Source Separation and Clustering of Phase-Locked Subspaces

Abstract

Abstract-It has been proven that there are synchrony (or phase-locking) phenomena present in multiple oscillating systems such as electrical circuits, lasers, chemical reactions, and human neurons. If the measurements of these systems cannot detect the individual oscillators but rather a superposition of them, as in brain electrophysiological signals (electo-and magneoencephalogram), spurious phase locking will be detected. Current source-extraction techniques attempt to undo this superposition by assuming properties on the data, which are not valid when underlying sources are phase-locked. Statistical independence of the sources is one such invalid assumption, as phase-locked sources are dependent. In this paper, we introduce methods for source separation and clustering which make adequate assumptions for data where synchrony is present, and show with simulated data that they perform well even in cases where independent component analysis and other well-known sourceseparation methods fail. The results in this paper provide a proof of concept that synchrony-based techniques are useful for lownoise applications.

A comparison of algorithms for separation of synchronous subspaces

“…FastICA yields good results despite being an ICA algorithm and not an ISA algorithm. Algorithms for the intra-subspace separation already exist for this type of sources [9,25]; thus, the full ISA task can, in theory, be satisfactorily performed if one devises a proper subspace detection procedure. Note, however, that this may depend strongly on the type of dependency in each subspace, since other authors have found rather different results on other types of data [14].…”

“…This is the fundamental assumption of Independent Component Analysis (ICA) [5,6]. Other possibilities include assuming that the mixing matrix and the sources are non-negative, which is known as Non-negative Matrix Factorization (NMF) [7,8], or assuming that the sources have perfect phase synchrony, which leads to Separation of Synchronous Sources [9].…”

“…We can thus safely assume that the sources follow the ISA model and, in addition, they are assumed to have perfect phase synchrony within each subspace, as measured by the Phase Locking Factor (PLF) [9]; in other words, within each subspace all pairwise PLFs are 1. Such signals follow a specific model: it can be shown that the sources of each subspace k are of the form [25] 3.…”

Separation of phase-locked sources in pseudo-real MEG data

“…In our case, independence of the sources is not a valid assumption, because phase-locked sources are highly mutually dependent. Also, phase-locking is not equivalent to frequency coherence: in fact, two signals may have a severe overlap between their frequency spectra but still exhibit low or no phase synchrony at all [14]. In this article, we address the problem of how to separate such phase-locked sources using a phase-specific criterion.…”

“…Recently, we have presented a two-stage algorithm called independent phase analysis (IPA) which performed very well in noiseless simulated data [15] and with moderate levels of added Gaussian white noise [14]. The http://asp.eurasipjournals.com/content/2013/1/32 separation algorithm we then proposed uses temporal decorrelation separation [16] as a first step, followed by the maximization of an objective function involving the phases of the estimated sources.…”