Hi,
As far as I researched, there is NO such thing as a 3D dendrogram. Since, if you imagine a 2D dendrogram as cluster of different objects, then 3D dendrogram would be cluster of clusters, but that ultimately would reduce down to a 2D dendrogram only.
I tried to create a 3D Dendrogram, which ultimately got reduced to 2D Dendrogram, thus concluding our point that 3D dendrogram doesn't exist.
Let us consider:
A 3D dendrogram tree diagram that shows the hierarchical relationship between different clusters or objects in three dimensions.
To create a 3D dendrogram, you can use hierarchical clustering algorithms to cluster your data based on a distance metric, and then use a visualization tool to plot the resulting dendrogram in 3D.
Here are the general steps I tried to create a 3D dendrogram:
- Choose a suitable distance metric and clustering algorithm to cluster your data. Common distance metrics include Euclidean distance, Manhattan distance, and cosine distance. Common clustering algorithms include hierarchical clustering, k-means clustering, and DBSCAN.
- Use the clustering algorithm to cluster your data into a hierarchical tree structure. In hierarchical clustering, this is done by repeatedly merging the closest pairs of clusters until all data points are in a single cluster.
- Use a visualization tool to plot the resulting dendrogram in 3D. There are several software packages and libraries that can be used for this purpose, such as DendroPy, Matplotlib, and Plotly.
- Customize the 3D dendrogram to improve its readability and aesthetics. This can include adjusting the size and color of the branches, adding labels to the nodes, and changing the layout and perspective of the plot.
Here's an example code snippet that shows how to create a 3D dendrogram in MATLAB:
% Example data
X = rand(100, 3); % 100 data points in 3D space
% Compute pairwise distance matrix using Euclidean distance
D = pdist(X);
% Cluster the data using hierarchical clustering with complete linkage
Z = linkage(D, 'complete');
% Plot the dendrogram in 3D
figure;
[dendroH,~,~] = dendrogram(Z, 0, 'orientation', 'top', 'colorthreshold', 'default');
set(dendroH,'LineWidth',2);
set(gca, 'TickDir', 'out');
xlabel('Data points');
ylabel('Distance');
zlabel('Height');
view(3);
In this example, we first compute the pairwise distance matrix between the data points using the pdist function with the Euclidean distance metric. Then, we use the linkage function to cluster the data using hierarchical clustering with complete linkage. Finally, we plot the dendrogram in 3D using the dendrogram function, with the orientation parameter set to 'top' to plot the dendrogram from the top view, and the view function is used to set the 3D perspective of the plot.
It's worth noting that 3D dendrograms can be challenging to interpret, especially if the branching structure is complex and the number of clusters is large. Therefore, it's important to choose a suitable clustering algorithm and distance metric, and to carefully design the visualization to highlight the most important features of the data.
But in doing so, we can trim down the whole figure to 2D concluding that only 2D dendrograms exists.
Hope it helps!!
