GSPBOX: A toolbox for signal processing on graphs

This document introduces the Graph Signal Processing Toolbox (GSPBox) a framework that can be used to tackle graph related problems with a signal processing approach. It explains the structure and the organization of this software. It also contains a general description of the important modules. 1 Toolbox organization In this document, we briefly describe the different modules available in the toolbox. For each of them, the main functions are briefly described. This chapter should help making the connection between the theoretical concepts introduced in [7, 9, 6] and the technical documentation provided with the toolbox. We highly recommend to read this document and the tutorial before using the toolbox. The documentation, the tutorials and other resources are available on-line1. The toolbox has first been implemented in MATLAB but a port to Python, called the PyGSP, has been made recently. As of the time of writing of this document, not all the functionalities have been ported to Python, but the main modules are already available. In the following, functions prefixed by [M]: refer to the MATLAB implementation and the ones prefixed with [P]: refer to the Python implementation. 1.1 General structure of the toolbox (MATLAB) The general design of the GSPBox focuses around the graph object [7], a MATLAB structure containing the necessary informations to use most of the algorithms. By default, only a few attributes are available (see section 2), allowing only the use of a subset of functions. In order to enable the use of more algorithms, additional fields can be added to the graph structure. For example, the following line will compute the graph Fourier basis enabling exact filtering operations. 1 G = gsp_compute_fourier_basis(G); Ideally, this operation should be done on the fly when exact filtering is required. Unfortunately, the lack of well defined class paradigm in MATLAB makes it too complicated to be implemented. Luckily, the above formulation prevents any unnecessary data copy of the data contained in the structure G. In order to avoid name conflicts, all functions in the GSPBox start with [M]: gsp_. A second important convention is that all functions applying a graph algorithm on a graph signal takes the graph as first argument. For example, the graph Fourier transform of the vector f is computed by 1 fhat = gsp_gft(G,f); 1See https://lts2.epfl.ch/gsp/doc/ for MATLAB and https://lts2.epfl.ch/pygsp for Python. The full documentation is also available in a single document: https://lts2.epfl.ch/gsp/gspbox.pdf 1 ar X iv :1 40 8. 57 81 v2 [ cs .I T ] 1 5 M ar 2 01 6 The graph operators are described in section 4. Filtering a signal on a graph is also a linear operation. However, since the design of special filters (kernels) is important, they are regrouped in a dedicated module (see section 5). The toolbox contains two additional important modules. The optimization module contains proximal operators, projections and solvers compatible with the UNLocBoX [5] (see section 6). These functions facilitate the definition of convex optimization problems using graphs. Finally, section ?? is composed of well known graph machine learning algorithms. 1.2 General structure of the toolbox (Python) The structure of the Python toolbox follows closely the MATLAB one. The major difference comes from the fact that the Python implementation is object-oriented and thus allows for a natural use of instances of the graph object. For example the equivalent of the MATLAB call: 1 G = gsp_estimate_lmax(G); can be achieved using a simple method call on the graph object: