Fix buildNewick Formula and Update Dendrogram Branch Representation

[kylacochrane]

This PR (currently indirectly) addresses ISSUE13.

Changes:

• Fixed the buildNewick formula to adjust branch lengths (both internal and leaf branches) to represent cophenetic distances rather than patristic distances.
• Branch lengths now reflect the distance from all samples to their most recent common ancestor.

Benefits:

• This approach mirrors how BioNumerics currently displays dendrograms.
• It aligns with how GAS's fcluster generates flat clusters based on user-provided thresholds, ensuring the dendrogram allows users to visually interpret cluster levels by assessing branch heights between clusters.

Key Considerations:
This method deviates from the traditional representation of distances in dendrograms. As noted in ISSUE13, branch lengths are typically represented by patristic distances along a tree typically correspond to the values in the distance matrix (i.e., the sum of branch lengths from Sample A to Sample B should equal the distance provided in the matrix).

To align buildNewick with this traditional approach, the formula can be updated with the following adjustments:

def buildNewick(self,node, newick, parentdist, leaf_names):
        if node.is_leaf():
            return "%s:%f%s" % (leaf_names[node.id], (parentdist - node.dist / 2), newick)
        else:
            if len(newick) > 0:
                newick = f"):{(parentdist - node.dist/2)}{newick}"
            else:
                newick = ");"
            newick = self.buildNewick(node.get_left(), newick, node.dist, leaf_names)
            newick = self.buildNewick(node.get_right(), ",%s" % (newick), node.dist, leaf_names)
            newick = "(%s" % (newick)
            return newick

[sgsutcliffe]

Running the changes on the example file we see the change on the left panel compared to the orginal code right panel @kylacochrane you got it!

[apetkau]

Thanks so much @kylacochrane for all your great work on this. And thanks so much @sgsutcliffe for testing this out on data to confirm it's working 😄

By the way, here is the tree (from Steven's comparison) with distances and internal node heights labeled:

This can be compared to distances in this example file to confirm that the cophenetic distances in the tree match distances in the distance matrix (other than differences due to average linkage distances between clusters):

genomic_address_service/genomic_address_service/example/mcluster/hamming/results.text

Lines 1 to 11 in b2eac69

	dists A B C D E F G H I J
	A 0 1 2 2 5 5 6 6 9 9
	B 1 0 3 3 6 6 7 7 9 9
	C 2 3 0 0 3 3 6 6 9 9
	D 2 3 0 0 3 3 6 6 9 9
	E 5 6 3 3 0 0 6 6 9 9
	F 5 6 3 3 0 0 6 6 9 9
	G 6 7 6 6 6 6 0 0 3 3
	H 6 7 6 6 6 6 0 0 3 3
	I 9 9 9 9 9 9 3 3 0 1
	J 9 9 9 9 9 9 3 3 1 0