Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

High-Capacity Directional Graph Networks

Deep Neural Networks (DNN) have proven themselves to be a useful tool in many computer vision problems. One of the most popular forms of the DNN is the Convolutional Neural Network (CNN). The CNN effectively learns features on images by learning a weighted sum of local neighborhoods of pixels, creating filtered versions of the image. Point cloud analysis seems like it would benefit from this useful model. However, point clouds are much less structured than images. Many analogues to CNNs for point clouds have been proposed in the literature, but they are often much more constrained networks than the typical CNN. This is a matter of necessity: common point cloud benchmark datasets are fairly small and thus require strong regularization to mitigate overfitting. In this dissertation we propose two point cloud network models based on graph structures that achieve the high-capacity modeling capability of CNNs. In addition to showing their effectiveness on point cloud classification and segmentation in typical benchmark scenarios, we also propose two novel point cloud problems: ATLAS Detector segmentation and Computational Fluid Dynamics (CFD) surrogate modeling. We show that our networks are much more effective than others on these new problems because they benefit from deeper networks and extra capacity that other researchers have not pursued. These novel networks and datasets pave the way for future development of deeper, more sophisticated point cloud networks

Detection of an anomalous cluster in a network

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with positive mean and unit variance, while the rest are i.i.d. standard normal. We also address surveillance settings where each sensor in the network collects information over time. The resulting model is similar, now with a time series attached to each node. We again observe the process over time and want to decide between the null, where all the variables are i.i.d. standard normal, and the alternative, where there is an emerging cluster of i.i.d. normal variables with positive mean and unit variance. The growth models used to represent the emerging cluster are quite general and, in particular, include cellular automata used in modeling epidemics. In both settings, we consider classes of clusters that are quite general, for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic, by far the most popular method in practice, achieves that same rate to within a logarithmic factor. Our results are not limited to the normal location model, but generalize to any one-parameter exponential family when the anomalous clusters are large enough.Comment: Published in at http://dx.doi.org/10.1214/10-AOS839 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A discordance analysis in manual labelling of urban mobile laser scanning data used for deep learning based semantic segmentation

Labelled point clouds are crucial to train supervised Deep Learning (DL) methods used for semantic segmentation. The objective of this research is to quantify discordances between the labels made by different people in order to assess whether such discordances can influence the success rates of a DL based semantic segmentation algorithm. An urban point cloud of 30 m road length in Santiago de Compostela (Spain) was labelled two times by ten persons. Discordances and its significance in manual labelling between individuals and rounds were calculated. In addition, a ratio test to signify discordance and concordance was proposed. Results show that most of the points were labelled accordingly with the same class by all the people. However, there were many points that were labelled with two or more classes. Class curb presented 5.9% of discordant points and 3.2 discordances for each point with concordance by all people. In addition, the percentage of significative labelling differences of the class curb was 86.7% comparing all the people in the same round and 100% comparing rounds of each person. Analysing the semantic segmentation results with a DL based algorithm, PointNet++, the percentage of concordance points are related with F-score value in R2 = 0.765, posing that manual labelling has significant impact on results of DL-based semantic segmentation methods.Xunta de Galicia | Ref. ED481B-2019-061Ministerio de Ciencia e Innovación | Ref. PID2019-105221RB-C43Ministère de l’Economie of the G. D. of Luxembourg | Ref. SOLSTICE 2019-05-030-24Universidade de Vigo/CISU