Correntropy as a Novel Measure for Nonlinearity Tests

Gündüz, Ayşegül; Hegde, A.; Prı́ncipe, José C.

doi:10.1109/ijcnn.2006.246906

Cited by 20 publications

(19 citation statements)

References 11 publications

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“…A S a nonlinear robust similarity measure, correntropy has been successfully applied in various areas of signal processing and machine learning, such as robust regression and filtering [1]- [6], robust classification [7], robust principal component analysis [8], spectral characterization [9], nonlinearity tests [10], period estimation [11], pitch detection in speech [12], and many others. In particular, the maximum correntropy criterion (MCC) has been shown to be a rather robust adaptation principle for adaptive system training in presence of heavy-tailed non-Gaussian noises [1]- [6].…”

Section: Introductionmentioning

confidence: 99%

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

Chen

Wang

Zhao

et al. 2015

IEEE Signal Process. Lett.

282

111

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The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.

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Section: Introductionmentioning

confidence: 99%

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

Chen

Wang

Zhao

et al. 2015

IEEE Signal Process. Lett.

282

111

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“…Correntropy proposed by [27] is a kernel based similarity measure which non-linearly maps the input space into some higher dimensional feature space in which inner products are computed efficiently. Correntropy similarity measure includes the statistical distribution information and time structure of signals in a single measure.…”

Section: Context-based Methodsmentioning

confidence: 99%

A survey of distance/similarity measures for categorical data

Alamuri

Bapi

Negi

2014

2014 International Joint Conference on Neural Networks (IJCNN)

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Similarity or distance between two objects plays a fundamental role in many data mining tasks like classification and clustering. Categorical data, unlike numeric data, conceptually is deficient of default ordering relations on the attribute values. This makes the task of devising similarity or distance metrics and data mining tasks such as classification and clustering of categorical data more challenging. In this paper we formulate a taxonomy of various distance or similarity measures used in conjunction with data whose attributes are categorical. We categorize the existing measures into two broad classes, namely, Context-free and Context-sensitive measures for categorical data. In addition, we suggest a taxonomy of the clustering approaches for categorical data. We also propose a hybrid approach for measuring similarity between objects. We make a relative comparison of the strengths and weaknesses of some of the similarity measures and point out future research directions.

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“…Following the literature, e.g. [10], in this paper we use a Gaussian kernel with Silverman's rule. As our calculations of coh-entropy coefficient normalises both signals and by mean and standard deviation before evaluating # , Silverman's rule determines the width to be = 0.4.…”

Section: Coh-entropy Coefficientmentioning

confidence: 99%

“…In the non-stationary case, we followed the methodology in [3,10,[58][59][60] by changing the coupling strength with time. In particular, we switched the coupling strength of from = 0 (no coupling) to = 0.9 (tightly coupling) at & = 50 and back to = 0 at & = 150.…”

Section: Simulated Data -Hénon Mapsmentioning

confidence: 99%

Detecting synchrony in EEG: A comparative study of functional connectivity measures

Bakhshayesh

Fitzgibbon

Janani

et al. 2019

Computers in Biology and Medicine

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In neuroscience, there is considerable current interest in investigating the connections between different parts of the brain. EEG is one modality for examining brain function, with advantages such as high temporal resolution and low cost. Many measures of connectivity have been proposed, but which is the best measure to use? In this paper, we address part of this question: which measure is best able to detect connections that do exist, in the challenging situation of non-stationary and noisy data from nonlinear systems, like EEG. This requires knowledge of the true relationship between signals, hence we compare 26 measures of functional connectivity on simulated data (unidirectionally coupled Hénon maps, and simulated EEG). To determine whether synchrony is detected, surrogate data were generated and analysed, and a threshold determined from the surrogate ensemble. No measure performed best in all tested situations. The correlation and coherence measures performed best on stationary data with many samples. S-estimator, correntropy, mean-phase coherence (Hilbert), mutual information (kernel), nonlinear interdependence (S) and nonlinear interdependence (N) performed most reliably on non-stationary data with small to medium window sizes. Of these, correlation and S-estimator have execution times that scale slower with the number of channels and the number of samples. Keywords-Connectivity, EEG, biomedical signal processing, nonstationarity. Highlights:• Extensive comparative study of 26 functional connectivity measures for EEG • Measures compared on simulated noisy and nonstationary data • Surrogates used to determine threshold for significant connectivity • 8 measures performed well, choice of best depends on the particular situation • Correlation coefficient and S-estimator measures performed best overall M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 2 synchronisation means adjustment of frequencies of periodic self-sustained oscillators due to weak interaction" [2]. The concept of synchronisation has been generalised to the case of chaotic oscillatory systems with irregular behaviour. The study of synchronisation between signals from such systems has been a topic of increasing interest, and has found applications in areas such as laser dynamics, solid state physics, electronics, biology, medicine, communication and even economics. There has been wide-ranging research aimed at detecting underlying relationships (which may be nonlinear and/or nonstationary) in multi-output dynamic systems, to give useful insight into their spatio-temporal organisation [3]. Synchronisation can manifest itself in different ways, hence a large variety of measures have been proposed to quantify synchronisation between signals. Synchronisation can occur due to one source driving another, and in such situations there is a direction to the relationship. Functional connectivity measures are symmetric and so cannot detect a direction in a relationship.Effective connectivity measures are not symmetric, and do detect a direction. T...

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Correntropy as a Novel Measure for Nonlinearity Tests

Cited by 20 publications

References 11 publications

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion

A survey of distance/similarity measures for categorical data

Detecting synchrony in EEG: A comparative study of functional connectivity measures

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