Time-frequency learning machines for nonstationarity detection using surrogates

Abstract

An operational framework has recently been developed for testing stationarity of any signal relatively to an observation scale. The originality is to extract time-frequency features from a set of stationarized surrogate signals, and to use them for defining the null hypothesis of stationarity. Our paper is a further contribution that explores a general framework embedding techniques from machine learning and timefrequency analysis, called time-frequency learning machines. Based on one-class support vector machines, our approach uses entire time-frequency representations and does not require arbitrary feature extraction. Its relevance is illustrated by simulation results, and spherical multidimensional scaling techniques to map data to a visible 3D space.

Testing Stationarity With Surrogates: A Time-Frequency Approach

“…It could be used as an indication to discriminate random processes from more deterministic ones. Interestingly, one can also remark that the location of the test signal in the (P, F ) plane turns out to provide some information about the type of nonstationarity, if any: F = 0 is characteristic of some FM structure, P > 0 indicates some AM, P < 0 is associated to a constant (maybe deterministic) behavior for the amplitude (see [33] for preliminary results in this direction).…”

Stationnarité relative et approches connexes

“…This allows not only for a specified confidence in the detection, but also for the obtention of by-products such as a degree and a typical scale of nonstationarity. A second approach (Section 3.2) considers the collection of surrogates as a learning set attached to the stationary hypothesis, with possible tests using techniques aimed at outlier detection, such as, e.g., one-class support vector machines or others (Xiao, Borgnat, Flandrin, Richard, 2007 ;Amoud et al, 2009b). This part is concluded (Section 3.3) by an example where detection is achieved in a specific feature space adapted to amplitude-and frequency-modulated waveforms.…”

“…Selon le contexte, nous avons été amenés à extraire des attributs tels que les variances temporelles de la puissance (P) et de la fréquence (F) instantanées, comme dans (Xiao, Borgnat, Flandrin, Richard, 2007 ;Amoud et al, 2009a ;Borgnat et al, 2010) (voir figure 2 également, issue de (Amoud et al, 2009a)). Nous avons également pu considérer les séquences temporelles directement, et/ou appliquer une transformation non linéaire aux données en introduisant un noyau reproduisant dans (13)-(14), comme dans (Amoud et al, 2009b).…”

A study on the Gaussianity and stationarity of the random noise in the seismic exploration

“…On purpose to reflect the properties of seismic prospecting noise accurately, we construct the receiver arrays under the requirement of actual seismic prospecting. The Gaussianity of the random noise uses the Shapiro-Wilk test (Royston, 1982a(Royston, ,b, 1992Shapiro and Wilk, 1965) in statistics and the stationarity test is the use of surrogate data (Schreiber and Schmitz, 2000;Theiler et al, 1992) and time-frequency analysis methods (Amoud et al, 2009;Borgnat and Flandrin, 2009;Xiao et al, 2007a,b).…”