29 accepted papers
Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA) projects data points onto the eigenvectors of their covariance matr
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces, such as simplicial or cell complexes. However, existing TDL…
CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to encode conditional independence, and are often precomputed in…
Graph filters are ubiquitous for processing data over graphs. However, most filters obtained from data are point-estimates and may be sensitive to changes in topology or data distributions. Thus, modeling uncertainty in filters is critical to quantify confidence in analyses or improve downstream tas…
Covariance-based data processing is widespread across signal processing and machine learning applications due to its ability to model data interconnectivities and dependencies. However, harmful biases in the data may become encoded in the sample covariance matrix and cause data-driven methods to tre…
Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise estimates, our method accounts for dynamic changes in the netwo…
This paper proposes a novel algorithm to retroactively compute the evolution of edge signals from a given sequence of partial observations from topological structures, a concept referred to as evolution backcasting. Our backcasting algorithm exploits the spatio-temporal dependencies present in the r…
Simplicial complexes prove effective in modeling data with multi-way dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces via the Hodge decomposition, resulting foundational in nume…
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized…
Inference of time varying data over graphs is of importance in real-world applications such as urban water networks, economics, and brain recordings. It typically relies on identifying a computationally affordable joint spatiotemporal method that can leverage the patterns in the data. While this per…
Graphs are widely used to represent complex information and signal domains with irregular support. Typically, the underlying graph topology is unknown and must be estimated from the available data. Common approaches assume pairwise node interactions and infer the graph topology based on this premise…
Temporal networks arise due to certain dynamics influencing their connections or due to the change in interactions between the nodes themselves, as seen for example in social networks. Such evolution can be algebraically represented by a three-way tensor, which lends itself to using tensor decomposi…
Simplicial convolutional filters can process signals defined over levels of a simplicial complex such as nodes, edges, triangles, and so on with applications in e.g., flow prediction in transportation or financial networks. However, the underlying topology expands over time in a way that new edges a…
Current spatiotemporal learning methods for complex data exploit the graph structure as an inductive bias to restrict the function space and improve data and computation efficiency. However, these methods work principally on graphs with a fixed size, whereas in several applications there are expandi…
Vector autoregressive (VAR) model is widely used to model time-varying processes, but it suffers from prohibitive growth of the parameters when the number of time series exceeds a few hundreds. We propose a simplicial VAR model to mitigate the curse of dimensionality of the VAR models when the time…
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 structures. These filters are built by following the shift-and…
Performing signal processing over graphs requires knowledge of the underlying fixed topology. However, graphs often grow in size with new nodes appearing over time, whose connectivity is typically unknown; hence, making more challenging the downstream tasks in applications like cold start recommenda…
Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks like graph signal reconstruction, graph or node classificat…
Graph convolutional neural networks (GCNNs) learn compositional representations from network data by nesting linear graph convolutions into nonlinearities. In this work, we approach GCNNs from a state-space perspective revealing that the graph convolutional module is a minimalistic linear state-spac…
Signal processing and machine learning algorithms for data sup-ported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the topology has to be learned from data. Topology identification…
To deal with high-dimensional data, graph filters have shown their power in both graph signal processing and data science. However, graph filters process signals exploiting only pairwise interactions between the nodes, and they are not able to exploit more complicated topological structures. Graph V…
Stochastic graph neural networks (SGNNs) are information processing architectures that can learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, but this training comes with no guarantee about the deviation of particular output realizations a…
Diffusion-based semi-supervised learning on graphs consists of diffusing labeled information of a few nodes to infer the labels on the remaining ones. The performance of these methods heavily relies on the initial labeled set, which is either generated randomly or using heuristics. The first sometim…
The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To t…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. However, current GNN implementations assume ideal distributed scenarios and ignore link fluctuations that occur due to environment or hu…
In this work, we jointly exploit tools from graph signal processing and control theory to drive a bandlimited graph signal that is being diffused on a random time-varying graph from a subset of nodes. As our main contribution, we rely only on the statistics of the graph to introduce the concept of c…
We present a novel implementation strategy for distributed autoregressive moving average (ARMA) graph filters. Differently from the state of the art implementation, the proposed approach has the following benefits: (i) the designed filter coefficients come with stability guarantees, (ii) the linear…
Generally in distributed signal processing, and specifically in distributed graph filters, reducing the communication and computational complexity plays a key role in the network lifetime. In this work we present a novel algorithm to sparsify the graph filtering operation in a random way, where each…