Understanding Dendrograms and the Need for Node Labeling

In the realm of data analysis and visualization, dendrograms are a crucial tool for representing hierarchical structures. A dendrogram is a graphical representation of a binary tree or a hierarchical structure where each node represents a split in the data. The leaves of the dendrogram represent individual samples or data points, while the internal nodes represent splits or partitions within those samples.

Dendrograms are widely used in various fields such as bioinformatics, machine learning, and data science to visualize relationships between different groups or data points. However, one common requirement when working with dendrograms is to assign a unique identifier (ID) to each node, which can be particularly useful for annotating the leaves of the tree.

The Problem: Assigning IDs to Nodes in a Dendrogram

The problem arises when trying to assign IDs to nodes in a dendrogram. For instance, if we have a binary tree with internal nodes and leaf nodes, assigning an ID to each node can be challenging. The problem statement asks for a function that assigns an increasing integer ID to all nodes in the tree.

Solution: Understanding the Code

The provided code snippet is taken from stats:::reorder.dendrogram and has been modified to suit the purpose of labeling the root and each leaf with an increasing integer. This function, labeled as funID, takes two arguments: tr (the dendrogram) and StartID (the starting ID).

Step 1: Checking for a Dendrogram

The function first checks if the input x is a dendrogram by checking if it inherits from the dendrogram class. If not, it stops the execution with an error message.

if (!inherits(x, "dendrogram")) 
    stop("we require a dendrogram")

Step 2: Creating a Leaf Function

The function then defines an inner function called oV, which takes two arguments: x and wts. The oV function checks if the current node x is a leaf by checking its length. If it’s not, it stops with an error message.

k <- length(x)
if (k == 0L) 
    stop("invalid (length 0) node in dendrogram")

Step 3: Assigning IDs

If the current node is a leaf, the function assigns an increasing integer ID to it and increments the counter N. The new ID is stored in the attribute of the node using attr(x, "ID") = N; N <- N+1.

if (is.leaf(x)) {
    attr(x, "ID") <- N; N <<- N+1
    return(x)
}

Step 4: Traversing the Tree

The oV function then traverses the tree by iterating over its children. For each child, it calls itself recursively with the updated node and weights.

for (j in 1L:k) { N <- N+1
    b <- oV(x[[j]], wts)
    x[[j]] <- b
    vals[j] <- N; N <- N+1
}

Step 5: Returning the Modified Tree

Finally, the oV function returns the modified tree with the assigned IDs.

x

Conclusion

In conclusion, the provided code defines a function funID that assigns an increasing integer ID to all nodes in a dendrogram. The function uses recursion and iteration to traverse the tree and assign IDs to each node. By understanding how this function works, we can leverage it to label our dendrograms with unique identifiers.

Implementing the Function

Here’s how you can implement the funID function:

label.leaves <- 
function (x, wts) 
{
    N=1
    if (!inherits(x, "dendrogram")) 
        stop("we require a dendrogram")
    
    oV <- function(x, wts) {
        k <- length(x)
        if (k == 0L) 
            stop("invalid (length 0) node in dendrogram")
        
        for (j in 1L:k) { N <- N+1
            b <- oV(x[[j]], wts)
            x[[j]] <- b
            vals[j] <- N; N <- N+1
        }
        return(stats:::midcache.dendrogram(oV(x, wts)))
    }
    
    stats:::midcache.dendrogram(oV(x, wts))
}

Testing the Function

You can test this function by creating a dendrogram and assigning IDs to its leaves:

D <- rbind(
+ c(1,1,1,1,1),
+ c(1,2,1,1,1),
+ c(2,2,2,2,2),
+ c(2,2,2,2,1),
+ c(3,3,3,3,3),
+ c(3,3,3,3,2))

Ddend <- as.dendrogram(hclust.vector(D))

Then you can use the label.leaves function to assign IDs to the leaves:

funID <- label.leaves(Ddend, StartID = 1)

Assigning Custom Starting ID

To assign a custom starting ID, you need to provide an additional argument to the label.leaves function.

Ddend.L <- label.leaves(Ddend, StartID = "custom")
funID <- Ddend.L

Conclusion

In this article, we have discussed how to assign a unique identifier (ID) to each node in a dendrogram using the label.leaves function. This function takes advantage of recursion and iteration to traverse the tree and assign IDs to each node. We also provided examples on how to implement this function and test it with custom starting IDs.

Last modified on 2023-10-09