Doc: Updated the Regularized CSP box documentation

plugins/processing/signal-processing/doc/Doc_BoxAlgorithm_RegularizedCSPTrainer.dox-part

@@ -17,7 +17,7 @@ __________________________________________________________________
 
  In principle CSP can be useful in two-class experiments where there is discriminative information in the variance (or power) of the signal conditions.
  
- The box implements some of the methods described e.g. in Lotte & Guan: "Regularizing common spatial patterns...", 2011. Especially, it 
+ The box implements some of the methods described e.g. by Lotte & Guan [1]. Especially, it 
  allows using the methods called "CSP with Diagonal Loading" and "CSP with Tikhonov Regularization" in the paper. In the approach of
  the paper, the filters for condition 1 are found by eigenvector decomposition of inv(Sigma1+rho*I)*Sigma2, where Sigma1 and Sigma2 are 
  empirical covariance matrices for the two conditions, rho the amount of Tikhonov regularization and I an identity matrix. For condition 2, 
@@ -25,13 +25,13 @@ __________________________________________________________________
  
  To avoid caching the whole dataset in the box, the algorithm tries to estimate the required covariances incrementally. The box supports
  a few different incremental ways to compute the covariances. The 'block average' approach takes an average of all the covariances of the incoming 
- signal chunks, whereas the incremental (per sample) method aims to implement Youngs & Cramer algorithm as described in Chan, Golub, Leveq, 
- "Updating formulae and a pairwise algorithm...", 1979. Which one gives better results may depend on the situation -- however, 
- taking an average of covariance matrices is not usually suggested as a method for computing covariance over the whole data. 
+ signal chunks, an approach described in [2], whereas the incremental (per sample) method aims to implement Youngs & Cramer 
+ algorithm as described in [3]. Which one gives better results may depend on the situation -- however, 
+ taking an average of covariance matrices is not your usual textbook method for computing covariance over the whole data. 
  
  Finally, the box also presents an option to try to compensate for the effect of changes in the average signal power over time. This is 
  can be done by enabling 'Trace Normalization' setting. When trace normalization is enabled, each data chunks contribution to 
- the covariance gets divided by its trace.
+ the covariance gets divided by its trace. See miscellaneous notes for details.
  
  * |OVP_DocEnd_BoxAlgorithm_RegularizedCSPTrainer_Description|
 __________________________________________________________________
@@ -113,19 +113,27 @@ __________________________________________________________________
  The suitable amount of regularization may depend on the variance of the data. You may need to try different values to find the one that suits your situation best.
  Before the CSP training, it may be useful to temporally filter the input data to remove bands which are believed to have no relevant discriminative information.
  
- Note that the usage of the CSP filters before classification training can make the cross-validation results optimistic, unless strictly non-overlapping 
- parts of the data were used to train the CSP and the classifier (disjoint sets for each). 
+ Note that the usage of the CSP filters before classification training can make the cross-validation results optimistic, unless strictly non-overlapping parts of the data were used to train the CSP and the classifier (disjoint sets for each). 
  
- The origin of the trace normalization trick has been lost. Presumably the idea is to normalize the scale of 
- each chunk in order to compensate for possible signal power drift over time during the EEG recording, 
+ The trace normalization can be found in the literature [2]. Presumably the idea is to normalize the 
+ scale of each chunk in order to compensate for a possible signal power drift over time during the EEG recording, 
  making each chunks' covariance contribute similarly to the aggregate regardless of the current chunks average power. 
 				
- To get the "CSP with Diagonal Loading" of Lotte & Guan paper, set shrinkage to a positive value and Tikhonov to 0. To get the 
- "CSP with Tikhonov regularization", do the opposite. You can also try a mixture of the two. Note that the Guan & Lotte paper does not use trace normalization.
+ To get the "CSP with Diagonal Loading" of Lotte & Guan paper [1], set shrinkage to a positive value and Tikhonov to 0. To get the 
+ "CSP with Tikhonov regularization", do the opposite. You can also try a mixture of the two. Note that the Guan & Lotte paper does not appear to use trace normalization.
  
  Once the spatial filters are computed and saved in the configuration file, you can load the configuration into the \ref Doc_BoxAlgorithm_SpatialFilter "Spatial Filter" box.
  
  For the moment the Regularized CSP Trainer supports only two classes. 
+
+ References
+ 
+ 1) Lotte & Guan: "Regularizing common spatial patterns...", 2011.
   
+ 2) Muller-Gerkin & al., "Designing optimal spatial filters for single-trial EEG classification in a movement task", 1999.
+ 
+ 3) Chan, Golub & Leveq, "Updating formulae and a pairwise algorithm...", 1979.
+ 
+
  * |OVP_DocEnd_BoxAlgorithm_RegularizedCSPTrainer_Miscellaneous|
  */