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Gentle Introduction to Signal Processing and Classification for Single-Trial ERP Analysis
Published on Apr 03, 20145241 Views
The aim of this lecture is to provide an illustrative tutorial on the methods for single-trial ERP analysis. Basic concepts of feature extraction and classification will be explained in a way that is
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Chapter list
Gentle Introduction to Signal Processing and Classification for Single-Trial ERP Analysis00:00
Overview of this Tutorial00:01
Introduction to ERP-based BCIs01:17
Non-Invasive Brain-Computer Interaction01:20
Different Occurences of Neural Activity01:34
Prototypical ERP03:06
From the Oddball Paradigm to a BCI Speller - 104:30
From the Oddball Paradigm to a BCI Speller - 205:45
From the Oddball Paradigm to a BCI Speller - 306:55
From the Oddball Paradigm to a BCI Speller - 407:54
Multi-channel Epochs09:21
ERPs in a Head Plot09:34
ERPs in a Grid Plot11:08
ERP Topographies11:22
Classical Investigation of Target vs Nontarget12:31
From Uni- to Multivariate Features13:42
First, a Simple Approach to Classification13:57
Univariate Features: Averages and Single-Trials14:54
Measures of Separability17:23
Area under the Curve (AUC) as Measure of Seperation18:42
Examples for ROC Curves and AUC Values19:38
Interlude: Representation as Matrix20:46
ERPs in a Grid Plot with AUC Scores22:29
ERP Topographies of AUC Scores22:59
AUC Matrix: Overview of Discriminative Information23:25
Generation of EEG Signals - 124:26
Generation of EEG Signals - 224:45
Volume Conduction in EEG25:35
Mind Spatial Smearing!27:28
From Uni- to Multivariate Features28:05
The Virtue of Multivariate Spatial Features28:43
The Virtue of Multivariate Temporal Features - 132:08
The Virtue of Multivariate Temporal Features - 232:43
Extraction of Spatio-Temporal Features33:15
Extraction of Temporal Features34:22
Extraction of Spatial Features34:34
Overview of Multivariate ERP Features34:47
Multivariate ERP Model35:34
Averaging across Trials39:22
Let's Start Simple: a 2D Feature40:45
Multivariate Gaussian Distributions43:04
Eigenvalue Decomposition (EVD)43:56
Characterization of Gaussian Distributions46:23
Visualizing 2D Features at Scatter Plot55:28
Classification of ERP Features58:23
Toward Classification for BCIs58:25
Distributions of ERP Features58:58
Nearest Centroid Classifier (NCC)59:35
Formalization of Separating Hyperplanes01:00:45
Can We Expect NCC to Perform Well for ERP Features?01:02:05
Linear Discriminant Analysis (LDA)01:02:50
Linear Disciminant Analysis01:03:58
Interlude: Illustration of Whitening Transform01:04:36
Correspondence between NCC and LDA01:04:55
Linear Discriminant Analysis - Assumptions for Optimality01:05:16
Covariance Matrices of ERP Features01:05:25
For Comparison: Covariances in Handwritten Digits01:06:13
Validation of Classification Procedures01:07:24
Results of Classifying Spatial Features01:08:23
Classification of Spatio-Temporal Features01:09:34
Overfitting of LDA01:10:22
Bias in Estimating Covariance Matrices01:11:12
Bias in Estimating Covariances01:12:05
A Remedy for the Estimation Bias01:13:42
Properties of the Shrunk Covariance Matrix01:14:56
Regularized Linear Discriminant Analysis01:15:39
LDA with Different Shrinkage Parameters01:16:54
Optimal Selection of Shrinkage Parameter - 101:17:17
Optimal Selection of Shrinkage Parameter - 201:17:30
Classification on Single Components and Combined01:19:04
Impact of Shrinkage as Trade-off - 101:20:11
Impact of Shrinkage as Trade-off - 201:21:12
Recap: NCC, LDA and Shrinkage-LDA01:21:57
Classification with Shrinkage-LDA at a Glance01:23:11
Understanding Spatial Filters01:24:58
LDA as a Spatial Filter01:25:03
Recap: AUC matrix in RSVP Speller01:26:12
LDA Weight Vector as Spatial Filter - Example01:26:40
Interpretation of Spatial Filters - 101:28:06
Interpretation of Spatial Filters - 201:31:33
Understanding Spatial Filters - 101:34:18
Understanding Spatial Filters - 201:34:25
The Blessing and Curse of Machine Learning01:35:33