Graph Variogram: A novel tool to measure spatial stationarity

Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive definition of classical stationarity. We introduce the concept of graph variogram, a novel tool for measuring spatial intrinsic stationarity at local and global scales for irregularly sampled signals by selecting subgraphs of local neighborhoods. Graph variograms are extensions of variograms used for signals defined on continuous Euclidean space. Our experiments with intrinsically stationary signals sampled on a graph, demonstrate that graph variograms yield estimates with small bias of true theoretical models, while being robust to sampling variation of the space.Comment: Submitted to IEEE Global Conference on Signal and Information Processing 2018 (IEEE GlobalSIP 2018), Nov 2018, Anaheim, CA, United States. (https://2018.ieeeglobalsip.org/

Stationary Graph Signals using an Isometric Graph Translation

International audienceIn this communication, we extend the concept of stationary temporal signals to stationary graph signals. We introduce the concept of strict sense stationary and wide sense stationary graph signals as a statistical invariance through an isometric graph translation. Using these definitions, we propose a spectral characterisation of WSS graph signals allowing to study stationarity using only the spectral components of a graph signal.Finally, we apply this characterisation a synthetic graph in order to study a few important stochastic graph signals. Also, using geographic data, we study weather readings on the graph of weather stations and show evidence of stationarity in the temperature readings

Generating Labels for Regression of Subjective Constructs using Triplet Embeddings

Human annotations serve an important role in computational models where the target constructs under study are hidden, such as dimensions of affect. This is especially relevant in machine learning, where subjective labels derived from related observable signals (e.g., audio, video, text) are needed to support model training and testing. Current research trends focus on correcting artifacts and biases introduced by annotators during the annotation process while fusing them into a single annotation. In this work, we propose a novel annotation approach using triplet embeddings. By lifting the absolute annotation process to relative annotations where the annotator compares individual target constructs in triplets, we leverage the accuracy of comparisons over absolute ratings by human annotators. We then build a 1-dimensional embedding in Euclidean space that is indexed in time and serves as a label for regression. In this setting, the annotation fusion occurs naturally as a union of sets of sampled triplet comparisons among different annotators. We show that by using our proposed sampling method to find an embedding, we are able to accurately represent synthetic hidden constructs in time under noisy sampling conditions. We further validate this approach using human annotations collected from Mechanical Turk and show that we can recover the underlying structure of the hidden construct up to bias and scaling factors.Comment: 9 pages, 5 figures, accepted journal pape

Signaux stationnaires sur graphe : étude d'un cas réel

National audienceBased on a real geographical dataset, we apply the stationarity characterisation of a graph signal, through the analysis of its spectral decomposition. In the course, we identify possible sources of non-stationarity and we elaborate on the impact of the graph used to model the structural coherence of the data.Sur un jeu de données géographiques réelles, nous appliquons la caractérisation de la propriété de stationnarité d'un signal sur graphe via l'analyse de ses coefficients spectraux. Nous identifions différentes sources possibles de non-stationnarité et isolons l'influence qu'a le graphe sous-jacent sur la cohérence structurelle des données

Traitement du Signal sur Graphe : Interprétation en termes de Filtre de l'Apprentissage Semi-Supervisé sur Graphe

National audienceNous montrons comment les outils de traitement du signal sur graphe peuvent dégager des notions de fréquences sur les graphes pour étudier des données portées par les nœud d'un graphe. Prenant l'exemple de l'apprentissage semi-supervisé, nous montrons alors qu'il peut s'interpréter comme le filtre d'un signal sur graphe

Translation on Graphs: An Isometric Shift Operator

International audienceIn this letter, we propose a new shift operator for graph signals, enforcing that our operator is isometric. Doing so, we ensure that as many properties of the time shift as possible get carried over. Finally, we show that our operator behaves reasonably for graph signals

Graphe de contacts et ondelettes

National audienceLes infections nosocomiales sont une source importante de mortalité lors d'un séjour hospitalier. En particulier, les bactéries multi-résistantes telles que les staphilocoques dorés présentent un problème sanitaire croissant puisque le nombre de traitements antibiotiques efficaces s'amenuise. Cette étude a pour but de comprendre le processus épidémique au sein d'un hôpital sur une durée de plusieurs mois. Pour cela, nous utilisons des outils inspirés du traitement du signal et appliqués aux graphes pour en déduire les différentes dimensions spatio-temporelles des données

Irregularity-Aware Graph Fourier Transforms

In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our approach includes traditional definitions of the GFT as special cases, while also leading to new GFT designs that are better at taking into account the irregular nature of the graph. As an illustration, in the context of sensor networks we use the Voronoi cell area of vertices in our GFT definition, showing that it leads to a more sensible definition of graph signal energy even when sampling is highly irregular.Comment: This article has been published in IEEE Transactions on Signal Processin