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…
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LUM\'AWIG: An Efficient Algorithm for Dimension Zero Bottleneck Distance Computation in Topological Data Analysis.
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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.
References
SHOWING 1-10 OF 10 REFERENCES
Studying brain networks via topological data analysis and hierarchical clustering
- Computer Science
- 2016
This thesis applies the idea of a barcode from persistent homology to four hierarchical clustering methods: single, average, complete, and Ward’s linkage and proves that average and complete quasi-barcodes possess a property that dendrograms do not.
Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
- MathematicsFound. Comput. Math.
- 2015
It is shown that maximum persistence at the point-cloud level can be used to quantify periodicity at the signal level, prove structural and convergence theorems for the resulting persistence diagrams, and derive estimates for their dependency on window size and embedding dimension.
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 Topological "Reading" Lesson: Classification of MNIST using TDA
- Computer Science2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA)
- 2019
A way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images and it is shown that this topological machine learning pipeline can be used as a highly relevant dimensionality reduction by applying it to the MNIST digits dataset.
A roadmap for the computation of persistent homology
- Computer ScienceEPJ Data Science
- 2017
A friendly introduction to PH is given, the pipeline for the computation of PH is navigated with an eye towards applications, and a range of synthetic and real-world data sets are used to evaluate currently available open-source implementations for the computations of PH.
Classification of Single-Lead Electrocardiograms: TDA Informed Machine Learning
- Computer Science2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA)
- 2019
It is demonstrated how topological features can be used to help accurately classify single lead electrocardiograms by derive features from persistent signatures, input them to a simple machine learning algorithm, and benchmark its performance against winning entries in the 2017 Physionet Computing in Cardiology Challenge.
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.
Persistent homology detects curvature
- MathematicsInverse Problems
- 2020
It is proved that persistent homology detects the curvature of disks from which points have been sampled, and a general computational framework for solving inverse problems using the average persistence landscape, a continuous mapping from metric spaces with a probability measure to a Hilbert space is described.
The MNIST dataset of handwritten digits
- 1999