IEEE Journal of Selected Topics in Signal Processing

In network science, the interplay between dynamical processes and the underlying topologies of complex systems has led to a diverse family of models with different interpretations. In graph signal processing, this is manifested in the form of different graph shifts and their induced algebraic systems. In this paper, we propose the unifying Z-Laplacian framework, whose instances can act as graph sh... View full abstract»

This paper considers the definition of the graph Fourier transform (GFT) and of the spectral decomposition of graph signals. Current literature does not address the lack of unicity of the GFT. The GFT is the mapping from the signal set into its representation by a direct sum of irreducible shift invariant subspaces: 1) this decomposition may not be unique; and 2) there is freedom in the choice of ... View full abstract»

The analysis of signals defined over a graph is relevant in many applications, such as social and economic networks, big data or biological networks, and so on. A key tool for analyzing these signals is the so-called graph Fourier transform (GFT). Alternative definitions of GFT have been suggested in the literature, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix... View full abstract»

The construction of spectral filters for graph wavelet transforms is addressed in this paper. Both the undecimated and decimated cases will be considered. The filter functions are polynomials and can be implemented efficiently without the need for any eigendecomposition, which is computationally expensive for large graphs. Polynomial filters also have the advantage of the vertex localization prope... View full abstract»

Graphs are fundamental mathematical structures used in various fields to represent data, signals, and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretations, and (iii) associated algorithms. Specifically, graph learning problems are ... View full abstract»

We consider the problem of recovering a smooth graph signal from noisy samples taken on a subset of graph nodes. The smoothness of the graph signal is quantified in terms of total variation. We formulate the signal recovery task as a convex optimization problem that minimizes the total variation of the graph signal while controlling its global or node-wise empirical error. We propose a first-order... View full abstract»

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the numbe... View full abstract»

Signal processing on graphs is an emerging research field dealing with signals living on an irregular domain that is captured by a graph, and has been applied to sensor networks, machine learning, climate analysis, etc. Existing works on sampling and reconstruction of graph signals mainly studied static bandlimited signals. However, many real-world graph signals are time-varying, and they evolve s... View full abstract»

Convolutional neural networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite-impulse response filters are learned on a hierarchy of layers, each contributing more abstract information than the previous layer. The simplicity and elegance of the convolutional filtering process makes them perfect for structured problems, such as imag... View full abstract»

In this paper, we propose an adaptation of partial difference equations (PDEs) level set method for nonmonotonic front propagation on weighted graphs. This adaptation leads to a PDE, whose coefficients are data geometry dependent. Our motivation is to extend their applications to any discrete data that can be represented by a weighted graph. This paper follows several preliminaries of our works, a... View full abstract»

Developing effective fusion schemes for multiple feature types has always been a hot issue in content-based image retrieval. In this paper, we propose a novel method for graph-based visual reranking, which addresses two major limitations in existing methods. First, in the phase of graph construction, our method introduces fine-grained measurements for image relations, by assigning the edge weights... View full abstract»