This paper addresses the problem of identifying brain regions with similar oscillatory patterns detected from electroencephalograms. We introduce the hierarchical spectral merger (HSM) clustering method where the feature of interest is the spectral curve and the similarity metric used is the total variance distance. The HSM method is compared with clustering using features derived from independent-component analysis. Moreover, the HSM method is applied to 2 different electroencephalogram datasets. The first was recorded at resting state where the participant was not engaged in any cognitive task; the second was recorded during a spontaneous epileptic seizure. The results of the analyses using the HSM method demonstrate that clustering could evolve over the duration of the resting state and during epileptic seizure.

A clustering procedure for time series based on the use of the total variation distance between normalized spectral densities is proposed in this work. The approach is thus based on classifying time series in the frequency domain by consideration of the similarity between their oscillatory characteristics. As an application of this procedure, an algorithm for determining stationary periods for time series of random sea waves is developed, a problem in which changes between stationary sea states is usually slow. The proposed clustering algorithm is compared to several other methods which are also based on features extracted from the original series, and the results show that its performance is comparable to the best methods available, and in some tests, it performs better. This clustering method may be of independent interest. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we study some geometrical properties of a stationary Gaussian field modeling the sea surface, using the energy spectrum. We consider the length of a crest and the mean speed of contours, which can be expressed as integrals over level sets. We also give central limit theorems for some of these quantities, using chaos expansions.

We present a new method for time series clustering which we call the Hierarchical Spectral Merger (HSM) method. This procedure is based on the spectral theory of time series and identifies series that share similar oscillations or waveforms. The extent of similarity between a pair of time series is measured using the total variation distance between their estimated spectral densities. At each step of the algorithm, every time two clusters merge, a new spectral density is estimated using the whole information present in both clusters, which is representative of all the series in the new cluster. The method is implemented in an R package HSMClust. We present two applications of the HSM method, one to data coming from wave-height measurements in oceanography and the other to electroencefalogram (EEG) data.

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