IMSCAND algorithm for EEG microstate analysis

A variant of the IMSCAND algorithm for EEG microstate detection

Implicit Slice Canonical Decomposition (IMSCAND) is a specialized tensor decomposition technique for symmetric higher-order arrays [1]. There is a theoretical equivalence between IMSCAND and the modified k-means algorithm [2], one of the most widely used methods for EEG microstate detection. The MATLAB script implements a variant of the IMSCAND algorithm in which the first two component matrices, A = B = M, are estimated without constraints, while the third matrix, Z, is constrained such that its elements are between 0 and 1 and each column sums to 1. Matrix Z can be estimated using either the Franz-Wolfe algorithm [3] or nonnegative least-squares regression [4,5].

[1] T. M. Selee, T. G. Kolda, W. P. Kegelmeyer, J. D. Griffin, Extracting clusters from large datasets with multiple similarity measures using IMSCAND, in: M. L. Parks, S. S. Collis (Eds.), CSRI Summer Proceedings 2007, Tech. Rep. SAND2007-7977, Sandia National Laboratories, 2007, 32 pp. 87–103. URL http://www.cs.sandia.gov/CSRI/Proceedings/CSRI2007.pdf

[2] Z. Rostakova, R. Rosipal, Equivalence of Modified k-Means algorithm and Tensor Decomposition in EEG Microstate Analysis, manuscript submitted to NeuroImage.

[3] C. Bauckhage, k-means clustering via the Frank-Wolfe algorithm, in: Proc. of KDML-LWDA, 2016. https://ceur-ws.org/Vol-1670/paper-65.pdf

[4] C.A. Andersson, R. Bro, The N-way Toolbox for MATLAB, Chemometrics and Intelligent Laboratory Systems, Volume 52, Issue 1, 2000,Pages 1-4, ISSN 01697439,https://doi.org/10.1016/S0169-7439(00)00071-X.

[5] N-way toolbox https://ucphchemometrics.com/nway/