English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Given a time series of multicomponent measurements of an evolving stimulus,nonlinear blind source separation (BSS) seeks to find a "source" time series,comprised of statistically independent combinations of the measured components.In this paper, we seek a source time series with local velocity crosscorrelations that vanish everywhere in stimulus state space. However, in anearlier paper the local velocity correlation matrix was shown to constitute ametric on state space. Therefore, nonlinear BSS maps onto a problem ofdifferential geometry: given the metric observed in the measurement coordinatesystem, find another coordinate system in which the metric is diagonaleverywhere. We show how to determine if the observed data are separable in thisway, and, if they are, we show how to construct the required transformation tothe source coordinate system, which is essentially unique except for an unknownrotation that can be found by applying the methods of linear BSS. Thus, theproposed technique solves nonlinear BSS in many situations or, at least,reduces it to linear BSS, without the use of probabilistic, parametric, oriterative procedures. This paper also describes a generalization of thismethodology that performs nonlinear independent subspace separation. In everycase, the resulting decomposition of the observed data is an intrinsic propertyof the stimulus' evolution in the sense that it does not depend on the way theobserver chooses to view it (e.g., the choice of the observing machine'ssensors). In other words, the decomposition is a property of the evolution ofthe "real" stimulus that is "out there" broadcasting energy to the observer.The technique is illustrated with analytic and numerical examples.

Using state space differential geometry for nonlinear blind source separation