Related papers: Convolutional Filtering in Simplicial Complexes

A complex system with many interacting individuals can be represented by a network consisting of nodes and links representing individuals and pairwise interactions, respectively. However, real-world systems grow with time and include many…

Topological Signal Processing (TSP) over simplicial complexes is a framework that has been recently proposed, as a generalization of graph signal processing (GSP), to extend GSP to analyzing signals defined over sets of any order (i.e., not…

Spectral graph convolutional network (SGCN) is a kind of graph neural networks (GNN) based on graph signal filters, and has shown compelling expressivity for modeling graph-structured data. Most SGCNs adopt polynomial filters and learn the…

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop TSP theories for the case where observations belong to general…

Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a…

Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…

Sparse coding (SC) is an automatic feature extraction and selection technique that is widely used in unsupervised learning. However, conventional SC vectorizes the input images, which breaks apart the local proximity of pixels and destructs…

The performance of multi-task learning in Convolutional Neural Networks (CNNs) hinges on the design of feature sharing between tasks within the architecture. The number of possible sharing patterns are combinatorial in the depth of the…

We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the…

In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of…

We study Graph Convolutional Networks (GCN) from the graph signal processing viewpoint by addressing a difference between learning graph filters with fully connected weights versus trainable polynomial coefficients. We find that by stacking…

A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs…

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated,…

This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…

A technique named Feature Learning from Image Markers (FLIM) was recently proposed to estimate convolutional filters, with no backpropagation, from strokes drawn by a user on very few images (e.g., 1-3) per class, and demonstrated for…

In this paper, we present an approach for minimizing the computational complexity of trained Convolutional Neural Networks (ConvNet). The idea is to approximate all elements of a given ConvNet and replace the original convolutional filters…

Compared to earlier multistage frameworks using CNN features, recent end-to-end deep approaches for fine-grained recognition essentially enhance the mid-level learning capability of CNNs. Previous approaches achieve this by introducing an…

Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a…