EMP: Effective Multidimensional Persistence for Graph Representation Learning
Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an exclusive topological imprint of data by tracing the evolution of latent structures as a scale parameter changes. Present PH tools are confined to analyzing data through a single filter parameter. However, many scenarios necessitate the consideration of multiple relevant parameters to attain finer insights into the data. We address this issue by introducing the Effective Multidimensional Persistence (EMP) framework. This framework empowers the exploration of data by simultaneously varying multiple scale parameters. The framework integrates descriptor functions into the analysis process, yielding a highly expressive data summary. It seamlessly integrates established single PH summaries into multidimensional counterparts like EMP Landscapes, Silhouettes, Images, and Surfaces. These summaries represent data's multidimensional aspects as matrices and arrays, aligning effectively with diverse ML models. We provide theoretical guarantees and stability proofs for EMP summaries. We demonstrate EMP's utility in graph classification tasks, showing its effectiveness. Results reveal that EMP enhances various single PH descriptors, outperforming cutting-edge methods on multiple benchmark datasets.
Code (0)
등록된 구현이 없습니다.
Tasks
Graph ClassificationGraph Representation LearningRepresentation LearningTopological Data AnalysisSimilar Papers 제목 키워드 기반
Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features ar…
BIG-bench Machine LearningClassificationGeneral ClassificationTime-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistence
Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing impli…
Computational EfficiencyDecision MakingRepresentation LearningGEFL: Extended Filtration Learning for Graph Classification
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by th…
ClassificationGraph ClassificationGraph Representation LearningRepresentation Learning+1Persistence Spheres: Bi-continuous Representations of Persistence Diagrams
We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods), persistence spheres provide a bi-contin…
Point CloudsTopological Machine Learning with Persistence Indicator Functions
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as m…
BIG-bench Machine LearningTopological Data Analysis