You can use ddumper^{Basic debugging checklist} to visualize the data structure you have (lesson courtesy of Basic debugging checklist and brian's Guide to Solving Any Perl Problem )

If I do that I see that the first row is indeed empty [[], [0.25], [0.25, 0.5], [1, 0.75, 0.75]];

Try to follow https://metacpan.org/source/MDEHOON/Algorithm-Cluster-1.52/perl/examples/ex5_treecluster

This is how you should write that, pass arguments (often references to arrays), return values, meaningful names

This is your code cleaned up, some comments, but the data unfixed (I would use ex5_treecluster data as starting point )

#!/usr/bin/perl --
#~ clust-brain.pl
#~ 2014-04-06-15:43:25
#~ 
#~ perltidy -olq  -csc -csci=10 -cscl="sub : BEGIN END if " -otr -opr 
+-ce -nibc -i=4 -pt=0   "-nsak=*"
#!/usr/bin/perl --
use strict;
use warnings;
use Data::Dump qw/ dd /;
Main( @ARGV );
exit( 0 );

sub Main {
## compact notation
## first stored in an arrayref
#    my $hd = [[], [0.25], [0.25, 0.5], [1, 0.75, 0.75]];

## then stored in a named array
#    my @the_hd = ([], [0.25], [0.25, 0.5], [1, 0.75, 0.75]);

## same thing more verbose notation
## array ref first
    my $hd_arrayref;
    $hd_arrayref->[1][0] = 0.25;    #d1
    $hd_arrayref->[2][0] = 0.25;    #d1
    $hd_arrayref->[2][1] = 0.5;     #d1
    $hd_arrayref->[3][0] = 1;       #d1
    $hd_arrayref->[3][1] = 0.75;    #d1
    $hd_arrayref->[3][2] = 0.75;    #d1
## named array second
    my @hd_array;
    $hd_array[1][0] = 0.25;         #d1
    $hd_array[2][0] = 0.25;         #d1
    $hd_array[2][1] = 0.5;          #d1
    $hd_array[3][0] = 1;            #d1
    $hd_array[3][1] = 0.75;         #d1
    $hd_array[3][2] = 0.75;         #d1

## putting values in an array ref without loops
#    my $cluster_ids = ( 0, 1, 2, 3 );
#    my $cluster_ids = [ 0 .. 3 ];
    my $hdt = 0.4;

## call clust_brain() function  ... no need for short names
#~     my $cluster_ids = clust_brain( $hd_arrayref, $hdt );
    my $cluster_ids = clust_brain( \@hd_array, $hdt );

## because we "import"ed dd from Data::Dump we don't have to type full
+ name
#    Data::Dump::dd( $cluster_ids );
    dd( $cluster_ids );
} ## end sub Main

sub clust_brain {
## ARGUMENT PASSING, first arg reference, second arg number
    my( $hd_ref, $some_hdt ) = @_;
    use Algorithm::Cluster::Thresh;
    use Algorithm::Cluster qw/treecluster/;
## you my $varname ONCE to make it
    my $tree = treecluster( data => $hd_ref, method => 'a' );
## then you call method cutthresh on $varname with argument
    my $var_i_call_cluster_ids_also = $tree->cutthresh( $some_hdt );
## you return the value
    return $var_i_call_cluster_ids_also;
} ## end sub clust_brain
__END__
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