Related papers: Learning graphs and simplicial complexes from data

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…

Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…

We explore the problem of sampling graph signals in scenarios where the graph structure is not predefined and must be inferred from data. In this scenario, existing approaches rely on a two-step process, where a graph is learned first,…

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by…

We consider the problem of inferring graph topology from smooth graph signals in a novel but practical scenario where data are located in distributed clients and prohibited from leaving local clients due to factors such as privacy concerns.…

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

Learning graph convolutional networks (GCNs) is an emerging field which aims at generalizing convolutional operations to arbitrary non-regular domains. In particular, GCNs operating on spatial domains show superior performances compared to…

Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Mining natural associations from high-dimensional spatiotemporal signals plays an important role in various fields including biology, climatology, and financial analysis. However, most existing works have mainly studied time-independent…

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…

In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which…

Multimodal signals on sensor networks are commonly modeled under the twofold graph assumption (TGA), which represents spatial structure and inter-modality relations as two separate graphs. Existing TGA-based signal restoration methods,…

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…

Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…

This paper proposes convolutional filtering for data whose structure can be modeled by a simplicial complex (SC). SCs are mathematical tools that not only capture pairwise relationships as graphs but account also for higher-order network…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…