# Intrinsic Hierarchical Clustering Behavior Recovers Higher Dimensional Shape Information

@article{Ignacio2020IntrinsicHC, title={Intrinsic Hierarchical Clustering Behavior Recovers Higher Dimensional Shape Information}, author={Paul Samuel P. Ignacio}, journal={2021 IEEE 11th Annual Computing and Communication Workshop and Conference (CCWC)}, year={2020}, pages={0206-0212} }

We show that specific higher dimensional shape information of point cloud data can be recovered by observing lower dimensional hierarchical clustering dynamics. We generate multiple point samples from point clouds and perform hierarchical clustering within each sample to produce dendrograms. From these dendrograms, we take cluster evolution and merging data that capture clustering behavior to construct simplified diagrams that record the lifetime of clusters akin to what zero dimensional…

## 3 Citations

### LUM\'AWIG: An Efficient Algorithm for Dimension Zero Bottleneck Distance Computation in Topological Data Analysis.

- Computer Science
- 2020

LUMAWIG is presented, a novel efficient algorithm to compute dimension zero bottleneck distance between two persistent diagrams which runs significantly faster and provides significantly sharper approximates with respect to the output of the original algorithm than any other available algorithm.

### A new non-archimedean metric on persistent homology

- Computer ScienceComputational Statistics
- 2022

It is shown that zeroth persistent homology together with the cophenetic metric and hierarchical clustering algorithms with a number of different metrics do deliver statistically verifiable commensurate topological information based on experimental results the authors obtained on different datasets.

### LUMÁWIG: An Efficient Algorithm for Dimension Zero Bottleneck Distance Computation in Topological Data Analysis

- Computer ScienceAlgorithms
- 2020

This work presents a novel efficient algorithm to compute dimension zero bottleneck distance between two persistent diagrams of a specific kind which runs significantly faster and provides significantly sharper approximates with respect to the output of the original algorithm than any other available algorithm.

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