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After couple days of looking up what on earth is clustering, k-means, etc. -- hopeless -- I took closer look at your code. Wow, so simple. Thanks, martink! Here is re-factored version, if I may, discarding all that was perceived superfluous and simplifying (to fit my brain). So it's, effectively, just 2 plain loops: over all attributes and all items. Loop over items doesn't add to example with pumpkins, but is required for other test cases.

I wonder, is it a mathematical fact, that even for 500 items and 75 attributes, there can be no more than 575 sets of common attributes? It somewhat contradicts to what I remember from combinatorics.

use strict; use warnings; use feature 'say'; use List::Util qw/ uniq all /; use Data::Dump 'dd'; my $item2attr = { apple => { red => 1, round => 1, plant => 1, fruit => 1 } +, orange => { orange => 1, round => 1, plant => 1, fruit => 1 } +, pumpkin => { orange => 1, round => 1, plant => 1, vegetable => 1 } +, ball => { red => 1, round => 1, toy => 1 }, }; # list of all items and attributes my @items = sort keys %$item2attr; my @attr = sort( uniq( map { keys %$_ } values %$item2attr )); # flip the hash my $attr2item; for my $attr ( @attr ) { for ( @items ) { $attr2item-> { $attr }{ $_ } = 1 if $item2attr-> { $_ }{ $attr } } } #dd $item2attr; #say '-----------------------------------'; #dd $attr2item; #say '-----------------------------------'; my %solutions; # hash, to prevent duplicates for ( @attr ) { my @items_ = keys %{ $attr2item-> { $_ }}; my @attr_ = grep { my $attr = $_; all { $item2attr-> { $_ }{ $attr }} @items_ } @attr; _add_solution( \@attr_, \@items_ ) } for ( @items ) { my @attr_ = keys %{ $item2attr-> { $_ }}; my @items_ = grep { my $item = $_; all { $attr2item-> { $_ }{ $item }} @attr_ } @items; _add_solution( \@attr_, \@items_ ) } dd values %solutions; # then filter solutions for required number of common # attributes, or find max set of common attributes, # or find max set of items with any common attributes, etc. sub _add_solution { # writes to %solutions my ( $attr, $items ) = @_; return unless $#$items; # skip uninteresting @$_ = sort @$_ for @_; $solutions{ join ',', @$attr } = [ scalar @$attr, # count of attributes scalar @$items, # count of items $attr, # attribute list $items # item list ] } __END__ ( [2, 2, ["red", "round"], ["apple", "ball"]], [2, 3, ["plant", "round"], ["apple", "orange", "pumpkin"]], [1, 4, ["round"], ["apple", "ball", "orange", "pumpkin"]], [3, 2, ["fruit", "plant", "round"], ["apple", "orange"]], [3, 2, ["orange", "plant", "round"], ["orange", "pumpkin"]], )

Edit: fixed issue with sorting.


In reply to Re^2: Groups of Objects with Common Attributes by vr
in thread Groups of Objects with Common Attributes by Dev Null

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