I'm fairly sure (untested) that this will produce the same results in @group whilst using minimal memory and much more quickly:

#! perl -slw
use strict;
use List::Util qw[ sum ];

sub distance {
    my( $iref, $wref, $dim, $s, $u ) = @_;
    return sqrt(
        sum( 
            map{ 
                ( $iref->[ $_ ][ $u ] - $wref->[ $_ ][ $s ] ) **2 
            } 0 .. $dim - 1 
        )
    ) / $dim;
}


my $U = my $S = 100000;
my $dimMax = 5;
my @group;
my @input_train = ...;
my @weights = ...;

for my $u ( 0 .. $U - 1 ) {   
    my $minDistance  = 100;
    $group[$u]    = -99;
    my $minS;

    for my $s ( 0 .. $S -1 ) {
        my $dist = distance( \@input_train, \@weights, $dimMax, $s, $u
+ );
        
        if( $dist < $minDistance ) {
            $minDistance = $distance[ $u ][ $s ];
            $minS = $s;
        }
    }
    
    $group[ $u ] = $minS;  
}
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