# Hierarchical Clustering and Heat Maps in Mathematica

Hierarchical Clustering and Heat Maps in Mathematica

Hierarchical clustering is a way to expose the hidden structure of a complex, high-dimensional dataset. Heat maps are a common way to visualize the results of such clustering algorithms. This Demonstration shows how to use the HierarchicalClustering package in Mathematica to generate heat maps with the dendrograms included on the sides of the heat map.

Specifically, a sample distribution (pictured on the left) is uniformly sampled with an added noise term (proportional to the sliders in the - and directions) in an " sampling density" by " sampling density" grid. The resulting matrix of function values is then hierarchically clustered in both the rows and the columns, often revealing a relatively simple underlying structure to the originally complex-structured data. You can vary the noise, the functions used in the hierarchical clustering, and the structure of the underlying distribution being sampled to see how these algorithms are both sensitive to the inputs given and powerful when used properly.

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