Learning metrics for persistence-based summaries and applications for graph classification

Abstract

Recently a new feature representation and data analysis methodology based on a topological tool called persistent homology (and its corresponding persistence diagram summary) has started to attract momentum. A series of methods have been developed to map a persistence diagram to a vector representation so as to facilitate the downstream use of machine learning tools, and in these approaches, the importance (weight) of different persistence features are often preset. However often in practice, the choice of the weight function should depend on the nature of the specific type of data one considers, and it is thus highly desirable to learn a best weight function (and thus metric for persistence diagrams) from labelled data. We study this problem and develop a new weighted kernel, called WKPI, for persistence summaries, as well as an optimization framework to learn a good metric for persistence summaries. Both our kernel and optimization problem have nice properties. We further apply the learned kernel to the challenging task of graph classification, and show that our WKPI-based classification framework obtains similar or (sometimes significantly) better results than the best results from a range of previous graph classification frameworks on a collection of benchmark datasets.

References in corpus (9)

• Statistical topological data analysis using persistence landscapes
• On Valid Optimal Assignment Kernels and Applications to Graph Classification
• Covariant Compositional Networks For Learning Graphs
• Sliced Wasserstein Kernel for Persistence Diagrams
• PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
• Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams
• RetGK: Graph Kernels based on Return Probabilities of Random Walks
• Diving into the shallows: a computational perspective on large-scale shallow learning
• Understanding and Predicting Links in Graphs: A Persistent Homology Perspective

Cited by in corpus (15)

• Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
• PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
• Graph Kernels: State-of-the-Art and Future Challenges
• Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence
• Topological Feature Vectors for Chatter Detection in Turning Processes
• Intrinsic-Extrinsic Convolution and Pooling for Learning on 3D Protein Structures
• Optimizing persistent homology based functions
• Revisiting 2D Convolutional Neural Networks for Graph-based Applications
• Elder-Rule-Staircodes for Augmented Metric Spaces
• Optimal quantization of the mean measure and applications to statistical learning
• Multi Layer Neural Networks as Replacement for Pooling Operations
• Understanding the Power of Persistence Pairing via Permutation Test
• Topological Graph Neural Networks
• Graph Filtration Learning
• A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering