Chinthaka Dinesh

Chinthaka Dinesh, Gene Cheung, Saghar Bagheri et al.

A basic premise in graph signal processing (GSP) is that a graph encoding pairwise (anti-)correlations of the targeted signal as edge weights is exploited for graph filtering. However, existing fast graph sampling schemes are designed and tested only for positive graphs describing positive correlations. In this paper, we show that for datasets with strong inherent anti-correlations, a suitable graph contains both positive and negative edge weights. In response, we propose a linear-time signed graph sampling method centered on the concept of balanced signed graphs. Specifically, given an empirical covariance data matrix $\bar{\bf{C}}$, we first learn a sparse inverse matrix (graph Laplacian) $\mathcal{L}$ corresponding to a signed graph $\mathcal{G}$. We define the eigenvectors of Laplacian $\mathcal{L}_B$ for a balanced signed graph $\mathcal{G}_B$ -- approximating $\mathcal{G}$ via edge weight augmentation -- as graph frequency components. Next, we choose samples to minimize the low-pass filter reconstruction error in two steps. We first align all Gershgorin disc left-ends of Laplacian $\mathcal{L}_B$ at smallest eigenvalue $λ_{\min}(\mathcal{L}_B)$ via similarity transform $\mathcal{L}_p = §\mathcal{L}_B §^{-1}$, leveraging a recent linear algebra theorem called Gershgorin disc perfect alignment (GDPA). We then perform sampling on $\mathcal{L}_p$ using a previous fast Gershgorin disc alignment sampling (GDAS) scheme. Experimental results show that our signed graph sampling method outperformed existing fast sampling schemes noticeably on various datasets.

Hanieh Naderi, Chinthaka Dinesh, Ivan V. Bajic et al.

Adversarial attacks pose serious challenges for deep neural network (DNN)-based analysis of various input signals. In the case of three-dimensional point clouds, methods have been developed to identify points that play a key role in network decision, and these become crucial in generating existing adversarial attacks. For example, a saliency map approach is a popular method for identifying adversarial drop points, whose removal would significantly impact the network decision. This paper seeks to enhance the understanding of three-dimensional adversarial attacks by exploring which point cloud features are most important for predicting adversarial points. Specifically, Fourteen key point cloud features such as edge intensity and distance from the centroid are defined, and multiple linear regression is employed to assess their predictive power for adversarial points. Based on critical feature selection insights, a new attack method has been developed to evaluate whether the selected features can generate an attack successfully. Unlike traditional attack methods that rely on model-specific vulnerabilities, this approach focuses on the intrinsic characteristics of the point clouds themselves. It is demonstrated that these features can predict adversarial points across four different DNN architectures, Point Network (PointNet), PointNet++, Dynamic Graph Convolutional Neural Networks (DGCNN), and Point Convolutional Network (PointConv) outperforming random guessing and achieving results comparable to saliency map-based attacks. This study has important engineering applications, such as enhancing the security and robustness of three-dimensional point cloud-based systems in fields like robotics and autonomous driving.

Saghar Bagheri, Chinthaka Dinesh, Gene Cheung et al.

Prediction of annual crop yields at a county granularity is important for national food production and price stability. In this paper, towards the goal of better crop yield prediction, leveraging recent graph signal processing (GSP) tools to exploit spatial correlation among neighboring counties, we denoise relevant features via graph spectral filtering that are inputs to a deep learning prediction model. Specifically, we first construct a combinatorial graph with edge weights that encode county-to-county similarities in soil and location features via metric learning. We then denoise features via a maximum a posteriori (MAP) formulation with a graph Laplacian regularizer (GLR). We focus on the challenge to estimate the crucial weight parameter $μ$, trading off the fidelity term and GLR, that is a function of noise variance in an unsupervised manner. We first estimate noise variance directly from noise-corrupted graph signals using a graph clique detection (GCD) procedure that discovers locally constant regions. We then compute an optimal $μ$ minimizing an approximate mean square error function via bias-variance analysis. Experimental results from collected USDA data show that using denoised features as input, performance of a crop yield prediction model can be improved noticeably.