title: How to validate similarity in linear transform models of event-related potentials between experimental conditions?
abstract: BACKGROUND
  It is well-known that data of event-related potentials (ERPs) conform to the linear transform model (LTM). For group-level ERP data processing using principal/independent component analysis (PCA/ICA), ERP data of different experimental conditions and different participants are often concatenated. It is theoretically assumed that different experimental conditions and different participants possess the same LTM. However, how to validate the assumption has been seldom reported in terms of signal processing methods.
  
  
  METHODS
  When ICA decomposition is globally optimized for ERP data of one stimulus, we gain the ratio between two coefficients mapping a source in brain to two points along the scalp. Based on such a ratio, we defined a relative mapping coefficient (RMC). If RMCs between two conditions for an ERP are not significantly different in practice, mapping coefficients of this ERP between the two conditions are statistically identical.
  
  
  RESULTS
  We examined whether the same LTM of ERP data could be applied for two different stimulus types of fearful and happy facial expressions. They were used in an ignore oddball paradigm in adult human participants. We found no significant difference in LTMs (based on ICASSO) of N170 responses to the fearful and the happy faces in terms of RMCs of N170.
  
  
  CONCLUSIONS
  We found no methods for straightforward comparison.
  
  
  CONCLUSIONS
  The proposed RMC in light of ICA decomposition is an effective approach for validating the similarity of LTMs of ERPs between experimental conditions. This is very fundamental to apply group-level PCA/ICA to process ERP data.
authors.affiliation: Department of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, China; Department of Mathematical Information Technology, University of Jyväskylä, Finland. Electronic address: cong@dlut.edu.cn.
authors.forename: Fengyu
authors.initials: F
authors.lastname: Cong
authors.affiliation: School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, China.
authors.forename: Qiu-Hua
authors.initials: QH
authors.lastname: Lin
authors.affiliation: Department of Psychology, University of Jyväskylä, Finland.
authors.forename: Piia
authors.initials: P
authors.lastname: Astikainen
authors.affiliation: Department of Mathematical Information Technology, University of Jyväskylä, Finland.
authors.forename: Tapani
authors.initials: T
authors.lastname: Ristaniemi
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000502:physiology*; D004569:Electroencephalography / Q000379:methods*; D005071:Evoked Potentials; D005149:Facial Expression; D005260:Female; D006801:Humans; D016014:Linear Models; D008297:Male; D008875:Middle Aged; D009483:Neuropsychological Tests; D010364:Pattern Recognition, Visual / Q000502:physiology; D010775:Photic Stimulation; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted
keywords: Event-related potentials; Independent component analysis; Linear transform model; Mapping coefficient