Detecting the origin of information or infection spread in networks is a fundamental challenge with applications in misinformation tracking, epidemiology, and beyond. We study the multi-source detection problem: given snapshot observations of node infection status on a graph, estimate the set of source nodes that initiated the propagation. Existing methods either lack statistical guarantees or are limited to specific diffusion models and assumptions. We propose a novel conformal prediction framework that provides statistically valid recall guarantees for source set detection, independent of the underlying diffusion process or data distribution. Our approach introduces principled score functions to quantify the alignment between predicted probabilities and true sources, and leverages a calibration set to construct prediction sets with user-specified recall and coverage levels. The method is applicable to both single- and multi-source scenarios, supports general network diffusion dynamics, and is computationally efficient for large graphs. Empirical results demonstrate that our method achieves rigorous coverage with competitive accuracy, outperforming existing baselines in both reliability and scalability.

We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding p-value. The goal is to make decisions for all hypotheses simultaneously, using all available p-values. In practice, this problem resembles the detection problem over a sensor network during a period of time. To solve this problem, we extend the traditional two-groups model such that the prior probability of the null hypothesis and the alternative distribution of p-values can be inhomogeneous over the joint domain. We model the inhomogeneity via a generalized graph signal. This more flexible statistical model yields a more powerful detection strategy by leveraging the information from the joint domain.

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we quantify signal localization across these domains, revealing a trade-off between them. This framework allows us to identify a class of signals with maximal energy concentration in both domains, forming the fundamental atoms for a new joint vertex-time dictionary. This dictionary enhances signal reconstruction under practical constraints, such as intermittent data, commonly encountered in sensor and social networks. Numerical experiments on real-world datasets demonstrate the effectiveness of the proposed approach, showing improved reconstruction accuracy and noise robustness compared to existing methods.

Ground-penetrating radar (GPR) is a vital tool in the domain of nondestructive testing; however, its capability to accurately discern subsurface targets faces challenges from substantial background clutter. Current methods aimed at clutter suppression often leave residual clutter or distort the hyperbolic tails of target-scattered signals, particularly in heterogeneous soil conditions. This study endeavors to tackle the complexities of clutter suppression in practical scenarios. To this end, we introduce a novel framework for GPR clutter suppression using stationary graph signal (SGS) processing techniques. In our proposed approach, GPR B-scan images are treated as graph signals and transformed into the graph frequency domain via graph Fourier transform (GFT). This framework incorporates B-scan images containing both targets and clutter alongside clutter-only B-scan images gathered within the same testing environment. B-scan images featuring both targets and clutter serve as reference data samples for constructing a graph shift operator (GSO), with clutter and targets’ scattering signals interpreted as SGS. Following the establishment of weak SGSs with respect to the GSO, a variant of the graph-based Wiener filter tailored for GPR applications is applied to effectuate clutter suppression. Through our proposed SGS processing-based filtering method, clutter can be effectively suppressed, thereby facilitating the restoration of target scattering signals. Extensive experiments conducted on both numerical simulation data and field test data underscore the efficacy of the proposed approach, which can be further applied to the general nondestructive testing realm.

Point cloud registration is a crucial technique in 3D computer vision with a wide range of applications. However, this task can be challenging, particularly in large fields of view with dynamic objects, environmental noise, or other perturbations. To address this challenge, we propose a model called PosDiffNet. Our approach performs hierarchical registration based on window-level, patch-level, and point-level correspondence. We leverage a graph neural partial differential equation (PDE) based on Beltrami flow to obtain high-dimensional features and position embeddings for point clouds. We incorporate position embeddings into a Transformer module based on a neural ordinary differential equation (ODE) to efficiently represent patches within points. We employ the multi-level correspondence derived from the high feature similarity scores to facilitate alignment between point clouds. Subsequently, we use registration methods such as SVD-based algorithms to predict the transformation using corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud datasets, verifying that it achieves state-of-the-art (SOTA) performance for point cloud registration in large fields of view with perturbations. The implementation code of experiments is available at https://github.com/AI-IT-AVs/PosDiffNet.

The utilization of multi-modal sensor data in visual place recognition (VPR) has demonstrated enhanced performance compared to single-modal counterparts. Nonetheless, integrating additional sensors comes with elevated costs and may not be feasible for systems that demand lightweight operation, thereby impacting the practical deployment of VPR. To address this issue, we resort to knowledge distillation, which empowers single-modal students to learn from cross-modal teachers without introducing additional sensors during inference. Despite the notable advancements achieved by current distillation approaches, the exploration of feature relationships remains an under-explored area. In order to tackle the challenge of cross-modal distillation in VPR, we present DistilVPR, a novel distillation pipeline for VPR. We propose leveraging feature relationships from multiple agents, including self-agents and cross-agents for teacher and student neural networks. Furthermore, we integrate various manifolds, characterized by different space curvatures for exploring feature relationships. This approach enhances the diversity of feature relationships, including Euclidean, spherical, and hyperbolic relationship modules, thereby enhancing the overall representational capacity. The experiments demonstrate that our proposed pipeline achieves state-of-the-art performance compared to other distillation baselines. We also conduct necessary ablation studies to show design effectiveness. The code is released at: https://github.com/sijieaaa/DistilVPR

Topological signal processing (TSP) utilizes simplicial complexes to model structures with higher order than vertices and edges. In this paper, we study the transferability of TSP via a generalized higher-order version of graphon, known as complexon. We recall the notion of a complexon as the limit of a simplicial complex sequence [1]. Inspired by the graphon shift operator and message-passing neural network, we construct a marginal complexon and complexon shift operator (CSO) according to components of all possible dimensions from the complexon. We investigate the CSO's eigenvalues and eigenvectors and relate them to a new family of weighted adjacency matrices. We prove that when a simplicial complex signal sequence converges to a complexon signal, the eigenvalues, eigenspaces, and Fourier transform of the corresponding CSOs converge to that of the limit complexon signal. This conclusion is further verified by two numerical experiments. These results hint at learning transferability on large simplicial complexes or simplicial complex sequences, which generalize the graphon signal processing framework.

In generalized graph signal processing (GGSP), a function (an element from a separable Hilbert space) is associated with each vertex. To perform non-linear filtering and regression under the GGSP framework, we formulate an operator-valued kernel ridge regression (KRR) filtering approach. Under a specific choice of separable kernels, we show that this problem is equivalent to learning a nonlinear frequency response on each frequency band. We specify the choice of the reproducing kernel according to the signal’s spectral properties and discuss its effect on the learning result. The proposed approach is validated on a real dataset and demonstrated to outperform other competing methods.

We consider a probabilistic model for graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. We introduce the notion of joint wide-sense stationarity in this generalized GSP (GGSP) framework, which allows us to characterize a random graph process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We also propose a method for joint power spectral density estimation in case of missing features. Experiment results corroborate the effectiveness of our estimation approach.