Cortical potential imaging using L-curve and GCV method to choose the regularisation parameter

Subramaniyam, Narayan Puthanmadam; Väisänen, Outi; Wendel, Katrina; Malmivuo, Jaakko

doi:10.1186/1753-4631-4-s1-s4

Cited by 5 publications

(8 citation statements)

References 26 publications

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“…To begin with, Fig. 7 confirms as in (Subramaniyam et al, 2010) that it is difficult to use the "L-curve" method to choose the optimal λ value. In this figure, the value of λ, λ MSE , which minimizes the MSE, is indicated but does not correspond to a discernible "corner of the L-curve".…”

Section: Generalized Cross-validation Proceduresmentioning

confidence: 62%

“…Usually possible values for λ are iteratively set by plotting for increasing values of λ, the "L-curve" which would be, here, x − Dâ reg (λ) against â reg (λ) 2 in a log-log graph (Engl & Grever, 1994;Hansen, 1992). Then, the optimal value, λ opt , is chosen at the "corner of the L" corresponding to the maximum of curvature of the "L-curve" but this "corner" can be difficult to discern (Subramaniyam et al, 2010). To overcome this difficulty in objectively finding the "corner of the L", we opted for a one-step method by using the generalized cross validation (GCV) (Golub et al, 1979) instead of the L-curve method.…”

Section: Regularization To Reduce the Number Of Trialsmentioning

confidence: 99%

“…To estimate this parameter automatically, the two classical methods are the generalized cross-validation (GCV) procedure (Golub, Heath, & Wahba, 1979) and the "L-curve" method (Engl & Grever, 1994). Also for EEG analysis, Subramaniyam and colleagues (Subramaniyam, Väisänen, Wendel, & Malmivuo, 2010) compared these two methods to estimate the visually evoked cortical potentials. In their study, the Tikhonov regularization was used to solve the inverse problem of the source localization to find the spatial cortical distribution at the presentation of emotional faces.…”

Section: Introductionmentioning

confidence: 99%

“…Here, in this study, two estimation methods of the regularization parameter are compared but in a context of temporal estimation of the evoked potentials. Moreover, an inter-subject analysis is carried out as is usual for ERP experimental designs instead of an intra-subject study as in (Subramaniyam et al, 2010). The regularization process is thus implemented at the overall level for the whole dataset, but also compared with a regularization for each subject.…”

Section: Introductionmentioning

confidence: 99%

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Regularization and a general linear model for event-related potential estimation

2017

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The usual event-related potential (ERP) estimation is the average across epochs time-locked on stimuli of interest. These stimuli are repeated several times to improve the signal-to-noise ratio (SNR) and only one evoked potential is estimated inside the temporal window of interest. Consequently, the average estimation does not take into account other neural responses within the same epoch that are due to short inter stimuli intervals. These adjacent neural responses may overlap and distort the evoked potential of interest. This overlapping process is a significant issue for the eye fixation-related potential (EFRP) technique in which the epochs are time-locked on the ocular fixations. The inter fixation intervals are not experimentally controlled and can be shorter than the neural response's latency. To begin, the Tikhonov regularization, applied to the classical average estimation, was introduced to improve the SNR for a given number of trials. The generalized cross validation was chosen to obtain the optimal value of the ridge parameter. Then, to deal with the issue of overlapping, the general linear model (GLM), was used to extract all neural responses inside an epoch. Finally, the regularization was also applied to it. The models (the classical average and the GLM with and without regularization) were compared on both simulated data and real datasets from a visual scene exploration in co-registration with an eye-tracker, and from a P300 Speller experiment. The regularization was found to improve the estimation by average for a given number of trials. The GLM was more robust and efficient, its efficiency actually reinforced by the regularization.

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Section: Generalized Cross-validation Proceduresmentioning

confidence: 62%

Section: Regularization To Reduce the Number Of Trialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Regularization and a general linear model for event-related potential estimation

2017

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“…The optimization of the GCV curve yields a λ that minimizes the tradeoff between the prediction error and the complexity of the model, thereby guarding against overfitting. The GCV is a model selection criteria that has been extensively used in the brain imaging literature (Subramaniyam et al, 2010) (Hu et al, 2018).…”

Section: Extraction Of Event-related Features At the Recording Levelmentioning

confidence: 99%

Automated EEG mega-analysis II: Cognitive aspects of event related features

Bigdely-Shamlo

Touryan

Ojeda³

et al. 2018

Preprint

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In this paper, we present the results of a large-scale analysis of event-related responses based on raw EEG data from 17 studies performed at six experimental sites associated with four different institutions. The analysis corpus represents 1,155 recordings containing approximately 7.8 million event instances acquired under several different experimental paradigms. Such large-scale analysis is predicated on consistent data organization and event annotation as well as an effective automated pre-processing pipeline to transform raw EEG into a form suitable for comparative analysis. A key component of this analysis is the annotation of study-specific event codes using a common vocabulary to describe relevant event features. We demonstrate that Hierarchical Event Descriptors (HED tags) capture statistically significant cognitive aspects of EEG events common across multiple recordings, subjects, studies, paradigms, headset configurations, and experimental sites. We use representational similarity analysis (RSA) to show that EEG responses annotated with the same cognitive aspect are significantly more similar than those that do not share that cognitive aspect. These RSA similarity results are supported by visualizations that exploit the non-linear similarities of these associations. We apply temporal overlap regression to reduce confounds caused by adjacent events instances and extract time and time-frequency EEG features (regressed ERPs and ERSPs) that are comparable across studies and replicate findings from prior, individual studies. Likewise, we use second-level linear regression to separate effects of different cognitive aspects on these features, across all studies. This work demonstrates that EEG mega-analysis (pooling of raw data across studies) can enable investigations of brain dynamics in a more generalized fashion than single studies afford. A companion paper complements this event-based analysis by addressing commonality of the time and frequency statistical properties of EEG across studies at the channel and dipole level.

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