• Corpus ID: 233209679

Smart Vectorizations for Single and Multiparameter Persistence

@article{Coskunuzer2021SmartVF,
  title={Smart Vectorizations for Single and Multiparameter Persistence},
  author={Baris Coskunuzer and Cuneyt Gurcan Akcora and Ignacio Segovia-Dominguez and Zhiwei Zhen and Murat Kantarcioglu and Yulia R. Gel},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.04787}
}
The machinery of topological data analysis becomes increasingly popular in a broad range of machine learning tasks, ranging from anomaly detection and manifold learning to graph classification. Persistent homology is one of the key approaches here, allowing us to systematically assess the evolution of various hidden patterns in the data as we vary a scale parameter. The extracted patterns, or homological features, along with information on how long such features persist throughout the… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 53 REFERENCES
Benchmark data sets for graph kernels, 2016
  • 2016
Random forests. Machine learning
  • 2001
Persistence Curves: A canonical framework for summarizing persistence diagrams
TLDR
This paper develops a general and unifying framework of vectorizing diagrams that it is shown that several well-known summaries, such as Persistence Landscapes, fall under the PC framework, and proposes several new summaries based on PC framework that provide a theoretical foundation for their stability analysis.
Learning Hyperbolic Representations of Topological Features
TLDR
A method to learn representations of persistence diagrams on hyperbolic spaces, more specifically on the Poincare ball, which represents features of infinite persistence infinitesimally close to the boundary of the ball so their distance to non-essential features approaches infinity, thereby their relative importance is preserved.
Multiparameter Persistence Image for Topological Machine Learning
TLDR
This work introduces a new descriptor for multiparameter persistence, which it calls the Multiparameter Persistence Image, that is suitable for machine learning and statistical frameworks, is robust to perturbations in the data, has finer resolution than existing descriptors based on slicing, and can be efficiently computed on data sets of realistic size.
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
TLDR
This work shows how graphs can be encoded by (extended) persistence diagrams in a provably stable way and proposes a general and versatile framework for learning vectorizations of persistence diagrams, which encompasses most of the vectorization techniques used in the literature.
A Persistent Weisfeiler-Lehman Procedure for Graph Classification
TLDR
This work leverages propagated node label information and transform unweighted graphs into metric ones to augment the subtree features with topological information obtained using persistent homology, a concept from topological data analysis.
Learning metrics for persistence-based summaries and applications for graph classification
TLDR
This work develops a new weighted kernel, called WKPI, for persistence summaries, as well as an optimization framework to learn a good metric for persistence sumaries, and applies the learned kernel to the challenging task of graph classification.
Learning representations of persistence
  • barcodes. JMLR,
  • 2019
Multiparameter persistence
  • In Lecture Notes,
  • 2019
...
1
2
3
4
5
...