeTraverser>
>
class NeighborSearch;
@endcode

By choosing different components for each of these template classes, a very
arbitrary neighbor searching object can be constructed.  Note that each of these
template parameters have defaults, so it is not necessary to specify each one.

@subsection sort_policy_doc_nstut SortPolicy policy class

The SortPolicy template parameter allows specification of how the NeighborSearch
object will decide which points are to be searched for.  The
mlpack::neighbor::NearestNeighborSort class is a well-documented example.  A
custom SortPolicy class must implement the same methods which
NearestNeighborSort does:

@code
static size_t SortDistance(const arma::vec& list, double newDistance);

static bool IsBetter(const double value, const double ref);

template<typename TreeType>
static double BestNodeToNodeDistance(const TreeType* queryNode,
                                     const TreeType* referenceNode);

template<typename TreeType>
static double BestPointToNodeDistance(const arma::vec& queryPoint,
                                      const TreeType* referenceNode);

static const double WorstDistance();

static const double BestDistance();
@endcode

The mlpack::neighbor::FurthestNeighborSort class is another implementation,
which is used to create the 'KFN' typedef class, which finds the furthest
neighbors, as opposed to the nearest neighbors.

@subsection metric_type_doc_nstut MetricType policy class

The MetricType policy class allows the neighbor search to take place in any
arbitrary metric space.  The mlpack::metric::LMetric class is a good example
implementation.  A MetricType class must provide the following functions:

@code
// Empty constructor is required.
MetricType();

// Compute the distance between two points.
template<typename VecType>
double Evaluate(const VecType& a, const VecType& b);
@endcode

Internally, the NeighborSearch class keeps an instantiated MetricType class
(which can be given in the constructor).   This is useful for a metric like the
Mahalanobis distance (mlpack::metric::MahalanobisDistance), which must store
state (the covariance matrix).  Therefore, you can write a non-static MetricType
class and use it seamlessly with NeighborSearch.

For more information on the MetricType policy, see the documentation
\ref metrics "here".

@subsection mat_type_doc_nstut MatType policy class

The MatType template parameter specifies the type of data matrix used.  This
type must implement the same operations as an Armadillo matrix, and so standard
choices are @c arma::mat and @c arma::sp_mat.

@subsection tree_type_doc_nstut TreeType policy class

The NeighborSearch class allows great extensibility in the selection of the type
of tree used for search.  This type must follow the typical mlpack TreeType
policy, documented \ref trees "here".

Typical choices might include mlpack::tree::KDTree, mlpack::tree::BallTree,
mlpack::tree::StandardCoverTree, mlpack::tree::RTree, or
mlpack::tree::RStarTree.  It is easily possible to make your own tree type for
use with NeighborSearch; consult the \ref trees "TreeType documentation" for
more details.

An example of using the NeighborSearch class with a ball tree is given below.

@code
// Construct a NeighborSearch object with ball bounds.
NeighborSearch<
    NearestNeighborSort,
    metric::EuclideanDistance,
    arma::mat,
    tree::BallTree
> neighborSearch(dataset);
@endcode

@subsection traverser_type_doc_nstut TraverserType policy class

The last template parameter the NeighborSearch class offers is the TraverserType
class.  The TraverserType class holds the strategy used to traverse the trees in
either single-tree or dual-tree search mode.  By default, it is set to use the
default traverser of the given @c TreeType (which is the member @c
TreeType::DualTreeTraverser).

This class must implement the following two methods:

@code
// Instantiate with a given RuleType.
TraverserType(RuleType& rule);

// Traverse with two trees.
void Traverse(TreeType& queryNode, TreeType& referenceNode);
@endcode

The RuleType class provides the following functions for use in the traverser:

@code
// Evaluate the base case between two points.
double BaseCase(const size_t queryIndex, const size_t referenceIndex);

// Score the two nodes to see if they can be pruned, returning DBL_MAX if they
// can be pruned.
double Score(TreeType& queryNode, TreeType& referenceNode);
@endcode

Note also that any traverser given must satisfy the definition of a pruning
dual-tree traversal given in the paper "Tree-independent dual-tree algorithms".

@section further_doc_nstut Further documentation

For further documentation on the NeighborSearch class, consult the
\ref mlpack::neighbor::NeighborSearch "complete API documentation".

*/