NAME¶
nstutorial - NeighborSearch tutorial (k-nearest-neighbors)
Introduction¶
Nearest-neighbors search is a common machine learning task. In this setting, we
have a
query and a
reference dataset. For each point in the
query dataset, we wish to know the $k$ points in the
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 $k$
nearest points to that point.
mlpack provides:
- •
- a simple command-line executable to run nearest-neighbors search
(and furthest-neighbors search)
- •
- a simple C++ interface to perform nearest-neighbors search (and
furthest-neighbors search)
- •
- a generic, extensible, and powerful C++ class (NeighborSearch) for
complex usage
Table of Contents¶
A list of all the sections this tutorial contains.
- •
- Introduction
- •
- Table of Contents
- •
- Command-Line 'allknn'
- •
- One dataset, 5 nearest neighbors
- •
- Query and reference dataset, 10 nearest neighbors
- •
- One dataset, 3 nearest neighbors, leaf size of 15 points
- •
- The 'AllkNN' class
- •
- 5 nearest neighbors on a single dataset
- •
- 10 nearest neighbors on a query and reference dataset
- •
- Naive (exhaustive) search for 6 nearest neighbors on one
dataset
- •
- The extensible 'NeighborSearch' class
- •
- SortPolicy policy class
- •
- MetricType policy class
- •
- TreeType policy class
- •
- Further documentation
Command-Line 'allknn'¶
The simplest way to perform nearest-neighbors search in
mlpack is to use
the allknn 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 '-v'
option is used so that output is given. Further documentation on each
individual option can be found by typing
$ allknn --help
One dataset, 5 nearest neighbors¶
$ allknn -r dataset.csv -n neighbors_out.csv -d distances_out.csv -k 5 -v
[INFO ] Loading 'dataset.csv' as CSV data.
[INFO ] Loaded reference data from 'dataset.csv'.
[INFO ] Building reference tree...
[INFO ] Trees built.
[INFO ] Computing 5 nearest neighbors...
[INFO ] Neighbors computed.
[INFO ] Re-mapping indices...
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] distances_file: distances_out.csv
[INFO ] help: false
[INFO ] info: ""
[INFO ] k: 5
[INFO ] leaf_size: 20
[INFO ] naive: false
[INFO ] neighbors_file: neighbors_out.csv
[INFO ] query_file: ""
[INFO ] reference_file: dataset.csv
[INFO ] single_mode: false
[INFO ] verbose: true
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.152495s
[INFO ] total_time: 0.201274s
[INFO ] tree_building: 0.005050s
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:
$ head neighbors_out.csv
14,5,13,16,27
90,79,80,15,10
39,84,10,123,1
81,43,109,12,37
15,1,79,90,10
0,14,16,13,27
90,79,11,1,15
41,45,12,37,49
11,81,13,6,15
41,7,45,49,47
$ head distances_out.csv
7.09614421e-04,2.05940173e-03,4.05346068e-03,4.66175278e-03,1.09757665e-02
8.92190948e-04,1.69442242e-03,2.82750475e-03,4.06590850e-03,7.54169243e-03
5.91539406e-03,6.83482612e-03,8.02877800e-03,9.04907425e-03,1.61458442e-02
7.15652913e-03,9.18228524e-03,1.00540941e-02,1.07541171e-02,1.28892864e-02
5.37535983e-03,9.05721409e-03,9.89017184e-03,1.01457735e-02,1.14021593e-02
2.05940173e-03,5.14437192e-03,9.97483954e-03,1.02463627e-02,1.44355783e-02
4.27355419e-03,6.36750547e-03,6.72478577e-03,8.77323532e-03,1.04530549e-02
1.99935847e-03,3.88240331e-03,4.19118273e-03,9.30693568e-03,1.21237481e-02
2.15454276e-03,8.18895210e-03,1.18360450e-02,1.25135454e-02,1.27783327e-02
8.43087996e-03,1.22946325e-02,1.60472209e-02,1.88661413e-02,1.89727686e-02
So, the nearest neighbor to point 0 is point 14, with a distance of 7.096144e-4.
The second nearest neighbor to point 0 is point 5, with a distance of
2.059402e-3. The third nearest neighbor to point 5 is point 16, with a
distance of 9.9748395e-3.
Query and reference dataset, 10 nearest neighbors¶
$ allknn -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.
[INFO ] Loaded reference data from 'reference_dataset.csv'.
[INFO ] Building reference tree...
[INFO ] Loading 'query_dataset.csv' as CSV data.
[INFO ] Query data loaded from 'query_dataset.csv'.
[INFO ] Building query tree...
[INFO ] Tree built.
[INFO ] Computing 10 nearest neighbors...
[INFO ] Neighbors computed.
[INFO ] Re-mapping indices...
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] distances_file: distances_out.csv
[INFO ] help: false
[INFO ] info: ""
[INFO ] k: 10
[INFO ] leaf_size: 20
[INFO ] naive: false
[INFO ] neighbors_file: neighbors_out.csv
[INFO ] query_file: query_dataset.csv
[INFO ] reference_file: reference_dataset.csv
[INFO ] single_mode: false
[INFO ] verbose: true
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.000081s
[INFO ] total_time: 0.062828s
[INFO ] tree_building: 0.004949s
One dataset, 3 nearest neighbors, leaf size of 15 points¶
$ allknn -r dataset.csv -n neighbors_out.csv -d distances_out.csv -k 3 -l 15 -v
[INFO ] Loading 'dataset.csv' as CSV data.
[INFO ] Loaded reference data from 'dataset.csv'.
[INFO ] Building reference tree...
[INFO ] Trees built.
[INFO ] Computing 3 nearest neighbors...
[INFO ] Neighbors computed.
[INFO ] Re-mapping indices...
[INFO ] Saving CSV data to 'distances_out.csv'.
[INFO ] Saving CSV data to 'neighbors_out.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] distances_file: distances_out.csv
[INFO ] help: false
[INFO ] info: ""
[INFO ] k: 3
[INFO ] leaf_size: 15
[INFO ] naive: false
[INFO ] neighbors_file: neighbors_out.csv
[INFO ] query_file: ""
[INFO ] reference_file: dataset.csv
[INFO ] single_mode: false
[INFO ] verbose: true
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.105119s
[INFO ] total_time: 0.145321s
[INFO ] tree_building: 0.005690s
Further documentation on options should be found by using the --help option.
The 'AllkNN' class¶
The 'AllkNN' class is, specifically, a typedef of the more extensible
NeighborSearch class, querying for nearest neighbors using the Euclidean
distance.
typedef NeighborSearch<NearestNeighborSort, metric::EuclideanDistance>
AllkNN;
Using the AllkNN 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 AllkNN class are given
below.
5 nearest neighbors on a single dataset¶
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>
using namespace mlpack::neighbor;
// Our dataset matrix, which is column-major.
extern arma::mat data;
AllkNN a(data);
// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;
a.Search(5, resultingNeighbors, resultingDistances);
The output of the search is stored in resultingNeighbors and resultingDistances.
10 nearest neighbors on a query and reference dataset¶
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>
using namespace mlpack::neighbor;
// Our dataset matrices, which are column-major.
extern arma::mat queryData, referenceData;
AllkNN a(referenceData, queryData);
// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;
a.Search(10, resultingNeighbors, resultingDistances);
Naive (exhaustive) search for 6 nearest neighbors on one dataset¶
This example uses the O(n^2) naive search (not the tree-based search).
#include <mlpack/methods/neighbor_search/neighbor_search.hpp>
using namespace mlpack::neighbor;
// Our dataset matrix, which is column-major.
extern arma::mat dataset;
AllkNN a(dataset, true);
// The matrices we will store output in.
arma::Mat<size_t> resultingNeighbors;
arma::mat resultingDistances;
a.Search(6, resultingNeighbors, resultingDistances);
Needless to say, naive search can be very slow...
The extensible 'NeighborSearch' class¶
The NeighborSearch class is very extensible, having the following template
arguments:
template<
typename SortPolicy = NearestNeighborSort,
typename MetricType = mlpack::metric::EuclideanDistance,
typename TreeType = mlpack::tree::BinarySpaceTree<bound::HRectBound<2>,
QueryStat<SortPolicy> >
>
class NeighborSearch;
By choosing different components for each of these template classes, a very
arbitrary neighbor searching object can be constructed.
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:
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();
The
mlpack::neighbor::FurthestNeighborSort class is another
implementation, which is used to create the 'AllkFN' typedef class, which
finds the furthest neighbors, as opposed to the nearest neighbors.
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:
// Empty constructor is required.
MetricType();
// Compute the distance between two points.
template<typename VecType>
double Evaluate(const VecType& a, const VecType& b);
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.
TreeType policy class¶
The NeighborSearch class also allows a custom tree to be used. The standard
MLPACK tree,
mlpack::tree::BinarySpaceTree, is also highly extensible
in its own right, and its documentation should be consulted for more
information. Currently, the NeighborSearch tree requires a tree which only has
left and right children, and no points in nodes (only in leaves), but this
support is planned to be extended.
A simple usage of the TreeType policy could be to use a different type of bound
with the tree. For instance, you could use a ball bound instead of a
rectangular bound:
// Construct a NeighborSearch object with ball bounds.
NeighborSearch<
NearestNeighborSort,
metric::EuclideanDistance,
tree::BinarySpaceTree<bound::BallBound<2>,
QueryStat<SortPolicy> >
> neighborSearch(dataset);
It is important to note that the NeighborSearch class requires use of the
QueryStat tree statistic to function properly. Therefore, if you write a
custom tree, be sure it can accept the QueryStat type. See the
mlpack::tree::BinarySpaceTree documentation for more information on
tree statistics.
Further documentation¶
For further documentation on the NeighborSearch class, consult the
complete
API documentation.