Recovering Wood and McCarthy’s ERP-prototypes by means of ERP-specific procrustes-rotation

• Published in: Journal of neuroscience methods Vol. 295; pp. 20 - 36
• Main Author: Beauducel, André
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.02.2018
• Subjects: Brain - physiology; Computer Simulation; Electroencephalography - methods; Event-related potential; Evoked Potentials; Humans; Misallocation of variance; Principal Component Analysis; Signal Processing, Computer-Assisted; Temporal principal component analysis; Event-related potential; Temporal principal component analysis; Misallocation of variance
• ISSN: 0165-0270; 1872-678X
• DOI: 10.1016/j.jneumeth.2017.11.011

•Conventional rotation methods fail to recover Wood and McCarthy’s prototypes.•Conventional rotations result in a substantial amount of variance misallocation.•Two new rotation-methods based on ERP-characteristics are proposed.•The new rotation-methods need no a priori knowledge on treatment-effects.•The new rotation-methods: reduce variance misallocation. The misallocation of treatment-variance on the wrong component has been discussed in the context of temporal principal component analysis of event-related potentials. There is, until now, no rotation-method that can perfectly recover Wood and McCarthy’s prototypes without making use of additional information on treatment-effects. In order to close this gap, two new methods: for component rotation were proposed. After Varimax-prerotation, the first method identifies very small slopes of successive loadings. The corresponding loadings are set to zero in a target-matrix for event-related orthogonal partial Procrustes- (EPP-) rotation. The second method generates Gaussian normal distributions around the peaks of the Varimax-loadings and performs orthogonal Procrustes-rotation towards these Gaussian distributions. Oblique versions of this Gaussian event-related Procrustes- (GEP) rotation and of EPP-rotation are based on Promax-rotation. A simulation study revealed that the new orthogonal rotations recover Wood and McCarthy’s prototypes and eliminate misallocation of treatment-variance. In an additional simulation study with a more pronounced overlap of the prototypes GEP Promax-rotation reduced the variance misallocation slightly more than EPP Promax-rotation. Comparison with Existing Method(s): Varimax- and conventional Promax-rotations resulted in substantial misallocations of variance in simulation studies when components had temporal overlap. A substantially reduced misallocation of variance occurred with the EPP-, EPP Promax-, GEP-, and GEP Promax-rotations. Misallocation of variance can be minimized by means of the new rotation methods: Making use of information on the temporal order of the loadings may allow for improvements of the rotation of temporal PCA components.