Manifold Graph Signal Restoration using Gradient Graph Laplacian Regularizer

In the graph signal processing (GSP) literature, graph Laplacian regularizer (GLR) was used for signal restoration to promote piecewise smooth / constant reconstruction with respect to an underlying graph. However, for signals slowly varying across graph kernels, GLR suffers from an undesirable "staircase" effect. In this paper, focusing on manifold graphs -- collections of uniform discrete samples on low-dimensional continuous manifolds -- we generalize GLR to gradient graph Laplacian regularizer (GGLR) that promotes planar / piecewise planar (PWP) signal reconstruction. Specifically, for a graph endowed with sampling coordinates (e.g., 2D images, 3D point clouds), we first define a gradient operator, using which we construct a gradient graph for nodes' gradients in sampling manifold space. This maps to a gradient-induced nodal graph (GNG) and a positive semi-definite (PSD) Laplacian matrix with planar signals as the 0 frequencies. For manifold graphs without explicit sampling coordinates, we propose a graph embedding method to obtain node coordinates via fast eigenvector computation. We derive the means-square-error minimizing weight parameter for GGLR efficiently, trading off bias and variance of the signal estimate. Experimental results show that GGLR outperformed previous graph signal priors like GLR and graph total variation (GTV) in a range of graph signal restoration tasks

Data-Driven Supervised Learning for Life Science Data

Life science data are often encoded in a non-standard way by means of alpha-numeric sequences, graph representations, numerical vectors of variable length, or other formats. Domain-specific or data-driven similarity measures like alignment functions have been employed with great success. The vast majority of more complex data analysis algorithms require fixed-length vectorial input data, asking for substantial preprocessing of life science data. Data-driven measures are widely ignored in favor of simple encodings. These preprocessing steps are not always easy to perform nor particularly effective, with a potential loss of information and interpretability. We present some strategies and concepts of how to employ data-driven similarity measures in the life science context and other complex biological systems. In particular, we show how to use data-driven similarity measures effectively in standard learning algorithms

Unsupervised Graph Spectral Feature Denoising for Crop Yield Prediction

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 $\mu$, 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 $\mu$ 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

Model selection-inspired coefficients optimization for polynomial-kernel graph learning

Graph learning has been extensively investigated for over a decade, in which the graph structure can be learnt from multiple graph signals (e.g., graphical Lasso) or node features (e.g., graph metric learning). Given partial graph signals, existing node feature-based graph learning approaches learn a pair-wise distance metric with gradient descent, where the number of optimization variables dramatically scale with the node feature size. To address this issue, in this paper, we propose a low-complexity model selection-inspired graph learning (MSGL) method with very few optimization variables independent with feature size, via leveraging on recent advances in graph spectral signal processing (GSP). We achieve this by 1) interpreting a finite-degree polynomial function of the graph Laplacian as a positive-definite precision matrix, 2) formulating a convex optimization problem with variables being the polynomial coefficients, 3) replacing the positive-definite cone constraint for the precision matrix with a set of linear constraints, and 4) solving efficiently the objective using the Frank-Wolfe algorithm. Using binary classification as an application example, our simulation results show that our proposed MSGL method achieves competitive performance with significant speed gains against existing node feature-based graph learning methods

Spectral Alignment of Networks

Network alignment refers to the problem of finding a bijective mapping across vertices of two or more graphs to maximize the number of overlapping edges and/or to minimize the number of mismatched interactions across networks. This paper introduces a network alignment algorithm inspired by eigenvector analysis which creates a simple relaxation for the underlying quadratic assignment problem. Our method relaxes binary assignment constraints along the leading eigenvector of an alignment matrix which captures the structure of matched and mismatched interactions across networks. Our proposed algorithm denoted by EigeAlign has two steps. First, it computes the Perron-Frobenius eigenvector of the alignment matrix. Second, it uses this eigenvector in a linear optimization framework of maximum weight bipartite matching to infer bijective mappings across vertices of two graphs. Unlike existing network alignment methods, EigenAlign considers both matched and mismatched interactions in its optimization and therefore, it is effective in aligning networks even with low similarity. We show that, when certain technical conditions hold, the relaxation given by EigenAlign is asymptotically exact over Erdos-Renyi graphs with high probability. Moreover, for modular network structures, we show that EigenAlign can be used to split the large quadratic assignment optimization into small subproblems, enabling the use of computationally expensive, but tight semidefinite relaxations over each subproblem. Through simulations, we show the effectiveness of the EigenAlign algorithm in aligning various network structures including Erdos-Renyi, power law, and stochastic block models, under different noise models. Finally, we apply EigenAlign to compare gene regulatory networks across human, fly and worm species which we infer by integrating genome-wide functional and physical genomics datasets from ENCODE and modENCODE consortia. EigenAlign infers conserved regulatory interactions across these species despite large evolutionary distances spanned. We find strong conservation of centrally-connected genes and some biological pathways, especially for human-fly comparisons

Metaverse: A Young Gamer's Perspective

When developing technologies for the Metaverse, it is important to understand the needs and requirements of end users. Relatively little is known about the specific perspectives on the use of the Metaverse by the youngest audience: children ten and under. This paper explores the Metaverse from the perspective of a young gamer. It examines their understanding of the Metaverse in relation to the physical world and other technologies they may be familiar with, looks at some of their expectations of the Metaverse, and then relates these to the specific multimedia signal processing (MMSP) research challenges. The perspectives presented in the paper may be useful for planning more detailed subjective experiments involving young gamers, as well as informing the research on MMSP technologies targeted at these users.Comment: 6 pages, 5 figures, IEEE MMSP 202

Model-Free Prediction of Adversarial Drop Points in 3D Point Clouds

Adversarial attacks pose serious challenges for deep neural network (DNN)-based analysis of various input signals. In the case of 3D point clouds, methods have been developed to identify points that play a key role in the 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. Generally, methods for identifying adversarial points rely on the deep model itself in order to determine which points are critically important for the model's decision. This paper aims to provide a novel viewpoint on this problem, in which adversarial points can be predicted independently of the model. To this end, we define 14 point cloud features and use multiple linear regression to examine whether these features can be used for model-free adversarial point prediction, and which combination of features is best suited for this purpose. Experiments show that a suitable combination of features is able to predict adversarial points of three different networks -- PointNet, PointNet++, and DGCNN -- significantly better than a random guess. The results also provide further insight into DNNs for point cloud analysis, by showing which features play key roles in their decision-making process.Comment: 10 pages, 6 figure