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Improving clustering by imposing network information.

Gerber S, Horenko I - Sci Adv (2015)

Bottom Line: Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines.The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification.This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios.

View Article: PubMed Central - PubMed

Affiliation: Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6900 Lugano, Switzerland.

ABSTRACT
Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines. We propose and justify a computationally efficient and straightforward-to-implement way of imposing the available information from networks/graphs (a priori available in many application areas) on a broad family of clustering methods. The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification. This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios. Applying this approach results in an exact unsupervised classification of very short signals, opening new possibilities for clustering methods in the area of a noninvasive brain-computer interface.

No MeSH data available.


Snapshots of the spatiotemporal dynamics of the most dominant eigenvectors.(A, C, E, and G) Several time instances of the extracted dominant wave pattern for the EEG with opened eyes. (B, D, F, and H) Snapshots for the dominant EEG pattern with closed eyes at the same time points. Red color stands for the positive component of the oscillation, and blue color for the negative component. Snapshots are taken in both experiments at time points t = 0.0 s (A and B), 0.018443 s (C and D), 0.043033 s (E and F), and 0.061475 s (G and H).
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Figure 3: Snapshots of the spatiotemporal dynamics of the most dominant eigenvectors.(A, C, E, and G) Several time instances of the extracted dominant wave pattern for the EEG with opened eyes. (B, D, F, and H) Snapshots for the dominant EEG pattern with closed eyes at the same time points. Red color stands for the positive component of the oscillation, and blue color for the negative component. Snapshots are taken in both experiments at time points t = 0.0 s (A and B), 0.018443 s (C and D), 0.043033 s (E and F), and 0.061475 s (G and H).

Mentions: With the help of the identified manifolds and their affiliated eigenvectors (constituting the columns of cluster projector matrices Θi), essential components of the underlying dynamical system can now be extracted from the available short, nonstationary, and noisy EEG time series. For this purpose, the experimental data are projected on the identified linear attractor manifolds Θi. Spectral analysis for the embedded projections of original EEG data on the dominant manifold dimensions (that is, on different columns of Θi as resulting from the regularized clustering) reveals the well-known α, β, γ, and μ waves of the brain (please see fig. S2). In contrast to the standard procedures of obtaining these signals (that involve a very long measurement series and a careful selection of points on the head where these measurements are performed), in the context of the presented methodology, these brain waves can be obtained from the full original EEG with a very short (down to 7 seconds) measurement length. In the next step, we are going to examine the spatiotemporal dynamics of these brain wave patterns. For this purpose, the snapshots of eigenvectors are visualized over a schematic representation of the head (indicating the positions and numbers of electrodes according to the international 10-10 system). Because of the embedding during the preprocessing, this visualization of embedded eigenvectors (representing the dominant manifold components) results in spatiotemporal animations of the essential dimensions of the underlying dynamics that can be extracted from the two identified clusters. A selection of these animations is provided as movies S1 to S8. A couple of snapshots from movies S1 (animating the most dominant attractor dimension for the experiment with opened eyes) and S2 (animating the most dominant attractor dimension for the experiment with closed eyes) are exemplarily presented in Fig. 3. The left column of Fig. 3 presents a series of snapshots taken from movie S1. These snapshots capture the dynamics in the most dominant manifold dimension (that is, the first column of the obtained Θi in the respective cluster) for the experiment with opened eyes. This dominant dynamics—a spatiotemporal oscillation—takes place in the anterior part of the brain: most evident frontally and propagating into the central (and even posterior) regions of the brain. These spatial characteristics (together with the observation of fig. S2) allow to conclude that the observed dominant pattern reflects a combination of rhythmical β activity [which is usually encountered over the frontal and central brain regions (41)] and γ waves [mainly observed in the visual cortex (42, 43)]. Furthermore, the movie reveals that the main spatiotemporal dynamics for the EEG with opened eyes can be explained by a traveling wave oscillating between the frontal and the posterior regions of the brain. This dynamic is hidden in the very noisy EEG signal and can be uncovered by the presented cluster analysis methodology.


Improving clustering by imposing network information.

Gerber S, Horenko I - Sci Adv (2015)

Snapshots of the spatiotemporal dynamics of the most dominant eigenvectors.(A, C, E, and G) Several time instances of the extracted dominant wave pattern for the EEG with opened eyes. (B, D, F, and H) Snapshots for the dominant EEG pattern with closed eyes at the same time points. Red color stands for the positive component of the oscillation, and blue color for the negative component. Snapshots are taken in both experiments at time points t = 0.0 s (A and B), 0.018443 s (C and D), 0.043033 s (E and F), and 0.061475 s (G and H).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4643807&req=5

Figure 3: Snapshots of the spatiotemporal dynamics of the most dominant eigenvectors.(A, C, E, and G) Several time instances of the extracted dominant wave pattern for the EEG with opened eyes. (B, D, F, and H) Snapshots for the dominant EEG pattern with closed eyes at the same time points. Red color stands for the positive component of the oscillation, and blue color for the negative component. Snapshots are taken in both experiments at time points t = 0.0 s (A and B), 0.018443 s (C and D), 0.043033 s (E and F), and 0.061475 s (G and H).
Mentions: With the help of the identified manifolds and their affiliated eigenvectors (constituting the columns of cluster projector matrices Θi), essential components of the underlying dynamical system can now be extracted from the available short, nonstationary, and noisy EEG time series. For this purpose, the experimental data are projected on the identified linear attractor manifolds Θi. Spectral analysis for the embedded projections of original EEG data on the dominant manifold dimensions (that is, on different columns of Θi as resulting from the regularized clustering) reveals the well-known α, β, γ, and μ waves of the brain (please see fig. S2). In contrast to the standard procedures of obtaining these signals (that involve a very long measurement series and a careful selection of points on the head where these measurements are performed), in the context of the presented methodology, these brain waves can be obtained from the full original EEG with a very short (down to 7 seconds) measurement length. In the next step, we are going to examine the spatiotemporal dynamics of these brain wave patterns. For this purpose, the snapshots of eigenvectors are visualized over a schematic representation of the head (indicating the positions and numbers of electrodes according to the international 10-10 system). Because of the embedding during the preprocessing, this visualization of embedded eigenvectors (representing the dominant manifold components) results in spatiotemporal animations of the essential dimensions of the underlying dynamics that can be extracted from the two identified clusters. A selection of these animations is provided as movies S1 to S8. A couple of snapshots from movies S1 (animating the most dominant attractor dimension for the experiment with opened eyes) and S2 (animating the most dominant attractor dimension for the experiment with closed eyes) are exemplarily presented in Fig. 3. The left column of Fig. 3 presents a series of snapshots taken from movie S1. These snapshots capture the dynamics in the most dominant manifold dimension (that is, the first column of the obtained Θi in the respective cluster) for the experiment with opened eyes. This dominant dynamics—a spatiotemporal oscillation—takes place in the anterior part of the brain: most evident frontally and propagating into the central (and even posterior) regions of the brain. These spatial characteristics (together with the observation of fig. S2) allow to conclude that the observed dominant pattern reflects a combination of rhythmical β activity [which is usually encountered over the frontal and central brain regions (41)] and γ waves [mainly observed in the visual cortex (42, 43)]. Furthermore, the movie reveals that the main spatiotemporal dynamics for the EEG with opened eyes can be explained by a traveling wave oscillating between the frontal and the posterior regions of the brain. This dynamic is hidden in the very noisy EEG signal and can be uncovered by the presented cluster analysis methodology.

Bottom Line: Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines.The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification.This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios.

View Article: PubMed Central - PubMed

Affiliation: Università della Svizzera Italiana, Via Giuseppe Buffi 13, 6900 Lugano, Switzerland.

ABSTRACT
Cluster analysis is one of the most popular data analysis tools in a wide range of applied disciplines. We propose and justify a computationally efficient and straightforward-to-implement way of imposing the available information from networks/graphs (a priori available in many application areas) on a broad family of clustering methods. The introduced approach is illustrated on the problem of a noninvasive unsupervised brain signal classification. This task is faced with several challenging difficulties such as nonstationary noisy signals and a small sample size, combined with a high-dimensional feature space and huge noise-to-signal ratios. Applying this approach results in an exact unsupervised classification of very short signals, opening new possibilities for clustering methods in the area of a noninvasive brain-computer interface.

No MeSH data available.