my $j=0; 
my $col_data; 
my @new_array; 
my $series; 
my @group; 
my $previous; 
for($i=0; $i <$nb_col ; $i++){  
$col_data= $partition->[$i]; 
@new_array = ();  
my @group= sort@{$group_id->[$i]}; 
print Dumper @group; 
for($j=0;$j <= $#$col_data; $j++){ 
	unless (defined $previous) {  
		$previous = $j;  
		$series = $j;  
		next;  
	} 
        if($group[$previous]== $group[$j]){ 
		$series .= "_" . $j;  
	}  
	else 
	{ 
		push @new_array, $series;  
		$series = $j;  
	}  
	$previous = $j; 
	} 
	push @new_array, $series; 
	print " @new_array\n"; 
	$size_col[$i] = $#new_array+1; 
}  
#print " @new_array\n"; 
print Dumper @size_col;

Its output is 
$VAR1 = '0'; 
$VAR2 = '0'; 
$VAR3 = '0'; 
$VAR4 = '1'; 
 0_1_2 3 
$VAR1 = '1'; 
$VAR2 = '1'; 
$VAR3 = '2'; 
Use of uninitialized value in numeric eq (==) at ./partition.pl line 62. 
 3 0_1 2 
$VAR1 = '1'; 
$VAR2 = '2'; 
$VAR3 = '3'; 
$VAR4 = '3'; 
 2 0 1 2_3 
$VAR1 = '2'; 
$VAR2 = '2'; 
$VAR3 = '2'; 
$VAR4 = '2'; 
$VAR5 = '2'; 
 2_3_0_1_2_3_4 
$VAR1 = '2'; 
$VAR2 = '3'; 
$VAR3 = '4'; 
$VAR4 = '1';