Related papers: Natural Graph Wavelet Packet Dictionaries
In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural…
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relatively little is known about the corresponding eigenvectors. Our…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
In many domains (e.g. Internet of Things, neuroimaging) signals are naturally supported on graphs. These graphs usually convey information on similarity between the values taken by the signal at the corresponding vertices. An interest of…
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph.…
Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Graph convolutional neural network provides good solutions for node classification and other tasks with non-Euclidean data. There are several graph convolutional models that attempt to develop deep networks but do not cause serious…