Searcharxiv⌕ Search

arXiv subjects

Pierre Vandergheynst

Publications and source records attributed to Pierre Vandergheynst.

At least 37 records · Page 2Linked to original sources
arXiv2019

A Graph-structured Dataset for Wikipedia Research

Wikipedia is a rich and invaluable source of information. Its central place on the Web makes it a particularly interesting object of study for scientists. Researchers from different domains used various complex datasets related to Wikipedia to study language, social behavior, knowledge organization, and network theory. While being a scientific treasure, the large size of the dataset hinders pre-processing and may be a challenging obstacle for potential new studies. This issue is particularly acute in scientific domains where researchers may not be technically and data processing savvy. On one hand, the size of Wikipedia dumps is large. It makes the parsing and extraction of relevant information cumbersome. On the other hand, the API is straightforward to use but restricted to a relatively small number of requests. The middle ground is at the mesoscopic scale when researchers need a subset of Wikipedia ranging from thousands to hundreds of thousands of pages but there exists no efficient solution at this scale. In this work, we propose an efficient data structure to make requests and access subnetworks of Wikipedia pages and categories. We provide convenient tools for accessing and filtering viewership statistics or "pagecounts" of Wikipedia web pages. The dataset organization leverages principles of graph databases that allows rapid and intuitive access to subgraphs of Wikipedia articles and categories. The dataset and deployment guidelines are available on the LTS2 website \url{https://lts2.epfl.ch/Datasets/Wikipedia/}.

cs.IR↗
arXiv2019

Anomaly detection in the dynamics of web and social networks

In this work, we propose a new, fast and scalable method for anomaly detection in large time-evolving graphs. It may be a static graph with dynamic node attributes (e.g. time-series), or a graph evolving in time, such as a temporal network. We define an anomaly as a localized increase in temporal activity in a cluster of nodes. The algorithm is unsupervised. It is able to detect and track anomalous activity in a dynamic network despite the noise from multiple interfering sources. We use the Hopfield network model of memory to combine the graph and time information. We show that anomalies can be spotted with a good precision using a memory network. The presented approach is scalable and we provide a distributed implementation of the algorithm. To demonstrate its efficiency, we apply it to two datasets: Enron Email dataset and Wikipedia page views. We show that the anomalous spikes are triggered by the real-world events that impact the network dynamics. Besides, the structure of the clusters and the analysis of the time evolution associated with the detected events reveals interesting facts on how humans interact, exchange and search for information, opening the door to new quantitative studies on collective and social behavior on large and dynamic datasets.

cs.SI↗
arXiv2018

Geodesic convolutional neural networks on Riemannian manifolds

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.

cs.CV↗
arXiv2018

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.

eess.SP↗
arXiv2018

Adaptive Graph-based Total Variation for Tomographic Reconstructions

Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional artefacts due to over-smoothing. Non-Local TV (NLTV) methods have been proposed as a solution to this but they either lack continuous updates due to computational constraints or limit the locality to a small region. In this paper, we propose Adaptive Graph-based TV (AGTV). The proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the entire image regardless of spatial distance. As compared to NLTV the proposed method is computationally efficient and involves updating the graph prior during every iteration making the connection between similar regions stronger. Moreover, it promotes sparsity in the wavelet and graph gradient domains. Since TV is a special case of graph TV the proposed method can also be seen as a generalization of SER and TV methods.

cs.CV↗
arXiv2018

FeTa: A DCA Pruning Algorithm with Generalization Error Guarantees

Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers, often with little or no drop in classification accuracy. However, most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. We start by proposing a cheap pruning algorithm for fully connected DNN layers based on difference of convex functions (DC) optimisation, that requires little or no retraining. We then provide a theoretical analysis for the growth in the Generalization Error (GE) of a DNN for the case of bounded perturbations to the hidden layers, of which weight pruning is a special case. Our pruning method is orders of magnitude faster than competing approaches, while our theoretical analysis sheds light to previously observed problems in DNN pruning. Experiments on commnon feedforward neural networks validate our results.

cs.LG↗
arXiv2018

Spectrally approximating large graphs with smaller graphs

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard graph-theoretic properties, such as the degree and eigenvalue distributions, as well as on the ratio between the coarsened and actual graph sizes. Our results carry implications for learning methods that utilize coarsening. For the particular case of spectral clustering, they imply that coarse eigenvectors can be used to derive good quality assignments even without refinement---this phenomenon was previously observed, but lacked formal justification.

cs.LG↗
arXiv2018

Joint Estimation of Room Geometry and Modes with Compressed Sensing

Acoustical behavior of a room for a given position of microphone and sound source is usually described using the room impulse response. If we rely on the standard uniform sampling, the estimation of room impulse response for arbitrary positions in the room requires a large number of measurements. In order to lower the required sampling rate, some solutions have emerged that exploit the sparse representation of the room wavefield in the terms of plane waves in the low-frequency domain. The plane wave representation has a simple form in rectangular rooms. In our solution, we observe the basic axial modes of the wave vector grid for extraction of the room geometry and then we propagate the knowledge to higher order modes out of the low-pass version of the measurements. Estimation of the approximate structure of the $k$-space should lead to the reduction in the terms of number of required measurements and in the increase of the speed of the reconstruction without great losses of quality.

eess.AS↗
arXiv2018

Wikipedia graph mining: dynamic structure of collective memory

Wikipedia is the biggest encyclopedia ever created and the fifth most visited website in the world. Tens of millions of people surf it every day, seeking answers to various questions. Collective user activity on its pages leaves publicly available footprints of human behavior, making Wikipedia an excellent source for analysis of collective behavior. In this work, we propose a distributed graph-based event extraction model, inspired by the Hebbian learning theory. The model exploits collective effect of the dynamics to discover events. We focus on data-streams with underlying graph structure and perform several large-scale experiments on the Wikipedia visitor activity data. We show that the presented model is scalable regarding time-series length and graph density, providing a distributed implementation of the proposed algorithm. We extract dynamical patterns of collective activity and demonstrate that they correspond to meaningful clusters of associated events, reflected in the Wikipedia articles. We also illustrate evolutionary dynamics of the graphs over time to highlight changing nature of visitors' interests. Finally, we discuss clusters of events that model collective recall process and represent collective memories - common memories shared by a group of people.

cs.IR↗
arXiv2017

FMA: A Dataset For Music Analysis

We introduce the Free Music Archive (FMA), an open and easily accessible dataset suitable for evaluating several tasks in MIR, a field concerned with browsing, searching, and organizing large music collections. The community's growing interest in feature and end-to-end learning is however restrained by the limited availability of large audio datasets. The FMA aims to overcome this hurdle by providing 917 GiB and 343 days of Creative Commons-licensed audio from 106,574 tracks from 16,341 artists and 14,854 albums, arranged in a hierarchical taxonomy of 161 genres. It provides full-length and high-quality audio, pre-computed features, together with track- and user-level metadata, tags, and free-form text such as biographies. We here describe the dataset and how it was created, propose a train/validation/test split and three subsets, discuss some suitable MIR tasks, and evaluate some baselines for genre recognition. Code, data, and usage examples are available at https://github.com/mdeff/fma

cs.SD↗
arXiv2017

Distributed Signal Processing via Chebyshev Polynomial Approximation

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of the graph multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be applied to distributed processing tasks such as smoothing, denoising, inverse filtering, and semi-supervised classification, and show that the communication requirements of the method scale gracefully with the size of the network.

cs.DC↗
arXiv2017

Localization of Sound Sources in a Room with One Microphone

Estimation of the location of sound sources is usually done using microphone arrays. Such settings provide an environment where we know the difference between the received signals among different microphones in the terms of phase or attenuation, which enables localization of the sound sources. In our solution we exploit the properties of the room transfer function in order to localize a sound source inside a room with only one microphone. The shape of the room and the position of the microphone are assumed to be known. The design guidelines and limitations of the sensing matrix are given. Implementation is based on the sparsity in the terms of voxels in a room that are occupied by a source. What is especially interesting about our solution is that we provide localization of the sound sources not only in the horizontal plane, but in the terms of the 3D coordinates inside the room.

cs.SD↗
arXiv2017

Fast Approximate Spectral Clustering for Dynamic Networks

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by using fast Chebyshev graph filtering of random signals. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded.

stat.ML↗
arXiv2017

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.

cs.CV↗
arXiv2017

Stationary signal processing on graphs

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is expressed through the graph localization operator reminiscent of translation. We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs. We leverage this new concept to derive Wiener-type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression.

cs.DS↗
arXiv2017

Compressive Embedding and Visualization using Graphs

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more important. In this work, we present a method which allows to apply any visualization or embedding algorithm on very large datasets by considering only a fraction of the data as input and then extending the information to all data points using a graph encoding its global similarity. We show that in most cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the information to all $N$ data points. In addition, we propose quantitative methods to measure the quality of embeddings and demonstrate the validity of our technique on both synthetic and real-world datasets.

cs.LG↗
arXiv2017

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

cs.LG↗