arXiv subjects

Wee Peng Tay

Publications and source records attributed to Wee Peng Tay.

At least 73 records · Page 4Linked to original sources

arXiv2023

Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks

Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space, with all nodes' representations embedded in a single space. However, a graph can have hyperbolic and Euclidean geometries at different regions of the graph. Thus, it is sub-optimal to indifferently embed an entire graph into a single space. In this paper, we explore and analyze two notions of local hyperbolicity, describing the underlying local geometry: geometric (Gromov) and model-based, to determine the preferred space of embedding for each node. The two hyperbolicities' distributions are aligned using the Wasserstein metric such that the calculated geometric hyperbolicity guides the choice of the learned model hyperbolicity. As such our model Joint Space Graph Neural Network (JSGNN) can leverage both Euclidean and hyperbolic spaces during learning by allowing node-specific geometry space selection. We evaluate our model on both node classification and link prediction tasks and observe promising performance compared to baseline models.

cs.LG↗

arXiv2023

Learning on heterogeneous graphs using high-order relations

A heterogeneous graph consists of different vertices and edges types. Learning on heterogeneous graphs typically employs meta-paths to deal with the heterogeneity by reducing the graph to a homogeneous network, guide random walks or capture semantics. These methods are however sensitive to the choice of meta-paths, with suboptimal paths leading to poor performance. In this paper, we propose an approach for learning on heterogeneous graphs without using meta-paths. Specifically, we decompose a heterogeneous graph into different homogeneous relation-type graphs, which are then combined to create higher-order relation-type representations. These representations preserve the heterogeneity of edges and retain their edge directions while capturing the interaction of different vertex types multiple hops apart. This is then complemented with attention mechanisms to distinguish the importance of the relation-type based neighbors and the relation-types themselves. Experiments demonstrate that our model generally outperforms other state-of-the-art baselines in the vertex classification task on three commonly studied heterogeneous graph datasets.

stat.ML↗

arXiv2023

Node Embedding from Hamiltonian Information Propagation in Graph Neural Networks

Graph neural networks (GNNs) have achieved success in various inference tasks on graph-structured data. However, common challenges faced by many GNNs in the literature include the problem of graph node embedding under various geometries and the over-smoothing problem. To address these issues, we propose a novel graph information propagation strategy called Hamiltonian Dynamic GNN (HDG) that uses a Hamiltonian mechanics approach to learn node embeddings in a graph. The Hamiltonian energy function in HDG is learnable and can adapt to the underlying geometry of any given graph dataset. We demonstrate the ability of HDG to automatically learn the underlying geometry of graph datasets, even those with complex and mixed geometries, through comprehensive evaluations against state-of-the-art baselines on various downstream tasks. We also verify that HDG is stable against small perturbations and can mitigate the over-smoothing problem when stacking many layers.

cs.LG↗

arXiv2023

Graph signal processing with categorical perspective

In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.

eess.SP↗

arXiv2023

On distributional graph signals

Graph signal processing (GSP) studies graph-structured data, where the central concept is the vector space of graph signals. To study a vector space, we have many useful tools up our sleeves. However, uncertainty is omnipresent in practice, and using a vector to model a real signal can be erroneous in some situations. In this paper, we want to use the Wasserstein space as a replacement for the vector space of graph signals, to account for signal stochasticity. The Wasserstein is strictly more general in which the classical graph signal space embeds isometrically. An element in the Wasserstein space is called a distributional graph signal. On the other hand, signal processing for a probability space of graphs has been proposed in the literature. In this work, we propose a unified framework that also encompasses existing theories regarding graph uncertainty. We develop signal processing tools to study the new notion of distributional graph signals. We also demonstrate how the theory can be applied by using real datasets.

eess.SP↗

arXiv2023

On the Relationship Between Information-Theoretic Privacy Metrics And Probabilistic Information Privacy

Information-theoretic (IT) measures based on $f$-divergences have recently gained interest as a measure of privacy leakage as they allow for trading off privacy against utility using only a single-value characterization. However, their operational interpretations in the privacy context are unclear. In this paper, we relate the notion of probabilistic information privacy (IP) to several IT privacy metrics based on $f$-divergences. We interpret probabilistic IP under both the detection and estimation frameworks and link it to differential privacy, thus allowing a precise operational interpretation of these IT privacy metrics. We show that the $χ^2$-divergence privacy metric is stronger than those based on total variation distance and Kullback-Leibler divergence. Therefore, we further develop a data-driven empirical risk framework based on the $χ^2$-divergence privacy metric and realized using deep neural networks. This framework is agnostic to the adversarial attack model. Empirical experiments demonstrate the efficacy of our approach.

cs.IT↗

arXiv2022

On semi shift invariant graph filters

In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant filters, defined as transformations commute with a preferred graph shift operator. Shift invariant filters have a wide range of applications in graph signal processing and graph neural networks. A shift invariant filter can be interpreted geometrically as an information aggregation procedure (from local neighborhood), and can be computed easily using matrix multiplication. However, there are still drawbacks to using solely shift invariant filters in applications, such as being restrictively homogeneous. In this paper, we generalize shift invariant filters by introducing and studying semi shift invariant filters. We give an application of semi shift invariant filters with a new signal processing framework, the subgraph signal processing. Moreover, we also demonstrate how semi shift invariant filters can be used in graph neural networks.

eess.SP↗

arXiv2022

Wide-Sense Stationarity in Generalized Graph Signal Processing

We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional scalar-valued graph signal, multichannel graph signal, and discrete- and continuous-time graph signals, allowing us to build a unified theory of graph random processes. We introduce the notion of joint wide-sense stationarity in this generalized GSP framework, which allows us to characterize a graph random process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We elucidate the relationship between the notions of wide-sense stationarity in different domains, and derive the Wiener filters for denoising and signal completion under this framework. Numerical experiments on both real and synthetic datasets demonstrate the utility of our generalized approach in achieving better estimation performance compared to traditional GSP or the time-vertex framework.

eess.SP↗

arXiv2022

SGAT: Simplicial Graph Attention Network

Heterogeneous graphs have multiple node and edge types and are semantically richer than homogeneous graphs. To learn such complex semantics, many graph neural network approaches for heterogeneous graphs use metapaths to capture multi-hop interactions between nodes. Typically, features from non-target nodes are not incorporated into the learning procedure. However, there can be nonlinear, high-order interactions involving multiple nodes or edges. In this paper, we present Simplicial Graph Attention Network (SGAT), a simplicial complex approach to represent such high-order interactions by placing features from non-target nodes on the simplices. We then use attention mechanisms and upper adjacencies to generate representations. We empirically demonstrate the efficacy of our approach with node classification tasks on heterogeneous graph datasets and further show SGAT's ability in extracting structural information by employing random node features. Numerical experiments indicate that SGAT performs better than other current state-of-the-art heterogeneous graph learning methods.

cs.LG↗

arXiv2022

Abstract message passing and distributed graph signal processing

Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed graph signal processing algorithms are needed to address challenges such as scalability and privacy. In this paper, we develop a theory of distributed graph signal processing based on the classical notion of message passing. However, we generalize the definition of a message to permit more abstract mathematical objects. The framework provides an alternative point of view that avoids the iterative nature of existing approaches to distributed graph signal processing. Moreover, our framework facilitates investigating theoretical questions such as solubility of distributed problems.

eess.SP↗

arXiv2022

Building Facade Parsing R-CNN

Building facade parsing, which predicts pixel-level labels for building facades, has applications in computer vision perception for autonomous vehicle (AV) driving. However, instead of a frontal view, an on-board camera of an AV captures a deformed view of the facade of the buildings on both sides of the road the AV is travelling on, due to the camera perspective. We propose Facade R-CNN, which includes a transconv module, generalized bounding box detection, and convex regularization, to perform parsing of deformed facade views. Experiments demonstrate that Facade R-CNN achieves better performance than the current state-of-the-art facade parsing models, which are primarily developed for frontal views. We also publish a new building facade parsing dataset derived from the Oxford RobotCar dataset, which we call the Oxford RobotCar Facade dataset. This dataset contains 500 street-view images from the Oxford RobotCar dataset augmented with accurate annotations of building facade objects. The published dataset is available at https://github.com/sijieaaa/Oxford-RobotCar-Facade

cs.CV↗

arXiv2021

Using Reconfigurable Intelligent Surfaces for UE Positioning in mmWave MIMO Systems

A reconfigurable intelligent surface (RIS) consists of massive meta elements, which results in a reflection path between a base station (BS) and user equipment (UE). In wireless localization, this reflection path aids in positioning accuracy, especially when the line-of-sight (LOS) path is subject to severe blockage and fading. We develop a RIS-aided positioning framework to locate a UE in environments where the LOS path may or may not be available. We first estimate the RIS-aided channel parameters from the received signals at the UE. To reduce algorithmic complexity, we propose a linear combination of the estimated UE positions from the direct and reflection paths, which is shown to be approximately the maximum likelihood estimator under the large-sample regime when the estimates from different paths are independent. We optimize the RIS phase shifts to improve the positioning accuracy, and extend the proposed approach to the case with multiple BSs and UEs. We derive the Cramer-Rao bound (CRB) and demonstrate numerically that our proposed method approaches the CRB.

eess.SP↗

arXiv2021

Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks

Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent studies have demonstrated that neural Ordinary Differential Equations (ODEs) are intrinsically more robust against adversarial attacks compared to vanilla DNNs. In this work, we propose a stable neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks (SODEF). By ensuring that the equilibrium points of the ODE solution used as part of SODEF is Lyapunov-stable, the ODE solution for an input with a small perturbation converges to the same solution as the unperturbed input. We provide theoretical results that give insights into the stability of SODEF as well as the choice of regularizers to ensure its stability. Our analysis suggests that our proposed regularizers force the extracted feature points to be within a neighborhood of the Lyapunov-stable equilibrium points of the ODE. SODEF is compatible with many defense methods and can be applied to any neural network's final regressor layer to enhance its stability against adversarial attacks.

cs.LG↗

arXiv2021

Sampling Theory of Bandlimited Continuous-Time Graph Signals

A continuous-time graph signal can be viewed as a time series of graph signals. It generalizes both the classical continuous-time signal and ordinary graph signal. Therefore, such a signal can be considered as a function on two domains: the graph domain and the time domain. In this paper, we consider the sampling theory of bandlimited continuous-time graph signals. To formulate the sampling problem, we need to consider the interaction between the graph and time domains. We describe an explicit procedure to determine a discrete sampling set for perfect signal recovery. Moreover, in analogous to the Nyquist-Shannon sampling theorem, we give an explicit formula for the minimal sample rate.

eess.SP↗

arXiv2021

Cost-Efficient RIS-Aided Channel Estimation via Rank-One Matrix Factorization

A reconfigurable intelligent surface (RIS) consists of massive meta elements, which can improve the performance of future wireless communication systems. Existing RIS-aided channel estimation methods try to estimate the cascaded channel directly, incurring high computational and training overhead especially when the number of elements of RIS is extremely large. In this paper, we propose a cost-efficient channel estimation method via rank-one matrix factorization (MF). Specifically, if the RIS is employed near base station (BS), it is found that the RIS- aided channel can be factorized into a product of low-dimensional matrices. To estimate these factorized matrices, we propose alternating minimization and gradient descent approaches to obtain the near optimal solutions. Compared to directly estimating the cascaded channel, the proposed MF method reduces training overhead substantially. Finally, the numerical simulations show the effectiveness of the proposed MF method.

cs.IT↗

arXiv2021

Error-Correcting Output Codes with Ensemble Diversity for Robust Learning in Neural Networks

Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-correcting output code (ECOC) based methods that train binary classifiers independently. ECNN is complementary to other existing defense approaches such as adversarial training and can be applied in conjunction with them. We empirically demonstrate that our proposed ECNN is effective against the state-of-the-art white-box and black-box attacks on several datasets while maintaining good classification accuracy on normal examples.

cs.LG↗

arXiv2021

Subgraph Signal Processing

Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing framework that relates a graph shift operator or filter on a subgraph with a filter on the ambient graph through an operator loss. It allows us to define shift operators for the subgraph signal, which has a meaningful interpretation and relation to mixtures of shift invariant filters restricted to different subgraphs of the ambient graph (which we call semi shift invariant). This leads to a notion of frequency domain for the subgraph signal consistent in some sense with that of the full graph signal. We apply the subgraph signal processing machinery to several applications and demonstrate the utility of this framework in cases where only partial graph signals are observed.

eess.SP↗

arXiv2021

An Unsupervised Bayesian Neural Network for Truth Discovery in Social Networks

The problem of estimating event truths from conflicting agent opinions in a social network is investigated. An autoencoder learns the complex relationships between event truths, agent reliabilities and agent observations. A Bayesian network model is proposed to guide the learning process by modeling the relationship of the autoencoder's outputs with different variables. At the same time, it also models the social relationships between agents in the network. The proposed approach is unsupervised and is applicable when ground truth labels of events are unavailable. A variational inference method is used to jointly estimate the hidden variables in the Bayesian network and the parameters in the autoencoder. Experiments on three real datasets demonstrate that our proposed approach is competitive with, and in most cases better than, several state-of-the-art benchmark methods.

cs.LG↗