Related papers: Sparse Dowker Nerves
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
Given two discrete Morse functions on a simplicial complex, we introduce the {\em connectedness homomorphism} between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in…
Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by…
We study two methods for computing network features with topological underpinnings: the Rips and Dowker persistent homology diagrams. Our formulations work for general networks, which may be asymmetric and may have any real number as an…
Radar perception models are trained with different inputs, from range-Doppler spectra to sparse point clouds. Dense spectra are assumed to outperform sparse point clouds, yet they can vary considerably across sensors and configurations,…
Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face…
Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…
Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compressed sensing which combines the pruning and training into a…
In the field of autonomous driving, a variety of sensor data types exist, each representing different modalities of the same scene. Therefore, it is feasible to utilize data from other sensors to facilitate image compression. However, few…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
Point clouds obtained from 3D sensors are usually sparse. Existing methods mainly focus on upsampling sparse point clouds in a supervised manner by using dense ground truth point clouds. In this paper, we propose a self-supervised point…
This paper proposes to learn high-performance deep ConvNets with sparse neural connections, referred to as sparse ConvNets, for face recognition. The sparse ConvNets are learned in an iterative way, each time one additional layer is…
Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation…
We develop a framework for computing the homology of weighted simplicial complexes with coefficients in a discrete valuation ring. A weighted simplicial complex, $(X,v)$, introduced by Dawson [Cah. Topol. G\'{e}om. Diff\'{e}r. Cat\'{e}g. 31…
A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the…
Point cloud obtained from 3D scanning is often sparse, noisy, and irregular. To cope with these issues, recent studies have been separately conducted to densify, denoise, and complete inaccurate point cloud. In this paper, we advocate that…
Modern Hopfield networks have enjoyed recent interest due to their connection to attention in transformers. Our paper provides a unified framework for sparse Hopfield networks by establishing a link with Fenchel-Young losses. The result is…
Neural network forms the foundation of deep learning and numerous AI applications. Classical neural networks are fully connected, expensive to train and prone to overfitting. Sparse networks tend to have convoluted structure search,…
High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…