Hierarchically-clustered Heatmap

Table of contents

  1. Introduction
  2. How to use
  3. Behavior
  4. Method
  5. References

Introduction

Hierarchically-clustered Heatmap groups spectra by similarity and displays the result as a clustered heatmap or dendrogram. In SpectraGuru, this feature uses Ward-linkage clustering to arrange similar spectra near each other.

How to use

  1. Upload data and finish preprocessing if needed.
  2. Open Analytics Page.
  3. In Select Analytics Plot, choose Hierarchically-clustered Heatmap.
  4. Use Show clustered heatmap to switch between the clustered heatmap and dendrogram-only view.

Behavior

When the heatmap toggle is enabled, SpectraGuru displays spectra as a heatmap ordered by hierarchical clustering, with a dendrogram showing the merge order. When the toggle is disabled, SpectraGuru shows the dendrogram with Ward distance on the vertical axis.

Method

The default distance between spectra is Euclidean:

\[d(x,y)=\sqrt{\sum_i (x_i-y_i)^2}\]

Ward linkage merges clusters to minimize within-cluster variance:

\[\Delta(A,B)=\frac{|A||B|}{|A|+|B|}\lVert \bar{x}_A-\bar{x}_B\rVert^2\]
Parameter Tunable or fixed Implementation
Show clustered heatmap Tunable Boolean toggle, default True
Linkage method Fixed Ward linkage
Heatmap output Fixed Clustered heatmap when enabled; dendrogram view when disabled

References

  1. Ward, J. H. Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236-244. https://doi.org/10.1080/01621459.1963.10500845
  2. SciPy Developers. scipy.cluster.hierarchy.linkage. https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html
  3. Waskom, M. L. (2021). Seaborn: statistical data visualization. Journal of Open Source Software, 6(60), 3021. https://doi.org/10.21105/joss.03021