Areas of interest

Inpainting of missing data in audio spectrograms

audio-inpainting

A variant of the Nonnegative Matrix Factorization (NMF) called Convex NMF (CNMF) has been extended to estimate missing coefficients in STFT representation of audio signals. The dictionary matrix is constrained to be a convex linear combination of a known matrix of examples, i.e, the combination coefficients forming each dictionary element are nonnegative and sum to 1. Compared to the fully unsupervised NMF setting, it is a source of supervision that may guide learning based on this additional data: in particular, an interesting case of CNMF consists in auto-encoding the data themselves, by defining the dictionary as the data matrix. This problem has been show of interest to application such as transcription, and might be useful to improve reconstruction in source separation techniques.

Duality between graphs and time series

duality-signal-graph

Many complex systems, whether physical, biological or social, can be naturally represented as networks, i.e., a set of relationships between entities. Network science has been widely developed to study such objects, generally supported by a graph structure. Based on prior work to transform graph into time series using multidimensional scaling, a technique used to reduce the dimensionality of data, a framework to transform graph into a collection of signals has been developed in order to study networks using a signal processing approach. Spectral analysis of this collection of signals associates a frequency pattern, obtained from signals, with a specific graph structure of the underlying graph.

Analysis of temporal networks

temporal-network

Temporal networks are common object to describe networks with a time evolution. The extension of the duality between graph and signals to the temporal case is easily achieved by considering temporal networks as discrete-time sequences of graph snapshots. At each time step, the transformation from graph to signals is performed: a temporal collection of signals is then obtained, and thus temporal frequency patterns. Tracking these patterns along time allows for the tracking of the graph structure. This is achieved by using NMF, which extracts automatically the relevant frequency patterns, as well as the associated activation coefficients over time. It is then possible to retrieve from each frequency pattern the underlying structure in the graph domain, and then by using the associated activation coefficients, to track the topology of the temporal network over time. Results showed that the method is able to successfully extract different types structures, such as for instance organization in communities or regular structures, as well as mixture of these structures.

Study of the Lyon's Bike Sharing System

velov

Many big cities in the world propose a bike sharing system in which bikes are made available at any time for short trips. In Lyon, the Vélo’v program has been deployed since May 2005 and consists of 350 stations spread over all the agglomeration in which bikes can be hired or returned back. Thanks to a partnership with the operator JCDecaux and the “Grand Lyon" City Hall, anonymized data for the year 2011 were made available to us. The study of such system has numerous goals as for instance viability of the system, its integration in the transportation scheme of the city or the social behaviors linked to the bike use. Study of Vélo'v system as a complex network is part of a broader project called "Vél'innov" and funded by the ANR.

Relabeling the vertices following the structure

relabeling

A new heuristic has been developed to find a labeling which follows the structure of the graph. The heuristic is a two-step algorithm: the first step consists of browsing the graph to find a set of paths which follow the structure of the graph, using a Jaccard-based index to jump from one vertex to the next one. The second step consists of merging all the previously obtained paths, based on a greedy approach that extends a partial solution by inserting a new path at the position that minimizes the cyclic bandwidth sum, a classical graph labeling problem.