# Clustering of ERP Data

**Hutt A. ^{1}, Kruggel F.^{3}**

*1 Max-Planck-Institute of Cognitive Neuroscience, Leipzig, 2 University of California, Irvine*

Multi-channel ERP data can be considered as trajectory in a high-dimensional space spanned by the number of channels. This trajectory passes several fixed points that show attractive and repelling properties, forming regions in space with a higher density of data points. The signal slows down when approaching a fixed point and accelerates when moving away from a fixed point, attracted by the next fixed point. Thus, spatio-temporal models for the whole signal are replaced by a sequence of meta-stable states, where each state describes the behaviour near a fixed point. Point clusters may be detected by classical clustering techniques such as the k-means algorithm. Cluster centers correspond to fixed points, and the Euclidean distance between a data point and a cluster center represents the degree of membership of a data point to a cluster. The smaller the distance from a data point to a cluster center, the more likely it is a member of this cluster.

Clustering yields a probability M(t) for each time point denoting the membership to a region near a fixed point. Local maxima of M(t) are found in temporal windows corresponding to ERP components P100 (60ms-110ms), N170 (130ms-170ms), P200 (190ms-270ms), and P300 (330ms-450ms).

**Read more...**

Hutt A., Kruggel F. (2002) **Fixed-Point Analysis: Dynamics of Non-Stationary Spatio-Temporal Signals.** In: Boccaletti S., Mancini H.L., Gonzalez-Vinas W., Burguete J., Valladares D.L. (eds.), *Space-Time Chaos: Characterization, Control and Synchronization, pp. 29-42.* World Scientific, Singapore.

Hutt A., Kruggel F. (2001) **Extension of Fixed-Point Clustering: A Cluster Criterion.** *Nonlinear Sciences 2001, 1-5 (e-print arvix.org/abs/nlin.CD/0102032).*

Hutt A., Svensen M., Kruggel F., Friedrich R. (2000) **Detection of Fixed Points in Spatio-Temporal Signals by a Clustering Method.** *Physical Review E 61, 4691-4693.*