NAME

Math::Vector::Real::kdTree - kd-Tree implementation on top of Math::Vector::Real

SYNOPSIS

use Math::Vector::Real::kdTree;

use Math::Vector::Real;
use Math::Vector::Real::Random;

my @v = map Math::Vector::Real->random_normal(4), 1..1000;

my $tree = Math::Vector::Real::kdTree->new(@v);

my $ix = $tree->find_nearest_vector(V(0, 0, 0, 0));

say "nearest vector is $ix, $v[$ix]";

DESCRIPTION

This module implements a kd-Tree data structure in Perl and common algorithms on top of it.

Methods

The following methods are provided:

$t = Math::Vector::Real::kdTree->new(@points)

Creates a new kd-Tree containing the given points.

$t2 = $t->clone

Creates a duplicate of the tree. The two trees will share internal read only data so this method is more efficient in terms of memory usage than others performing a deep copy.

my $ix = $t->insert($p0, $p1, ...)

Inserts the given points into the kd-Tree.

Returns the index assigned to the first point inserted.

$s = $t->size

Returns the number of points inside the tree.

$p = $t->at($ix)

Returns the point at the given index inside the tree.

$t->move($ix, $p)

Moves the point at index $ix to the new given position readjusting the tree structure accordingly.

($ix, $d) = $t->find_nearest_vector($p, $max_d, @but_ix)

($ix, $d) = $t->find_nearest_vector($p, $max_d, \%but_ix)

Find the nearest vector for the given point $p and returns its index and the distance between the two points (in scalar context the index is returned).

If $max_d is defined, the search is limited to the points within that distance

Optionally, a list of point indexes to be excluded from the search can be passed or, alternatively, a reference to a hash containing the indexes of the points to be excluded.

@ix = $t->find_nearest_vector_all_internal

Returns the index of the nearest vector from the tree.

It is equivalent to the following code (though, it uses a better algorithm):

@ix = map {
          scalar $t->nearest_vector($t->at($_), undef, $_)
      } 0..($t->size - 1);

$ix = $t->find_nearest_vector_in_box($p, $a, $b, $max_d, @but_ix)

$ix = $t->find_nearest_vector_in_box($p, $a, $b, $max_d, \%but_ix)

Returns the nearest vector for the given point from those that are also inside the box defined by $a and $b.

The other arguments have the same meaning as for the method find_nearest_vector.

$ix = $t->find_nearest_vector_in_box_chebyshev($p, $a, $b, $max_d, @but_ix)

$ix = $t->find_nearest_vector_in_box_chebyshev($p, $a, $b, $max_d, \%but_ix)

This method is similar to find_nearest_vector_in_box but using the Chebyshev metric.

$ix = $t->find_farthest_vector($p, $min_d, @but_ix)

Find the point from the tree farthest from the given $p.

The optional argument $min_d specifies a minimal distance. Undef is returned when not point farthest that it is found.

@but_ix specifies points that should not be considered when looking for the farthest point.

$ix = $t->find_farthest_vector_internal($ix, $min_d, @but_ix)

Given the index of a point on the tree this method returns the index of the farthest vector also from the tree.

($ix0, $ix1, $d) = $t->find_two_nearest_vectors

This method returns the indexes of two vectors from the three such that the distance between them is minimal. The distance is returned as the third output value.

In scalar context, just the distance is returned.

@k = $t->k_means_seed($n)

This method uses the internal tree structure to generate a set of point that can be used as seeds for other k_means methods.

There isn't any guarantee on the quality of the generated seeds, but the used algorithm seems to perform well in practice.

@k = $t->k_means_step(@k)

Performs a step of the Lloyd's algorithm for k-means calculation.

@k = $t->k_means_loop(@k)

Iterates until the Lloyd's algorithm converges and returns the final means.

@ix = $t->k_means_assign(@k)

Returns for every point in the three the index of the cluster it belongs to.

@ix = $t->find_in_ball($z, $d, $but)

$n = $t->find_in_ball($z, $d, $but)

Finds the points inside the tree contained in the hypersphere with center $z and radius $d.

In scalar context returns the number of points found. In list context returns the indexes of the points.

If the extra argument $but is provided. The point with that index is ignored.

@ix = $t->find_in_box($a, $b, $but)

$n = $t->find_in_box($a, $b, $but)

Finds the points inside the tree contained in the axis-aligned box defined by two opposite vertices $a and $b.

In scalar context returns the number of points found. In list context returns the indexes of the points.

If the extra argument $but is provided. The point with that index is ignored.

@ix = $t->ordered_by_proximity

Returns the indexes of the points in an ordered where is likely that the indexes of near vectors are also in near positions in the list.

k-means

The module can be used to calculate the k-means of a set of vectors as follows:

# inputs
my @v = ...; my $k = ...;

# k-mean calculation
my $t = Math::Vector::Real::kdTree->new(@v);
my @means = $t->k_means_seed($k);
@means = $t->k_means_loop(@means);
@assign = $t->k_means_assign(@means);
my @cluster = map [], 1..$k;
for (0..$#assign) {
  my $cluster_ix = $assign[$_];
  my $cluster = $cluster[$cluster_ix];
  push @$cluster, $t->at($_);
}

use Data::Dumper;
print Dumper \@cluster;

SEE ALSO

Wikipedia k-d Tree entry.

K-means filtering algorithm.

Math::Vector::Real

COPYRIGHT AND LICENSE

Copyright (C) 2011-2015 by Salvador Fandiño <sfandino@yahoo.com>

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.12.3 or, at your option, any later version of Perl 5 you may have available.