Learning the Topology of a Simplicial Complex Using Simplicial Signals: A Greedy Approach
Graphs are ubiquitous to model the irregular (non-Euclidean) structure of complex data, but they are limited to pairwise relationships and fail to model the complexities of the datasets exhibiting higher-order interactions. In that context, simplicial complexes (SCs) are emerging as a tractable candidate to handle such domains. The first step in using SC-based processing and learning schemes is to identify the topology of the SC, which is the problem investigated in this paper. In particular, we assume that we observe a number of signals (features) associated with the nodes of the SC (simplices of order 0) as well as signals (features) associated with a subset of the edges of the SC (simplices of order 1). The goal is then to use these signals to learn the remaining edges as well as the triangles that are filled (simplices of order 2). To address this problem, we assume that the signals are smooth on the unknown SC and that the higher-order relations are sparse. We then postulate the learning problem as a nonconvex optimization and develop an efficient (block-coordinate) algorithm to identify the SC topology.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Topological Signal Processing over Simplicial Complexes
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definitio…
Topological Signal Processing over Cell Complexes
The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inc…
Pooling Strategies for Simplicial Convolutional Networks
The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: …
Graph ClassificationTopoSRL: Topology preserving self-supervised Simplicial Representation Learning
In this paper, we introduce $\texttt{TopoSRL}$, a novel self-supervised learning (SSL) method for simplicial complexes to effectively capture higher-order interactions and preserve topology in the learned representations…
Sampling and Recovery of Signals on a Simplicial Complex using Neighbourhood Aggregation
In this work, we focus on sampling and recovery of signals over simplicial complexes. In particular, we subsample a simplicial signal of a certain order and focus on recovering multi-order bandlimited simplicial signals …