mlpack implements multiple strategies for approximate furthest neighbor
search in its mlpack_approx_kfn
and mlpack_kfn
command-line programs (each
program corresponds to different techniques). This tutorial discusses what
problems these algorithms solve and how to use each of the techniques that
mlpack implements.
Note that these functions are available as bindings to other languages too, and all the examples here can be adapted accordingly.
mlpack implements five approximate furthest neighbor search algorithms:
- brute-force search (in
mlpack_kfn
) - single-tree search (in
mlpack_kfn
) - dual-tree search (in
mlpack_kfn
) - query-dependent approximate furthest neighbor (QDAFN) (in
mlpack_approx_kfn
) - DrusillaSelect (in
mlpack_approx_kfn
)
These methods are described in the following papers:
@inproceedings{curtin2013tree,
title={Tree-Independent Dual-Tree Algorithms},
author={Curtin, Ryan R. and March, William B. and Ram, Parikshit and Anderson,
David V. and Gray, Alexander G. and Isbell Jr., Charles L.},
booktitle={Proceedings of The 30th International Conference on Machine
Learning (ICML '13)},
pages={1435--1443},
year={2013}
}
@incollection{pagh2015approximate,
title={Approximate furthest neighbor in high dimensions},
author={Pagh, Rasmus and Silvestri, Francesco and Sivertsen, Johan and Skala,
Matthew},
booktitle={Similarity Search and Applications},
pages={3--14},
year={2015},
publisher={Springer}
}
@incollection{curtin2016fast,
title={Fast approximate furthest neighbors with data-dependent candidate
selection},
author={Curtin, Ryan R., and Gardner, Andrew B.},
booktitle={Similarity Search and Applications},
pages={221--235},
year={2016},
publisher={Springer}
}
@article{curtin2018exploiting,
title={Exploiting the structure of furthest neighbor search for fast
approximate results},
author={Curtin, Ryan R., and Echauz, Javier, and Gardner, Andrew B.},
journal={Information Systems},
year={2018},
publisher={Elsevier}
}
The problem of furthest neighbor search is simple, and is the opposite of the
much-more-studied nearest neighbor search problem. Given a set of reference
points R
(the set in which we are searching), and a set of query points Q
(the set of points for which we want the furthest neighbor), our goal is to
return the k
furthest neighbors for each query point in Q
:
k-argmax_{p_r in R} d(p_q, p_r).
In order to solve this problem, mlpack provides a number of interfaces.
- two simple command-line executables to calculate approximate furthest neighbors
- a simple C++ class for QDAFN
- a simple C++ class for DrusillaSelect
- a simple C++ class for tree-based and brute-force search
There are three algorithms for furthest neighbor search that mlpack implements, and each is suited to a different setting. Below is some basic guidance on what should be used. Note that the question of "which algorithm should be used" is a very difficult question to answer, so the guidance below is just that---guidance---and may not be right for a particular problem.
DrusillaSelect
is very fast and will perform extremely well for datasets with outliers or datasets with structure (like low-dimensional datasets embedded in high dimensions)QDAFN
is a random approach and therefore should be well-suited for datasets with little to no structure- The tree-based approaches (the
KFN
class and themlpack_kfn
program) is best suited for low-dimensional datasets, and is most effective when very small levels of approximation are desired, or when exact results are desired. - Dual-tree search is most useful when the query set is large and structured (like for all-furthest-neighbor search).
- Single-tree search is more useful when the query set is small.
mlpack provides two command-line programs to solve approximate furthest neighbor search:
mlpack_approx_kfn
, for the QDAFN and DrusillaSelect approachesmlpack_kfn
, for exact and approximate tree-based approaches
These two programs allow a large number of algorithms to be used to find
approximate furthest neighbors. Note that the mlpack_kfn
program is also
documented in the KNN tutorial page, as it shares options
with the mlpack_knn
program.
Below are several examples of how the mlpack_approx_kfn
and mlpack_kfn
programs might be used. The first examples focus on the mlpack_approx_kfn
program, and the last few show how mlpack_kfn
can be used to produce
approximate results.
Here we have a query dataset queries.csv
and a reference dataset refs.csv
and we wish to find the 5 furthest neighbors of every query point in the
reference dataset. We may do that with the mlpack_approx_kfn
algorithm,
using the default of the DrusillaSelect
algorithm with default parameters.
$ mlpack_approx_kfn -q queries.csv -r refs.csv -v -k 5 -n n.csv -d d.csv
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building DrusillaSelect model...
[INFO ] Model built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 5 furthest neighbors with DrusillaSelect...
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: ds
[INFO ] calculate_error: false
[INFO ] distances_file: d.csv
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 5
[INFO ] neighbors_file: n.csv
[INFO ] num_projections: 5
[INFO ] num_tables: 5
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] drusilla_select_construct: 0.000342s
[INFO ] drusilla_select_search: 0.000780s
[INFO ] loading_data: 0.010689s
[INFO ] saving_data: 0.005585s
[INFO ] total_time: 0.018592s
Convenient timers for parts of the program operation are printed. The results,
saved in n.csv
and d.csv
, indicate the furthest neighbors and distances for
each query point. The row of the output file indicates the query point that the
results are for. The neighbors are listed from furthest to nearest; so, the 4th
element in the 3rd row of d.csv
indicates the distance between the 3rd query
point in queries.csv
and its approximate 4th furthest neighbor. Similarly,
the same element in n.csv
indicates the index of the approximate 4th furthest
neighbor (with respect to refs.csv
).
The -p
(--num_projections
) and -t
(--num_tables
) parameters affect the
running of the DrusillaSelect
algorithm and the QDAFN algorithm.
Specifically, larger values for each of these parameters will search more
possible candidate furthest neighbors and produce better results (at the cost of
runtime). More details on how each of these parameters works is available in
the original papers, the mlpack source, or the documentation given by --help
.
In the example below, we run DrusillaSelect
to find 4 furthest neighbors using
10 tables and 2 points in each table. In this case we have chosen to omit the
-n n.csv
option, meaning that only the output candidate distances will be
written to d.csv
.
$ mlpack_approx_kfn -q queries.csv -r refs.csv -v -k 4 -n n.csv -d d.csv -t 10 -p 2
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building DrusillaSelect model...
[INFO ] Model built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 4 furthest neighbors with DrusillaSelect...
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: ds
[INFO ] calculate_error: false
[INFO ] distances_file: d.csv
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 4
[INFO ] neighbors_file: n.csv
[INFO ] num_projections: 2
[INFO ] num_tables: 10
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] drusilla_select_construct: 0.000645s
[INFO ] drusilla_select_search: 0.000551s
[INFO ] loading_data: 0.008518s
[INFO ] saving_data: 0.003734s
[INFO ] total_time: 0.014019s
The algorithm to be used for approximate furthest neighbor search can be
specified with the --algorithm
(-a
) option to the mlpack_approx_kfn
program. Below, we use the QDAFN algorithm instead of the default. We leave
the -p
and -t
options at their defaults---even though QDAFN often requires
more tables and points to get the same quality of results.
$ mlpack_approx_kfn -q queries.csv -r refs.csv -v -k 3 -n n.csv -d d.csv -a qdafn
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building QDAFN model...
[INFO ] Model built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 3 furthest neighbors with QDAFN...
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: qdafn
[INFO ] calculate_error: false
[INFO ] distances_file: d.csv
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 3
[INFO ] neighbors_file: n.csv
[INFO ] num_projections: 5
[INFO ] num_tables: 5
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] loading_data: 0.008380s
[INFO ] qdafn_construct: 0.003399s
[INFO ] qdafn_search: 0.000886s
[INFO ] saving_data: 0.002253s
[INFO ] total_time: 0.015465s
The mlpack_approx_kfn
program can calculate the quality of the results if the
--calculate_error
(-e
) flag is specified. Below we use the program with its
default parameters and calculate the error, which is displayed in the output.
The error is only calculated for the furthest neighbor, not all k; therefore, in
this example we have set -k
to 1
.
$ mlpack_approx_kfn -q queries.csv -r refs.csv -v -k 1 -e -q -n n.csv
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building DrusillaSelect model...
[INFO ] Model built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 1 furthest neighbors with DrusillaSelect...
[INFO ] Search complete.
[INFO ] Calculating exact distances...
[INFO ] 28891 node combinations were scored.
[INFO ] 37735 base cases were calculated.
[INFO ] Calculation complete.
[INFO ] Average error: 1.08417.
[INFO ] Maximum error: 1.28712.
[INFO ] Minimum error: 1.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: ds
[INFO ] calculate_error: true
[INFO ] distances_file: ""
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 3
[INFO ] neighbors_file: ""
[INFO ] num_projections: 5
[INFO ] num_tables: 5
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.001476s
[INFO ] drusilla_select_construct: 0.000309s
[INFO ] drusilla_select_search: 0.000495s
[INFO ] loading_data: 0.008462s
[INFO ] total_time: 0.011670s
[INFO ] tree_building: 0.000202s
Note that the output includes three lines indicating the error:
[INFO ] Average error: 1.08417.
[INFO ] Maximum error: 1.28712.
[INFO ] Minimum error: 1.
In this case, a minimum error of 1 indicates an exact result, and over the entire query set the algorithm has returned a furthest neighbor candidate with maximum error 1.28712.
However, for large datasets, calculating the error may take a long time, because
the exact furthest neighbors must be calculated. Therefore, if the exact
furthest neighbor distances are already known, they may be passed in with the
--exact_distances_file
(-x
) option in order to avoid the calculation. In
the example below, we assume exact.csv
contains the exact furthest neighbor
distances. We run the qdafn
algorithm in this example.
Note that the -e
option must be specified for the -x
option have any effect.
$ mlpack_approx_kfn -q queries.csv -r refs.csv -k 1 -e -x exact.csv -n n.csv -v -a qdafn
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building QDAFN model...
[INFO ] Model built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 1 furthest neighbors with QDAFN...
[INFO ] Search complete.
[INFO ] Loading 'exact.csv' as raw ASCII formatted data. Size is 1 x 1000.
[INFO ] Average error: 1.06914.
[INFO ] Maximum error: 1.67407.
[INFO ] Minimum error: 1.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: qdafn
[INFO ] calculate_error: true
[INFO ] distances_file: ""
[INFO ] exact_distances_file: exact.csv
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 1
[INFO ] neighbors_file: n.csv
[INFO ] num_projections: 5
[INFO ] num_tables: 5
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] loading_data: 0.010348s
[INFO ] qdafn_construct: 0.000318s
[INFO ] qdafn_search: 0.000793s
[INFO ] saving_data: 0.000259s
[INFO ] total_time: 0.012254s
The mlpack_kfn
algorithm allows specifying a desired approximation level with
the --epsilon
(-e
) option. The parameter must be greater than or equal to 0
and less than 1. A setting of 0 indicates exact search.
The example below runs dual-tree furthest neighbor search (the default algorithm) with the approximation parameter set to 0.5.
$ mlpack_kfn -q queries.csv -r refs.csv -v -k 3 -e 0.5 -n n.csv -d d.csv
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Loaded reference data from 'refs.csv' (3x1000).
[INFO ] Building reference tree...
[INFO ] Tree built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Loaded query data from 'queries.csv' (3x1000).
[INFO ] Searching for 3 neighbors with dual-tree kd-tree search...
[INFO ] 1611 node combinations were scored.
[INFO ] 13938 base cases were calculated.
[INFO ] 1611 node combinations were scored.
[INFO ] 13938 base cases were calculated.
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: dual_tree
[INFO ] distances_file: d.csv
[INFO ] epsilon: 0.5
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 3
[INFO ] leaf_size: 20
[INFO ] naive: false
[INFO ] neighbors_file: n.csv
[INFO ] output_model_file: ""
[INFO ] percentage: 1
[INFO ] query_file: queries.csv
[INFO ] random_basis: false
[INFO ] reference_file: refs.csv
[INFO ] seed: 0
[INFO ] single_mode: false
[INFO ] tree_type: kd
[INFO ] true_distances_file: ""
[INFO ] true_neighbors_file: ""
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.000442s
[INFO ] loading_data: 0.008060s
[INFO ] saving_data: 0.002850s
[INFO ] total_time: 0.012667s
[INFO ] tree_building: 0.000251s
Note that the format of the output files d.csv
and n.csv
are the same as
for mlpack_approx_kfn
.
The mlpack_kfn
program offers a large number of different algorithms that can
be used. The --algorithm
(-a
) parameter may be used to specify three main
different algorithm types: naive
(brute-force search), single_tree
(single-tree search), dual_tree
(dual-tree search, the default), and greedy
("defeatist" greedy search, which goes to one leaf node of the tree then
terminates). The example below uses single-tree search to find approximate
neighbors with epsilon set to 0.1.
mlpack_kfn -q queries.csv -r refs.csv -v -k 3 -e 0.1 -n n.csv -d d.csv -a single_tree
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Loaded reference data from 'refs.csv' (3x1000).
[INFO ] Building reference tree...
[INFO ] Tree built.
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Loaded query data from 'queries.csv' (3x1000).
[INFO ] Searching for 3 neighbors with single-tree kd-tree search...
[INFO ] 13240 node combinations were scored.
[INFO ] 15924 base cases were calculated.
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: single_tree
[INFO ] distances_file: d.csv
[INFO ] epsilon: 0.1
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 3
[INFO ] leaf_size: 20
[INFO ] naive: false
[INFO ] neighbors_file: n.csv
[INFO ] output_model_file: ""
[INFO ] percentage: 1
[INFO ] query_file: queries.csv
[INFO ] random_basis: false
[INFO ] reference_file: refs.csv
[INFO ] seed: 0
[INFO ] single_mode: false
[INFO ] tree_type: kd
[INFO ] true_distances_file: ""
[INFO ] true_neighbors_file: ""
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] computing_neighbors: 0.000850s
[INFO ] loading_data: 0.007858s
[INFO ] saving_data: 0.003445s
[INFO ] total_time: 0.013084s
[INFO ] tree_building: 0.000250s
The mlpack_approx_kfn
and mlpack_kfn
programs both allow models to be saved
and loaded for future use. The --output_model_file
(-M
) option allows
specifying where to save a model, and the --input_model_file
(-m
) option
allows a model to be loaded instead of trained. So, if you specify
--input_model_file
then you do not need to specify --reference_file
(-r
),
--num_projections
(-p
), or --num_tables
(-t
).
The example below saves a model with 10 projections and 5 tables. Note that
neither --query_file
(-q
) nor -k
are specified; this run only builds the
model and saves it to model.bin
.
$ mlpack_approx_kfn -r refs.csv -t 5 -p 10 -v -M model.bin
[INFO ] Loading 'refs.csv' as CSV data. Size is 3 x 1000.
[INFO ] Building DrusillaSelect model...
[INFO ] Model built.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: ds
[INFO ] calculate_error: false
[INFO ] distances_file: ""
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: ""
[INFO ] k: 0
[INFO ] neighbors_file: ""
[INFO ] num_projections: 10
[INFO ] num_tables: 5
[INFO ] output_model_file: model.bin
[INFO ] query_file: ""
[INFO ] reference_file: refs.csv
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] drusilla_select_construct: 0.000321s
[INFO ] loading_data: 0.004700s
[INFO ] total_time: 0.007320s
Now, with the model saved, we can run approximate furthest neighbor search on a query set using the saved model:
$ mlpack_approx_kfn -m model.bin -q queries.csv -k 3 -d d.csv -n n.csv -v
[INFO ] Loading 'queries.csv' as CSV data. Size is 3 x 1000.
[INFO ] Searching for 3 furthest neighbors with DrusillaSelect...
[INFO ] Search complete.
[INFO ] Saving CSV data to 'n.csv'.
[INFO ] Saving CSV data to 'd.csv'.
[INFO ]
[INFO ] Execution parameters:
[INFO ] algorithm: ds
[INFO ] calculate_error: false
[INFO ] distances_file: d.csv
[INFO ] exact_distances_file: ""
[INFO ] help: false
[INFO ] info: ""
[INFO ] input_model_file: model.bin
[INFO ] k: 3
[INFO ] neighbors_file: n.csv
[INFO ] num_projections: 5
[INFO ] num_tables: 5
[INFO ] output_model_file: ""
[INFO ] query_file: queries.csv
[INFO ] reference_file: ""
[INFO ] verbose: true
[INFO ] version: false
[INFO ]
[INFO ] Program timers:
[INFO ] drusilla_select_search: 0.000878s
[INFO ] loading_data: 0.004599s
[INFO ] saving_data: 0.003006s
[INFO ] total_time: 0.009234s
These options work in the same way for both the mlpack_approx_kfn
and
mlpack_kfn
programs.
Both the mlpack_kfn
and mlpack_approx_kfn
programs contain numerous options
not fully documented in these short examples. You can run each program with the
--help
(-h
) option for more information.
mlpack provides a simple DrusillaSelect
C++ class that can be used inside of
C++ programs to perform approximate furthest neighbor search. The class has
only one template parameter---MatType
---which specifies the type of matrix to
be use. That means the class can be used with either dense data (of type
arma::mat
) or sparse data (of type arma::sp_mat
).
The following examples show simple usage of this class.
The code below builds a DrusillaSelect
model with default options on the
matrix dataset
, then queries for the approximate furthest neighbor of every
point in the queries
matrix.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// The query set.
extern arma::mat queries;
// Construct the model with defaults.
DrusillaSelect<> ds(dataset);
// Query the model, putting output into the following two matrices.
arma::mat distances;
arma::Mat<size_t> neighbors;
ds.Search(queries, 1, neighbors, distances);
At the end of this code, both the distances
and neighbors
matrices will have
number of columns equal to the number of columns in the queries
matrix. So,
each column of the distances
and neighbors
matrices are the distances or
neighbors of the corresponding column in the queries
matrix.
The following example constructs a DrusillaSelect
model with 10 tables and 5
projections. Once that is done it performs the same task as the previous
example.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// The query set.
extern arma::mat queries;
// Construct the model with custom parameters.
DrusillaSelect<> ds(dataset, 10, 5);
// Query the model, putting output into the following two matrices.
arma::mat distances;
arma::Mat<size_t> neighbors;
ds.Search(queries, 1, neighbors, distances);
The DrusillaSelect
algorithm merely scans the reference set and extracts a
number of points that will be queried in a brute-force fashion when the
Search()
method is called. We can access this set with the CandidateSet()
method. The code below prints the fifth point of the candidate set.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// Construct the model with custom parameters.
DrusillaSelect<> ds(dataset, 10, 5);
// Print the fifth point of the candidate set.
std::cout << ds.CandidateSet().col(4).t();
It is possible to retrain a DrusillaSelect
model with new parameters or with a
new reference set. This is functionally equivalent to creating a new model.
The example code below creates a first DrusillaSelect
model using 3 tables
and 10 projections, and then retrains this with the same reference set using 10
tables and 3 projections.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// Construct the model with initial parameters.
DrusillaSelect<> ds(dataset, 3, 10);
// Now retrain with different parameters.
ds.Train(dataset, 10, 3);
We can set the template parameter for DrusillaSelect
to arma::sp_mat
in
order to perform furthest neighbor search on sparse data. This code below
creates a DrusillaSelect
model using 4 tables and 6 projections with sparse
input data, then searches for 3 approximate furthest neighbors.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::sp_mat dataset;
// The query dataset.
extern arma::sp_mat querySet;
// Construct the model on sparse data.
DrusillaSelect<arma::sp_mat> ds(dataset, 4, 6);
// Search on query data.
arma::Mat<size_t> neighbors;
arma::mat distances;
ds.Search(querySet, 3, neighbors, distances);
mlpack also provides a standalone simple QDAFN
class for furthest neighbor
search. The API for this class is virtually identical to the DrusillaSelect
class, and also has one template parameter to specify the type of matrix to be
used (dense or sparse or other).
The following subsections demonstrate usage of the QDAFN
class in the same way
as the previous section's examples for DrusillaSelect
.
The code below builds a QDAFN
model with default options on the matrix
dataset
, then queries for the approximate furthest neighbor of every point in
the queries
matrix.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// The query set.
extern arma::mat queries;
// Construct the model with defaults.
QDAFN<> qd(dataset);
// Query the model, putting output into the following two matrices.
arma::mat distances;
arma::Mat<size_t> neighbors;
qd.Search(queries, 1, neighbors, distances);
At the end of this code, both the distances
and neighbors
matrices will have
number of columns equal to the number of columns in the queries
matrix. So,
each column of the distances
and neighbors
matrices are the distances or
neighbors of the corresponding column in the queries
matrix.
The following example constructs a QDAFN
model with 15 tables and 30
projections. Once that is done it performs the same task as the previous
example.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// The query set.
extern arma::mat queries;
// Construct the model with custom parameters.
QDAFN<> qdafn(dataset, 15, 30);
// Query the model, putting output into the following two matrices.
arma::mat distances;
arma::Mat<size_t> neighbors;
qdafn.Search(queries, 1, neighbors, distances);
The QDAFN
algorithm scans the reference set, extracting points that have been
projected onto random directions. Each random direction corresponds to a single
table. The QDAFN
class stores these points as a vector of matrices, which can
be accessed with the CandidateSet()
method. The code below prints the fifth
point of the candidate set of the third table.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// Construct the model with custom parameters.
QDAFN<> qdafn(dataset, 10, 5);
// Print the fifth point of the candidate set.
std::cout << qdafn.CandidateSet(2).col(4).t();
It is possible to retrain a QDAFN
model with new parameters or with a new
reference set. This is functionally equivalent to creating a new model. The
example code below creates a first QDAFN
model using 10 tables and 40
projections, and then retrains this with the same reference set using 15 tables
and 25 projections.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// Construct the model with initial parameters.
QDAFN<> qdafn(dataset, 3, 10);
// Now retrain with different parameters.
qdafn.Train(dataset, 10, 3);
We can set the template parameter for QDAFN
to arma::sp_mat
in order to
perform furthest neighbor search on sparse data. This code below creates a
QDAFN
model using 20 tables and 60 projections with sparse input data, then
searches for 3 approximate furthest neighbors.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::sp_mat dataset;
// The query dataset.
extern arma::sp_mat querySet;
// Construct the model on sparse data.
QDAFN<arma::sp_mat> qdafn(dataset, 20, 60);
// Search on query data.
arma::Mat<size_t> neighbors;
arma::mat distances;
qdafn.Search(querySet, 3, neighbors, distances);
The extensive NeighborSearch
class also provides a way to search for
approximate furthest neighbors using a different, tree-based technique. For
full documentation on this class, see the NeighborSearch
tutorial. The KFN
class is a convenient typedef of the
NeighborSearch
class that can be used to perform the furthest neighbors task
with kd
-trees.
In the following subsections, the KFN
class is used in short code examples.
The KFN
class has construction semantics similar to DrusillaSelect
and
QDAFN
. The example below constructs a KFN
object (which will build the
tree on the reference set), but note that the third parameter to the constructor
allows us to specify our desired level of approximation. In this example we
choose epsilon = 0.05
. Then, the code searches for 3 approximate furthest
neighbors.
#include <mlpack.hpp>
using namespace mlpack;
// The reference dataset.
extern arma::mat dataset;
// The query set.
extern arma::mat querySet;
// Construct the object, performing the default dual-tree search with
// approximation level epsilon = 0.05.
KFN kfn(dataset, DUAL_TREE_MODE, 0.05);
// Search for approximate furthest neighbors.
arma::Mat<size_t> neighbors;
arma::mat distances;
kfn.Search(querySet, 3, neighbors, distances);
Like the QDAFN
and DrusillaSelect
classes, the KFN
class is capable of
retraining on a new reference set. The code below demonstrates this.
#include <mlpack.hpp>
using namespace mlpack;
// The original reference set we train on.
extern arma::mat dataset;
// The new reference set we retrain on.
extern arma::mat newDataset;
// Construct the object with approximation level 0.1.
KFN kfn(dataset, DUAL_TREE_MODE, 0.1);
// Retrain on the new reference set.
kfn.Train(newDataset);
The particular mode to be used in search can be specified in the constructor. In this example, we use single-tree search (as opposed to the default of dual-tree search).
#include <mlpack.hpp>
using namespace mlpack;
// The reference set.
extern arma::mat dataset;
// The query set.
extern arma::mat querySet;
// Construct the object with approximation level 0.25 and in single tree search
// mode.
KFN kfn(dataset, SINGLE_TREE_MODE, 0.25);
// Search for 5 approximate furthest neighbors.
arma::Mat<size_t> neighbors;
arma::mat distances;
kfn.Search(querySet, 5, neighbors, distances);
If desired, brute-force search ("naive search") can be used to find the furthest
neighbors; however, the result will not be approximate---it will be exact (since
every possibility will be considered). The code below performs exact furthest
neighbor search by using the KFN
class in brute-force mode.
#include <mlpack.hpp>
using namespace mlpack;
// The reference set.
extern arma::mat dataset;
// The query set.
extern arma::mat querySet;
// Construct the object in brute-force mode. We can leave the approximation
// parameter to its default (0) since brute-force will provide exact results.
KFN kfn(dataset, NAIVE_MODE);
// Perform the search for 2 furthest neighbors.
arma::Mat<size_t> neighbors;
arma::mat distances;
kfn.Search(querySet, 2, neighbors, distances);
For further documentation on the approximate furthest neighbor facilities
offered by mlpack, see also the NeighborSearch tutorial. Also,
each class (QDAFN
, DrusillaSelect
, NeighborSelect
) are well-documented,
and more details can be found in the source code documentation.