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#!/usr/bin/env perl

# axis-vs-extended.pl
#
# Isolation Forest comes in two flavours here:
#   mode => 'axis'      classic, axis-parallel splits (the original algorithm)
#   mode => 'extended'  Extended Isolation Forest, random *hyperplane* splits
#
# Axis-parallel splits can only cut straight across one feature at a time, which
# leaves a rectangular, axis-aligned bias in the score field. On data whose
# features are correlated (a diagonal band), that bias shows up two ways:
#   * points that sit off the diagonal but still inside each feature's range
#     get under-scored by axis mode, and
#   * points on the diagonal can get spuriously inflated scores.
# Extended mode, using oblique cuts, softens both effects.
#
# This script trains one forest of each kind on the same diagonal band and
# compares how they score a few hand-picked probe points.
#
#     perl -Ilib examples/axis-vs-extended.pl

use strict;
use warnings;
use Algorithm::Classifier::IsolationForest;

srand(3);    # reproducible data

# A tight band along the line y = x, with both features spanning roughly [-3, 3].
my @data;
for ( 1 .. 400 ) {
	my $t = -3 + 6 * rand();
	push @data, [ $t + 0.05 * ( rand() - 0.5 ), $t + 0.05 * ( rand() - 0.5 ) ];
}

my $axis = Algorithm::Classifier::IsolationForest->new(
	mode        => 'axis',
	n_trees     => 200,
	sample_size => 256,
	seed        => 1
)->fit( \@data );

my $ext = Algorithm::Classifier::IsolationForest->new(
	mode        => 'extended',
	n_trees     => 200,
	sample_size => 256,
	seed        => 1
)->fit( \@data );

# name => [x, y], with a note on what we expect
my @probes = (
	[ 'on the line, centre',    [  0,  0 ], 'normal' ],
	[ 'on the line, far end',   [  3,  3 ], 'edge of normal' ],
	[ 'off-diagonal, in range', [  3, -3 ], 'ANOMALY (within each axis range)' ],
	[ 'off-diagonal, in range', [ -3,  3 ], 'ANOMALY (within each axis range)' ],
	[ 'far outside everything', [ 10, 10 ], 'ANOMALY (obvious)' ],
);

print "Anomaly scores (higher = more anomalous), trained on a diagonal band:\n\n";
printf "  %-26s %-11s  %-6s  %-9s  %s\n", 'probe point', '(x, y)', 'axis', 'extended', 'note';
print '  ', '-' x 78, "\n";

for my $p (@probes) {
	my ( $name, $xy, $note ) = @$p;
	my $a = $axis->score_samples( [$xy] )->[0];
	my $e = $ext->score_samples( [$xy] )->[0];
	printf "  %-26s (%-3g,%3g)  %-6.3f  %-9.3f  %s\n", $name, $xy->[0], $xy->[1], $a, $e, $note;