Pierre Borgnat

Testing Stationarity With Surrogates: A Time-Frequency Approach

An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local time-frequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a one-class classifier, the time- frequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.

Time-frequency localization from sparsity constraints

In the case of multicomponent AM-FM signals, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum l1-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased.

Multitaper Estimation of Frequency-Warped Cepstra With Application to Speaker Verification

Usually the mel-frequency cepstral coefficients are estimated either from a periodogram or from a windowed periodogram. We state a general estimator which also includes multitaper estimators. We propose approximations of the variance and bias of the estimate of each coefficient. By using Monte Carlo computations, we demonstrate that the approximations are accurate. Using the proposed formulas, the peak matched multitaper estimator is shown to have low mean square error (squared bias + variance) on speech-like processes. It is also shown to perform slightly better in the NIST 2006 speaker verification task as compared to the Hamming window conventionally used in this context.

Mining anomalous electricity consumption using Ensemble Empirical Mode Decomposition

Sensor deployments in large buildings allow the administrators to supervise the building infrastructure and identify abnormalities. Nevertheless, the numerous data streams reported by the increasing number of sensors overwhelm the building administrators. We propose a methodology that assists them to identify abnormal devices usages. The proposed method takes advantage of Ensemble Empirical Mode Decomposition (E-EMD) to uncover the patterns of power-draw signals, thereby enabling us to estimate the intrinsic inter-device correlations. By monitoring the devices correlations over time we compute the usual usage of the devices and report the devices that deviate from their normal usage. Our evaluation with 10 weeks of real data shows the efficiency of the proposed method to uncover the devices intrinsic relationships and detect peculiar events that require the administrators attention.

A new nonparametric method for testing stationarity based on trend analysis in the time marginal distribution

In this manuscript, we propose a novel nonparametric test for nonstationarities that are seen as a trend or an evolution in the local energy of the signal. The idea of the proposed technique consists in applying empirical mode decomposition for estimating and further quantifying the trend in the time marginal of the estimated time-frequency representation. Such methodology allows for the detection of slowly-varying nonstationarities of first and second-order.