Online Edge Flow Prediction Over Expanding Simplicial Complexes

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 and triangles form. For example, in a...

Simplicial Convolutional Filters

We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces, etc. To process such signals, we develop simplicial convolutional filters defined as matrix polynomials of the lower and...

Simplicial Convolutional Neural Networks

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 classifications, and link prediction. However, these...

Simplicial Trend Filtering (Invited Paper)

Reconstructing simplicial signals, e.g., signals defined on nodes, edges, triangles, etc., of a network, from (partial) noisy observation is of interest in water/traffic flow estimation or currency exchange markets. Typically, this concerns solving a regularised problem w.r.t. the l2 norm of the divergence or the curl of the signal, i.e., the...

Convolutional Filtering in Simplicial Complexes

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-sum principle of the convolution operation and...

Node-Adaptive Regularization for Graph Signal Reconstruction

A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal reconstruction, which surmounts the conventional Tikhonov regularization, giving rise to more degrees of...

Topological Volterra Filters

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 Volterra models, on the other hand, are also...

Finite Impulse Response Filters for Simplicial Complexes

In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be...

Node varying regularization for graph signals

While regularization on graphs has been successful for signal reconstruction, strategies for controlling the bias-variance trade-off of such methods have not been completely explored. In this work, we put forth a node varying regularizer for graph signal reconstruction and develop a minmax approach to design the vector of regularization...