Cauchy Nonnegative Matrix Factorization

International audienceNonnegative matrix factorization (NMF) is an effective and popular low-rank model for nonnegative data. It enjoys a rich background, both from an optimization and probabilistic signal processing viewpoint. In this study, we propose a new cost-function for NMF fitting, which is introduced as arising naturally when adopting a Cauchy process model for audio waveforms. As we recall, this Cauchy process model is the only probabilistic framework known to date that is compatible with having additive magnitude spectrograms for additive independent audio sources. Similarly to the Gaussian power-spectral density, this Cauchy model features time-frequency nonnegative scale parameters, on which an NMF structure may be imposed. The Cauchy cost function we propose is optimal under that model in a maximum likelihood sense. It thus appears as an interesting newcomer in the inventory of useful cost-functions for NMF in audio. We provide multiplicative updates for Cauchy-NMF and show that they give good performance in audio source separation as well as in extracting nonnegative low-rank structures from data buried in very adverse noise

Extraction of Temporal Network Structures from Graph-based Signals

International audienceA new framework to track the structure of temporal networks with a signal processing approach is introduced. The method is based on the duality between static networks and signals, obtained using a multidimensional scaling technique, that makes possible the study of the network structure from frequency patterns of the corresponding signals. In this paper, we propose an approach to identify structures in temporal networks by extracting the most significant frequency patterns and their activation coefficients over time, using nonnegative matrix factorization of the temporal spectra. The framework, inspired by audio decomposition, allows transforming back these frequency patterns into networks, to highlight the evolution of the underlying structure of the network over time. The effectiveness of the method is first evidenced on a synthetic example, prior being used to study a temporal network of face-to-face contacts. The extracted sub-networks highlight significant structures decomposed on time intervals that validates the relevance of the approach on real-world data

Majorization-minimization algorithm for smooth Itakura-Saito nonnegative matrix factorization

Nonnegative matrix factorization (NMF) with the Itakura-Saito divergence has proven efficient for audio source separation and music transcription, where the signal power spectrogram is factored into a “dictionary ” matrix times an “activation” matrix. Given the nature of audio signals it is expected that the activation coefficients exhibit smoothness along time frames. This may be enforced by penalizing the NMF objective function with an extra term reflecting smoothness of the activation coefficients. We propose a novel regularization term that solves some deficiencies of our previous work and leadstoanefficient implementation using a majorizationminimization procedure. Index Terms — Nonnegative matrix factorization (NMF), Itakura-Saito divergence, regularization by smoothness, audio signal representation, single-channel source separation. 1

Classificação de petróleos

The identification of patterns in the crude oil assay data provides useful information for crude oil properties estimation as well as for the refinery operation and logistics. The a priori information about the characteristics of a determined crude improves the logistic concerning which refineries should process it, together with pricing. This work explores data mining techniques over some characterization properties of crude oil assays, in order to group similar crude oils in an unsupervised way. The results show that the derived models are able to find patterns, clustering crudes according these properties. Afterwards, these are compared to a standard classification which is aware only about the oil crude density.A identificação de padrões em dados de ensaios de óleo bruto fornece informações importantes sobre a estimação das propriedades do petróleo, assim como para a operação e cadeia logística das refinarias. A informação a priori sobre as características de determinada amostra de óleo melhora a logística em relação a maneira que as refinarias devem processá-lo, assim como a sua precificação. Essa tese explora técnicas de mineração de dados usando algumas propriedades relevantes para a caracterização dos ensaios, de maneira a agrupar amostras de óleos brutos similares de maneira não-supervisionada. Os resultados mostram que os modelos obtidos são capazes de encontrar padrões ao agrupar as amostras de acordo com essas propriedades. Estes são então comparados à uma classificação comumente usada na indústria, baseada apenas na mensuração da densidade do petróleo

Radio frequency non-destructive testing and evaluation of defects under insulation

PhD ThesisThe use of insulation such as paint coatings has grown rapidly over the past decades. However, defects and corrosion under insulation (CUI) still present challenges for current non-destructive testing and evaluation (NDT&E) techniques. One of such challenges is the large lift-off introduced by thick insulation layer. Inaccessibility due to insulation leads corrosion and defects to be undetected, which can lead to catastrophic failure. Furthermore, lift-off effects due to the insulation layers reduce the sensitivities. The limitations of existing NDT&E techniques heighten the need for novel approaches to the characterisation of corrosion and defects under insulation. This research project is conducted in collaboration with International Paint®, and a radio frequency non-destructive evaluation for monitoring structural condition is proposed. High frequency (HF) passive RFID in conjunction with microwave NDT is proposed for monitoring and imaging under insulation. The small-size, battery-free and cost-efficient nature of RFID makes it attractive for long-term condition monitoring. To overcome the limitations of RFID-based sensing system such as effective monitoring area and lift-off tolerance, microwave NDT is proposed for the imaging of larger areas under thick insulation layers. Experimental studies are carried out in conjunction with specially designed mild steel sample sets to demonstrate the detection capabilities of the proposed systems. The contributions of this research can be summarised as follows. Corrosion detection using HF passive RFID-based sensing and microwave NDT is demonstrated in experimental feasibility studies considering variance in surface roughness, conductivity and permeability. The lift-off effects introduced by insulation layers are reduced by applying feature extraction with principal component analysis and non-negative matrix factorisation. The problem of thick insulation layers is overcome by employing a linear sweep frequency with PCA to improve the sensitivity and resolution of microwave NDT-based imaging. Finally, the merits of microwave NDT are identified for imaging defects under thick insulation in a realistic test scenario. In conclusion, HF passive RFID can be adapted for long term corrosion monitoring of steel under insulation, but sensing area and lift-off tolerance are limited. In contrast, the microwave NDT&E has shown greater potential and capability for monitoring corrosion and defects under insulation