Repository: alexandrebarachant/bci-challenge-ner-2015
Branch: master
Commit: d185067fc0ea
Files: 14
Total size: 426.8 KB

Directory structure:
gitextract_0n05c5vc/

├── .gitignore
├── Licence.txt
├── README.md
├── classif.py
├── cross_valid.py
├── parameters_Leak.yaml
├── parameters_noLeak.yaml
├── prediction.py
├── preproc/
│   ├── metadata.csv
│   └── preproc.py
├── results/
│   ├── submission_Leak.csv
│   └── submission_noLeak.csv
└── riemann/
    ├── __init__.py
    └── utils.py

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FILE: Licence.txt
================================================
                    GNU GENERAL PUBLIC LICENSE
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    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail.

  If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:

    <program>  Copyright (C) <year>  <name of author>
    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License.  Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".

  You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.

  The GNU General Public License does not permit incorporating your program
into proprietary programs.  If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library.  If this is what you want to do, use the GNU Lesser General
Public License instead of this License.  But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.


================================================
FILE: README.md
================================================
# BCI Challenge @ NER 2015

Code and documentation for the winning solution at the BCI Challenge @ NER 2015 : https://www.kaggle.com/c/inria-bci-challenge

**Authors**:
* [Alexandre Barachant](http://alexandre.barachant.org) 
* Rafal Cycon
* Cédric Gouy-Pailler

**Contents** :

- [Signal Processing & Classification Pipeline ](#signal-processing-classification-pipeline)
    - [Introduction](#introduction)
    - [Classification Pipeline](#classification-pipeline)
    - [Results](#results)
    - [Discussion](#Discussion)
    - [References ](#references)
- [Code](#code)
- [Parameter file](#parameter-file)


**Licence** : GLPv3. see Licence.txt

# Signal Processing & Classification Pipeline 

## Introduction

The goal of this challenge was to detect error related potential recorded during a p300 spelling task. The classification must be done across subjects,
i.e. training and test sets were composed by different subjects. This is a hard task due to the high inter-subjects variability of EEG. 
However, our Riemannian Geometry framework has been proven very powerful for dealing with this problem (see [2], [3], and the [decMeg2014 kaggle challenge](http://www.kaggle.com/c/decoding-the-human-brain)).
This is partly due to the property of invariance by congruent transformation of the Riemannian metric.

Starting from here, the main difficulties of this challenge were to deal with the relatively high number of electrodes and to avoid overfitting.
We overcome the first issue by using a channel selection algorithm, and the second by using a bagging procedure and an appropriate cross-validation methodology.

**The leak** : By analyzing the time between feedback events in session 5, it was possible to catch the output of the online detection Error. 
The idea is that when an error is detected, the correction of this error induces a small delay that can be detected with more or less reliability.
Given that the online Error detection was properly calibrated for the current subject, this analysis gave us two insights :

1. the output of the online error detection for session 5. Of course, there is a higher probability of error when the online classifier detects an error, but it depends on the accuracy of the online classifier.
This can be used to increase detection accuracy, but only for the session 5.

2. the percentage of error in session 5 i.e. a rough estimate of the class balance for each subjects. This second information is really important, because it can help to optimize the global AUC criterion, by adjusting the prediction to match the error probability of each subjects.
Of course, this only helps the global AUC performance, and has little effect on the subject performance.

We propose two different models. The first one does not make any use of the
leakage information and satisfies an "online processing" constraint, which means
that any trial performed by a subject can be classified without the need for
future complementary data or information. The second model uses the leak, thus
it is not online-compatible.
The two models are built upon the same classification pipeline, but with parameters tuned independently to achieve the highest performance.

## Classification Pipeline

#### Preprocessing
EEG Signals are bandpass filtered by a 5th order Butterworth filter between 1 and 40 Hz. 
Then, signals are epoched to take only 1.3 second after the feedback event. The EOG channel is removed prior to any preprocessing.

#### Feature Extraction

The EEG-based Feature extraction is done in 4 steps :

1. *Xdawn Covariances* : Two sets of 5 XDAWN [1] spatial filters are estimated, one for each class (Error and Correct).
The grand average evoked potential of each class is then filtered by the corresponding set of spatial filters, and concatenated to each epochs.
The covariance matrix of each resulting epoch is then used as feature for the next steps. This process is similar to the one described in [2] and [3].
2. *Electrode Selection* : A channel selection is applied to keep only relevant channels. The procedure consist in a backward elimination with the Riemannian distance between the 
Riemannian Geometric mean of the covariances of each class as the criterion. The algorithm is described in [4].
3. *Tangent Space* : Reduced Covariances matrices are then projected in the tangent space, as described in [5] and [6].
4. *Normalization* : Feature Normalization using a l1 norm.

After these 4 steps, a set of Meta Feature are added to the EEG-based features.
The basic set of Meta feature is the following :

* *Session id*  : the session number of the current epoch. 
* *FeedBack*    : the Feedback count since the beginning of the session. 
* *Letter*      : the Letter position in the current word. 
* *Word*        : the word count since the beginning of the session. 
* *FeedBackTot* : the feedback count since the first session.
* *WordTot*     : the word count since the first session.
* *isLong*      : was the current word flashed 8 times, i.e. a long sequence of flashes.

**For the leak only**, two other features are added :
* *OnlineErr*   : 1 if the online Error detection has detected an error (only available in session 5).
* *Err Prop*    : the percentage of errors detected in the session 5.

#### Classification 

All the above features are inputted to an Elastic Net algorithm.

**For the leak only**, *Err Prop* is added to the prediction with a coefficient of 0.8. 
As an effect, it biases the results with an estimation of the classes balances. This has no effect on the AUC of a single subject, 
but acts as on optimization for the Global AUC, which was the target metric.

### Bagging

The above pipeline is applied on a number of random subsets of subjects, and predictions are averaged across bagged models. 
Each bagged model is built on an unique set of features (high diversity of features between subsets of subjects is achieved mostly due to the Electrode Selection step in feature extraction) and thus represents a different point of view of the training data.
Ensembling bagged models improves generalization and effectively counters overfitting.

Final submission was an average of predictions of 500 bagged models, each trained on 9 subjects (out of 16, just one more subject above 50%). In 4-fold CV 150 bagged models were used.

### Cross-validation

The validation approach was a 4-fold CV with data randomly split into folds subject-wise. The splitting was repeated several times (10 in most cases) and obtained AUCs averaged. The method proved to produce a reliable measure of performance.

## Results

#### AUC 

|         Submission         | Public LB | Private LB | Fold-wise CV (std) | Subject-wise CV (std) |
|----------------------------|-----------|------------|--------------------|-----------------------|
| No Leak (online compatible)| 0.85083   | 0.84585    | 0.7294  (0.037)    | 0.7696 (0.004)        |
| Leak                       | 0.85145   | 0.87224    | 0.8008  (0.039)    | 0.7801 (0.004)        |


CV results are given for 150 models, using the CV procedure described above. Fold-CV refers to the average AUC evaluated on all the predictions of the tests subjects. 
Subject-wise CV refers to the average AUC evaluated for each subject independently. Subject-wise CV represents performance of the model in a real case scenario, i.e. the performance a single user could expect in a online experiment. 

Results across Public and Private LB are quite stable and exhibit very good performance of both models.

In cross validation, the introduction of the leak has a little effect (0.01 AUC) on subject specific performance, but has a tremendous effect on Fold CV.
Shifting the predictions according to the leak effectively improves the Fold AUC.

Interestingly, this effect is not as strong for LB results. Indeed, the no-leak model is able to correctly catch the class balance of each subject and bias the prediction accordingly.
This effect was not observed in CV results due to a smaller test set size.

#### Effect of the number of electrodes

A very important parameter was the number of electrodes in the electrode selection step ('nelec') of feature extraction.
Riemannian geometry works best with a moderately low number of electrodes. The number of features in the tangent space is N(N+1)/2 with N the number of channels.
A too high number of electrodes can lead to overfitting and estimation issues, while a too small number of channels leads to a loss of information. 

Varying the number of electrodes gives the following results (for the no-leak model) :

![elec numbers](https://raw.githubusercontent.com/alexandrebarachant/bci-challenge-ner-2015/master/results/ElecNumbers.png)

The electrode selection already achieves very high performance for a number of electrodes as low as 15.
Interestingly, using all electrodes gives the best AUC for private LB, but an optimal choice of number of electrodes may be different when using more bagged models.

The introduction of bagged model stabilizes results by making the prediction less sensitive to the electrode subset. 
This effect is bigger when the number of electrodes in the subset decreases. 

The final no-leak model was set to 35 electrodes, and only 23 for the leak model.
These values were chosen according mainly to CV results, but also partially to public LB scores.

#### Effect of the number of bagged models

For the final submission we used 500 bagged models, each composed of 9 randomly selected subjects. The number of models for the final submissions was chosen based on the fact that adding more models could improve generalization 
(up to some 'plateau' point, which was unknown at the time), but too many models could not hurt the performance. 
It was the safest choice while keeping the processing time reasonable. 

Post-competition tests indicated that as few as 10 models were already enough to provide good performance in private LB (tests made with the no-leak model):

![bag numbers](https://raw.githubusercontent.com/alexandrebarachant/bci-challenge-ner-2015/master/results/BagsNumbers.png)

## Discussion

The proposed method shows very good performance. For the specific combination of subjects in the private LB, electrode selection and ensembling did not improve significantly results.
However, they did help to prevent overfitting and increase significantly performances in cross-validation. 

The introduction of Meta features improve the results by 0.015 AUC on private LB. While some of them seem odd, they are acting as a support for the classifier to take into account
the possible shift in error prediction due to mental fatigue of the subject and other source of variability that occurs in long EEG sessions.

For this challenge, the evaluation criterion was the AUC calculated from the predictions of all the subjects put together. 
However, the fact that the subjects have different classes balances allow to optimize the score without making any prediction.
As a matter of fact, submitting the estimation of class balance of each subject (thanks to the leak) results in a Private LB score of 0.746, enough to be ranked in the top10.

## References 

> [1] Rivet, B.; Souloumiac, A.; Attina, V.; Gibert, G., "xDAWN Algorithm to Enhance Evoked Potentials: Application to Brain–Computer Interface," IEEE Transactions on Biomedical Engineering, vol.56, no.8, pp.2035,2043, Aug. 2009
>
> [2] A. Barachant, M. Congedo ,"A Plug&Play P300 BCI Using Information Geometry", arXiv:1409.0107. [link](http://arxiv.org/abs/1409.0107)
>
> [3] M. Congedo, A. Barachant, A. Andreev ,"A New generation of Brain-Computer Interface Based on Riemannian Geometry", arXiv: 1310.8115. [link](http://arxiv.org/abs/1310.8115)
>
> [4] A. Barachant and S. Bonnet, "Channel selection procedure using riemannian distance for BCI applications," in 2011 5th International IEEE/EMBS Conference on Neural Engineering (NER), 2011, 348-351. [pdf](http://hal.archives-ouvertes.fr/docs/00/60/27/07/PDF/NER11_0016_FI.pdf)
>
> [5] A. Barachant, S. Bonnet, M. Congedo and C. Jutten, “Multiclass Brain-Computer Interface Classification by Riemannian Geometry,” in IEEE Transactions on Biomedical Engineering, vol. 59, no. 4, p. 920-928, 2012. [pdf](http://hal.archives-ouvertes.fr/docs/00/68/13/28/PDF/Barachant_tbme_final.pdf)
>
> [6] A. Barachant, S. Bonnet, M. Congedo and C. Jutten, “Classification of covariance matrices using a Riemannian-based kernel for BCI applications“, in NeuroComputing, vol. 112, p. 172-178, 2013. [pdf](http://hal.archives-ouvertes.fr/docs/00/82/04/75/PDF/BARACHANT_Neurocomputing_ForHal.pdf)

# Code

### Dependencies & Requirements

The code is written in python. At least 8GB of RAM is required.
The following packages are used :

* sklearn
* numpy
* scipy
* pylab
* pandas
* pyyaml
* glob
* multiprocessing

### Usage

#### Preprocessing
Extract train.zip and test.zip in the data folder. Put file TrainLabels.csv in the folder data/train.

Apply preprocessing on the data (one time only) :

```bash
cd preproc/
python preproc.py
```

#### Generating Submissions

run prediction.py with the desired parameter file from the main folder. 

For the submission with the leak :
```bash
python prediction.py parameters_Leak.yaml
```

For the submission without the leak :
```bash
python prediction.py parameters_noLeak.yaml
```

:warning: Generating a submission takes around 70 minutes on a 12-core, 64Gb RAM computer.
You may adjust the 'core' parameters in the yaml files to fit your configuration. 
Default is 4 cores.

#### Cross validation

run cross_valid.py with the desired parameter file from the main folder. 

For the submission with the leak :
```bash
python cross_valid.py parameters_Leak.yaml
```

For the submission without the leak :
```bash
python cross_valid.py parameters_noLeak.yaml
```

CV takes around 12h to run on a 12-core, 64GB RAM computer

### Troubleshooting

If you get Memory Error, decrease the number of cores in the parameters file.
By default 4 cores are used, which should work fine on a computer with 16GB RAM. 

# Parameter file

For this challenge, we built a framework based on the sklearn Pipeline system allowing us to quickly test different ideas and parameters without changing a line of code.
The classification pipeline is described in a parameter file, using a yaml syntax, and then parsed and built on the fly by the scripts.
Parameters files can be shared between team-mates, and Version Controlled, reducing the chance of errors. 

The parameter file for the no-leak submission looks like this :

```yaml
imports:
  sklearn.linear_model :
    - ElasticNet
  sklearn.preprocessing:
    - Normalizer
  classif:
    - XdawnCovariances
    - TangentSpace
    - AddMeta
    - ElectrodeSelect
  
CrossVal:
  cores: 4
  folds: 4
  repetitions: 10
  path: results.csv
  comments: 'model-final-noLeak'

Submission:
  path: submission-noLeak.csv
  cores: 4

MetaPipeline:
  #leak:
  bagging:
     bag_size: 0.51 
     models: 500 

pipeline:
  - XdawnCovariances:
      nfilter: 5
      subelec: range(0,56,1)
  - ElectrodeSelect:
      nfilters: 5
      nelec: 35
      metric: "'riemann'"
  - TangentSpace:
      metric: "'logeuclid'"
      tsupdate: False
  - Normalizer:
      norm: '"l1"'
  - AddMeta:
  - ElasticNet:
      l1_ratio: 0.5
      alpha: 2e-4
      normalize: True
```

#### Imports
The import section lists packages to import :
The following section  :

```yaml
sklearn.linear_model :
  - ElasticNet
```

is evaluated as :

```python
from sklearn.linear_model import ElasticNet
```

#### Pipeline

The different steps in the classification pipeline are described in the pipeline section.
They are build and pipelined in the order of appearance in the yaml list.

The last element should implement two methods : fit and predict.
All the intermediate element should implement a fit_transform and a transform methods.
For more information about sklearn pipeline, see [sklearn.pipeline](http://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html)

the folowing section
```yaml
- ElasticNet:
    l1_ratio: 0.5
    alpha: 2e-4
    normalize: True
```

is evaluated as :

```python
ElasticNet(l1_ratio=0.5 , alpha=2e-4 , normalize=True)
```

### Build your own pipeline

Modifying or adding new steps in the pipeline can't be easier.
Let say you want to add a PCA before the classification step.

Just declare the sklearn pca in the import section

```yaml
imports:
  sklearn.linear_model :
    - ElasticNet
  sklearn.decomposition: 
    - PCA
```

and add it in the pipeline :

```yaml
pipeline:
  - XdawnCovariances:
      nfilter: 5
      subelec: range(0,56,1)
  - ElectrodeSelect:
      nfilters: 5
      nelec: 35
      metric: "'riemann'"
  - TangentSpace:
      metric: "'logeuclid'"
      tsupdate: False
  - Normalizer:
      norm: '"l1"'
  - AddMeta:
  - PCA:
      n_components: 10
  - ElasticNet:
      l1_ratio: 0.5
      alpha: 2e-4
      normalize: True
```

and then run the prediction.py (or cross_valid.py) script :

```
python prediction.py parameters.yaml
```

Voilà!


================================================
FILE: classif.py
================================================
# -*- coding: utf-8 -*-
"""
@author: alexandrebarachant
"""
import numpy
from scipy.linalg import eig as geig
import riemann
from sklearn.base  import BaseEstimator, ClassifierMixin, TransformerMixin
###############################################################################
class XdawnCovariances(BaseEstimator,TransformerMixin):
    """ 
    Compute double xdawn, project the signal and compute the covariances

    """    
    def __init__(self,nfilter=4,subelec=-1):
        self.nfilter = nfilter
        self.subelec = subelec
        
    def fit(self,X,y):
        Nt,Ne,Ns = X.shape
        # Prototyped responce for each class
        P1 = numpy.mean(X[y==1,:,:],axis=0)
        P0 = numpy.mean(X[y==0,:,:],axis=0)
        
        # Covariance matrix of the prototyper response & signal
        C1 = numpy.matrix(numpy.cov(P1))
        C0 = numpy.matrix(numpy.cov(P0))
        
        #FIXME : too many reshape operation        
        tmp = X.transpose((1,2,0))
        Cx = numpy.matrix(numpy.cov(tmp.reshape(Ne,Ns*Nt)))
        
        # Spatial filters
        D,V1 = geig(C1,Cx)        
        D,V0 = geig(C0,Cx)
        
        # create the reduced prototyped response
        self.P = numpy.concatenate((numpy.dot(V1[:,0:self.nfilter].T,P1),numpy.dot(V0[:,0:self.nfilter].T,P0)),axis=0)
    
    def transform(self,X):
        covmats = riemann.covariances_EP(X[:,self.subelec,:],self.P)
        return covmats
    
    def fit_transform(self,X,y):
        self.fit(X,y)
        return self.transform(X)
###############################################################################
class TangentSpace(BaseEstimator, TransformerMixin):

    def __init__(self,metric='riemann',tsupdate = False):

        self.metric = metric
        self.tsupdate = tsupdate 

        
    def fit(self,X,y=None):
        # compute mean covariance
        self.Cr = riemann.mean_covariance(X,metric=self.metric)
        
    def transform(self,X):
       
        if self.tsupdate:
            Cr = riemann.mean_covariance(X,metric=self.metric)
        else:
            Cr = self.Cr
        return riemann.tangent_space(X,Cr)

    def fit_transform(self,X,y=None):
        # compute mean covariance
        self.Cr = riemann.mean_covariance(X,metric=self.metric)
        return riemann.tangent_space(X,self.Cr)
###############################################################################
class AddMeta(BaseEstimator, TransformerMixin):

    def __init__(self,meta=None):
        self.meta = meta
    
    def fit(self,X,y=None):
        pass
        
    def transform(self,X):
        if self.meta is not None:
            return numpy.c_[X,self.meta]
        else:
            return X

    def fit_transform(self,X,y=None):
        return self.transform(X)

###############################################################################
class ElectrodeSelect(BaseEstimator, TransformerMixin):

    def __init__(self,nelec = 20,nfilters=5,metric='riemann'):
        self.nelec = nelec
        self.metric = metric
        self.nfilters = nfilters
        self.subelec = -1
        self.dist = []
    
    def fit(self,X,y=None):
        C1 = riemann.mean_covariance(X[y==1,...],self.metric)
        C0 = riemann.mean_covariance(X[y==0,...],self.metric)
        
        Ne,_ = C0.shape
        
        self.subelec = range(0,Ne,1) 
        while (len(self.subelec)-2*self.nfilters)>self.nelec:
            di = numpy.zeros((len(self.subelec),1))
            for idx in range(2*self.nfilters,len(self.subelec)):
                sub = self.subelec[:]
                sub.pop(idx)
                di[idx] = riemann.distance(C0[:,sub][sub,:],C1[:,sub][sub,:])
            #print di
            torm = di.argmax()
            self.dist.append(di.max())
            self.subelec.pop(torm)        
        #print self.subelec
        
    def transform(self,X):
       return X[:,self.subelec,:][:,:,self.subelec]

    def fit_transform(self,X,y=None):
        self.fit(X,y)
        return self.transform(X)
###############################################################################
def updateMeta(clf,Meta):
    if clf.named_steps.has_key('addmeta'):
        clf.set_params(addmeta__meta=Meta) 

def baggingIterator(opts,users):
    mdls = opts['bagging']['models']
    bag_size = 1-opts['bagging']['bag_size']
    bag_size = numpy.floor(bag_size*len(users))
    if bag_size == 0:
        return [[u] for u in users]
    else:
        return [numpy.random.choice(users,size=bag_size,replace=False) for i in range(mdls)]

================================================
FILE: cross_valid.py
================================================
# -*- coding: utf-8 -*-

import yaml
import sys
import numpy as np
import pandas as pd
from time import time


from sklearn.pipeline import make_pipeline
from sklearn.metrics import roc_auc_score
from sklearn.cross_validation import KFold, LeaveOneLabelOut

from collections import OrderedDict
from multiprocessing import Pool
from functools import partial

# local import
from classif import updateMeta, baggingIterator

def from_yaml_to_func(method,params):
    prm = dict()
    if params!=None:
        for key,val in params.iteritems():
            prm[key] = eval(str(val))
    return eval(method)(**prm)

def makeCV(kfolds,X,Labels,User,Meta,clf,opts):
    users = np.unique(User)
    toPredData=[]
    Gauc = []
    for train_users,test_users in kfolds[1]:
        allProb = 0 
        test_index = np.array([True if u in set(users[test_users]) else False for u in User])

        if opts.has_key('bagging'):
            bagging = baggingIterator(opts,[users[i] for i in train_users])
        else:
            bagging = [[-1]]
        
        for bag in bagging:
            bagUsers = np.array([True if u in set(bag) else False for u in User])
            train_index = np.logical_xor(np.negative(test_index), bagUsers)
            
            try:
                # train
                updateMeta(clf,Meta[train_index])
                clf.fit(X[train_index,:,:],Labels[train_index])
                
                # predict
                prob = []
                for ut in np.unique(users[test_users]):
                    updateMeta(clf,Meta[User==ut,...])
                    prob.extend(clf.predict(X[User==ut,...]))
                prob = np.array(prob)
                
                allProb += prob/len(bagging)
            except:
                print kfolds[0]
                print [users[i] for i in train_users]
                print bag
                continue
        
        # save & return
        predictions = OrderedDict()
        predictions['user']=User[test_index]
        predictions['label'] = Labels[test_index]
        predictions['prediction']=allProb
        if opts.has_key('leak'):
             predictions['prediction'] += opts['leak']['coeff']*(1-Meta[test_index,-1])
        predictions = pd.DataFrame(predictions)
        
        Gauc.append(roc_auc_score(predictions.label,predictions.prediction))
        toPredData.append(predictions)
    predData = pd.concat(toPredData)
    
    Sauc = [roc_auc_score(predData.loc[predData.user==i].label,predData.loc[predData.user==i].prediction) for i in np.unique(predData.user)]
    
    print 'Rep %d: gAUC (mean of folds) %0.5f, sAUC %0.5f (%0.5f)' % (kfolds[0],np.mean(Gauc),np.mean(Sauc),np.std(Sauc)) 
    
    return [Gauc,Sauc]
    
# load parameters file
yml = yaml.load(open(sys.argv[1]))

# imports 
for pkg, functions in yml['imports'].iteritems():
    stri = 'from ' + pkg + ' import ' + ','.join(functions)
    exec(stri)

# parse pipe function from parameters
pipe = []
for item in yml['pipeline']:
    for method,params in item.iteritems():
        pipe.append(from_yaml_to_func(method,params))

# create pipeline
clf = make_pipeline(*pipe)
opts=yml['MetaPipeline']
if opts is None:
    opts = {}
# load files
X = np.load('./preproc/epochs.npy')
Labels,User = np.load('./preproc/infos.npy')
Meta = np.load('./preproc/meta_leak.npy') if opts.has_key('leak') else np.load('./preproc/meta.npy')
users=np.unique(User)




# parallel CV
np.random.seed(5)
folds = yml['CrossVal']['folds']
repetitions = yml['CrossVal']['repetitions']
cores = yml['CrossVal']['cores']

kfolds = [[i,KFold(len(users),folds,shuffle=True)] for i in range(repetitions)]
np.random.seed(432432)
t = time()
pMakeCV = partial(makeCV,X=X,Labels=Labels,User=User,Meta=Meta,clf=clf,opts=opts) # pool function is able to process only 1 argument, so the rest has to be set fixed
pool = Pool(processes = cores) # define number of cores
results = pool.map(pMakeCV,kfolds,chunksize=1) # apply parallel processing
pool.close() # close parallel processes after execution (frees memory)
print "Done in " + str(time()-t) + " second"
# calculating performance

gAUC = np.concatenate([i[0] for i in results]) # mean of folds
sAUC = [np.mean(i[1]) for i in results]
indAUC = np.array([i[1] for i in results])
indAUC = np.mean(indAUC,axis=0)

print 'Global AUC : %.5f (%.5f)'  % (np.mean(gAUC),np.std(gAUC))
print 'Subject AUC : %.5f (%.5f)'  % (np.mean(sAUC),np.std(sAUC))

# writing it down
import os
comment = yml['CrossVal']['comments']
path = yml['CrossVal']['path']
pipelineSteps = [str(clf.steps[i][1]).replace('\n','').replace(' ','') for i in range(len(clf.steps))]
if not os.path.isfile(path):
    fd = open(path,'w')
    fd.write('comment;folds;reps;gAUC mean;gAUC std;sAUC mean;sAUC std;user'+ ";user".join(map(str,map(int,users))) + ';leak;bagging;pipeline\n')
    fd.close()
fd = open(path,'a')
leakStr = 'on' if opts.has_key('leak') else 'off'
bagStr = '-'.join([str(opts['bagging']['bag_size']),str(opts['bagging']['models'])]) if opts.has_key('bagging') else 'off'
toWrite = [comment] + map(str,[folds,repetitions,np.mean(gAUC),np.std(gAUC),np.mean(sAUC),np.std(sAUC)]) + [str(i) for i in indAUC] + [leakStr,bagStr] + pipelineSteps
fd.write(';'.join(toWrite) + '\n')
fd.close()



================================================
FILE: parameters_Leak.yaml
================================================
imports:
  sklearn.linear_model :
    - ElasticNet
  sklearn.preprocessing:
    - Normalizer
  classif:
    - XdawnCovariances
    - TangentSpace
    - AddMeta
    - ElectrodeSelect
  
CrossVal:
  cores: 4
  folds: 4
  repetitions: 10
  path: results.csv
  comments: 'model-final-leak'

Submission:
  path: submission_leak.csv
  cores: 4

MetaPipeline:
  leak:
    coeff: 0.8
  bagging:
     bag_size: 0.51 # % of subjects to train on in each bagged model. If bag_size==1 then LOSO bagging is performed 
     models: 500 # ignored for LOSO bagging

pipeline:
  - XdawnCovariances:
      nfilter: 5
      subelec: range(0,56,1)
  - ElectrodeSelect:
      nfilters: 5
      nelec: 23
      metric: "'riemann'"
  - TangentSpace:
      metric: "'logeuclid'"
      tsupdate: True
  - Normalizer:
      norm: '"l1"'
  - AddMeta:
  - ElasticNet:
      l1_ratio: 0.5
      alpha: 1.5e-4
      normalize: True


================================================
FILE: parameters_noLeak.yaml
================================================
imports:
  sklearn.linear_model :
    - ElasticNet
  sklearn.preprocessing:
    - Normalizer
  classif:
    - XdawnCovariances
    - TangentSpace
    - AddMeta
    - ElectrodeSelect
  
CrossVal:
  cores: 4
  folds: 4
  repetitions: 10
  path: results.csv
  comments: 'model-final-noLeak'

Submission:
  path: submission-noLeak.csv
  cores: 4

MetaPipeline:
  #leak:
  bagging:
     bag_size: 0.51 # % of subjects to train on in each bagged model. If bag_size==1 then LOSO bagging is performed 
     models: 500 # ignored for LOSO bagging

pipeline:
  - XdawnCovariances:
      nfilter: 5
      subelec: range(0,56,1)
  - ElectrodeSelect:
      nfilters: 5
      nelec: 35
      metric: "'riemann'"
  - TangentSpace:
      metric: "'logeuclid'"
      tsupdate: False
  - Normalizer:
      norm: '"l1"'
  - AddMeta:
  - ElasticNet:
      l1_ratio: 0.5
      alpha: 2e-4
      normalize: True


================================================
FILE: prediction.py
================================================
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 27 22:23:02 2014

@author: kirsh
"""

from time import time
import numpy as np
import pandas as pd
from sklearn.pipeline import make_pipeline
import yaml
import sys
from classif import updateMeta, baggingIterator
from multiprocessing import Pool
from functools import partial

def from_yaml_to_func(method,params):
    prm = dict()
    if params!=None:
        for key,val in params.iteritems():
            prm[key] = eval(str(val))
    return eval(method)(**prm)


def BaggingFunc(bag,Labels,X,Meta,User,X_test,Meta_test,User_test):
    bagUsers = np.array([True if u in set(bag) else False for u in User])
    train_index = np.negative(bagUsers)
    updateMeta(clf,Meta[train_index])
    clf.fit(X[train_index,:,:],Labels[train_index])
    
    ### predicting
    prob = []
    for ut in users_test:
        updateMeta(clf,Meta_test[User_test==ut,...])
        prob.extend(clf.predict(X_test[User_test==ut,...]))
    prob = np.array(prob)
    
    return prob

# load parameters file
yml = yaml.load(open(sys.argv[1]))

# imports 
for pkg, functions in yml['imports'].iteritems():
    stri = 'from ' + pkg + ' import ' + ','.join(functions)
    exec(stri)

# parse pipe function from parameters
pipe = []
for item in yml['pipeline']:
    for method,params in item.iteritems():
        pipe.append(from_yaml_to_func(method,params))

# create pipeline
clf = make_pipeline(*pipe)
opts=yml['MetaPipeline']
if opts is None:
    opts = {}

cores = yml['Submission']['cores']

# load data
X = np.load('./preproc/epochs.npy')
Labels,User = np.load('./preproc/infos.npy')
users = np.unique(User)
Meta = np.load('./preproc/meta_leak.npy') if opts.has_key('leak') else np.load('./preproc/meta.npy')

X_test = np.load('./preproc/test_epochs.npy')
feedbackid,User_test = np.load('./preproc/test_infos.npy')
User_test = np.array(map(int, User_test))
users_test = np.unique(User_test)
Meta_test = np.load('./preproc/test_meta_leak.npy') if opts.has_key('leak') else np.load('./preproc/test_meta.npy')

### training
np.random.seed(5)
allProb = 0 

if opts.has_key('bagging'):
    bagging = baggingIterator(opts,users)
else:
    bagging = [[-1]]

t = time()
pBaggingFunc = partial(BaggingFunc,Labels=Labels,X=X,Meta=Meta,User=User,X_test=X_test,Meta_test=Meta_test,User_test=User_test)
pool = Pool(processes = cores)
allProb = pool.map(pBaggingFunc,bagging,chunksize=1)
allProb = np.vstack(allProb)
allProb = np.mean(allProb,axis=0)

if opts.has_key('leak'):
    allProb += opts['leak']['coeff']*(1-Meta_test[:,-1])

print "Done in " + str(time()-t) + " second"

submission = yml['Submission']['path']
df = pd.DataFrame({'IdFeedBack':feedbackid,'Prediction':allProb})
df.to_csv(submission,index=False)

================================================
FILE: preproc/metadata.csv
================================================
subject,session,isLong,longProp,onlineErr
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26,3,1,0.5,0
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26,3,0,0.5,0
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26,3,1,0.5,0
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26,3,0,0.5,0
26,3,0,0.5,0
26,3,0,0.5,0
26,4,0,0.5,0
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26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,0,0.5,0
26,4,0,0.5,0
26,4,0,0.5,0
26,4,0,0.5,0
26,4,0,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
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26,4,1,0.5,0
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26,4,1,0.5,0
26,4,1,0.5,0
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26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
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26,4,0,0.5,0
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26,4,1,0.5,0
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26,4,1,0.5,0
26,4,1,0.5,0
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26,4,1,0.5,0
26,4,1,0.5,0
26,4,1,0.5,0
26,4,0,0.5,0
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26,4,0,0.5,0
26,4,0,0.5,0
26,5,0,0.5,1
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26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,0
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26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
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26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
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26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,0
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26,5,0,0.5,0
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26,5,0,0.5,0
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26,5,0,0.5,1
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26,5,0,0.5,1
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26,5,0,0.5,0
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26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,1
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26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,0
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26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,0
26,5,0,0.5,1
26,5,0,0.5,1
26,5,0,0.5,0


================================================
FILE: preproc/preproc.py
================================================
# -*- coding: utf-8 -*-
"""
Created on Thu Nov 20 12:19:34 2014

@author: alexandre barachant
"""
from numpy import *
import numpy as np
import glob
import re
from pylab import *
from scipy.signal import *
import pandas as pd

def bandpass(sig,band,fs):
    B,A = butter(5, array(band)/(fs/2), btype='bandpass')
    return lfilter(B, A, sig, axis=0)

for test in [False,True] : 

    prefix = '' if test is False else 'test_'
    DataFolder = '../data/train/' if test is False else '../data/test/'
    list_of_files = glob.glob(DataFolder + 'Data_*.csv')
    list_of_files.sort()

    reg = re.compile('\d+')
    


    freq = 200.0

    epoc_window = 1.3*freq

    X = []
    User = []
    idFeedBack = []
    Session = []
    Feedback = []
    Letter = []
    Word = []
    FeedbackTot = []
    LetterTot = []
    WordTot = []

    for f in list_of_files:
        print f
        user,session = reg.findall(f)
        sig = np.array(pd.io.parsers.read_csv(f))

        EEG = sig[:,1:-2]
        EOG = sig[:,-2]
        Trigger = sig[:,-1]

        sigF = bandpass(EEG,[1.0,40.0],freq)
    
    
        idxFeedBack = np.where(Trigger==1)[0]
    
        for fbkNum,idx in enumerate(idxFeedBack):
            X.append(sigF[idx:idx+epoc_window,:])
            User.append(int(user))
            idFeedBack.append('S' + user + '_Sess' + session + '_FB' + '%03d' % (fbkNum+1) )
            Session.append(int(session))
            Feedback.append(fbkNum)
            Letter.append(mod(fbkNum,5) + 1)
            Word.append(floor(fbkNum/5)+1)
            FeedbackTot.append(fbkNum + (int(session)-1)*60)
            WordTot.append(floor(fbkNum/5)+1 + (int(session)-1)*12)
	
    Meta = array([Session,Feedback,Letter,Word,FeedbackTot,WordTot]).transpose()
    
    Meta2 = pd.read_csv('metadata.csv')
    currentUserSet = [True if val in set(User) else False for val in Meta2.subject]

    isLong = Meta2.isLong[currentUserSet].values
    Meta = np.c_[Meta,isLong]

    onlineErr = Meta2.onlineErr[currentUserSet].values
    longProp = Meta2.longProp[currentUserSet].values
    Meta_Leak = np.c_[Meta,onlineErr,longProp]

    if test is False:
        Labels = genfromtxt(DataFolder + 'TrainLabels.csv',delimiter=',',skip_header=1)[:,1]
        info = array([Labels,User])
    else:
        info = array([idFeedBack,User])

    X = array(X).transpose((0,2,1)) # Ns,Ne,Nt

    save(prefix + 'infos.npy',info)
    save(prefix + 'epochs.npy',X)
    save(prefix + 'meta.npy',Meta)
    save(prefix + 'meta_leak.npy',Meta_Leak)




================================================
FILE: results/submission_Leak.csv
================================================
IdFeedBack,Prediction
S01_Sess01_FB001,1.2042524637624576
S01_Sess01_FB002,1.384815789963214
S01_Sess01_FB003,1.0657049246558592
S01_Sess01_FB004,1.0948818625101477
S01_Sess01_FB005,1.2463781596342418
S01_Sess01_FB006,1.299165075863088
S01_Sess01_FB007,1.3268473703104111
S01_Sess01_FB008,1.0820500842526726
S01_Sess01_FB009,1.2911933512159837
S01_Sess01_FB010,1.0272775649864556
S01_Sess01_FB011,1.3933652616764203
S01_Sess01_FB012,1.5659297447237592
S01_Sess01_FB013,1.361128323526758
S01_Sess01_FB014,1.5130055003079779
S01_Sess01_FB015,1.4558773157189777
S01_Sess01_FB016,1.2197661720713882
S01_Sess01_FB017,1.565506621924476
S01_Sess01_FB018,1.5887459176135064
S01_Sess01_FB019,1.221481967363967
S01_Sess01_FB020,1.2327020644029842
S01_Sess01_FB021,1.1962286115480336
S01_Sess01_FB022,1.3789051418712908
S01_Sess01_FB023,1.261357254405306
S01_Sess01_FB024,1.264560365854679
S01_Sess01_FB025,1.6197785351500427
S01_Sess01_FB026,1.233915175126858
S01_Sess01_FB027,1.29892229489777
S01_Sess01_FB028,0.9534399115648807
S01_Sess01_FB029,1.3988684627230064
S01_Sess01_FB030,1.0665352155135541
S01_Sess01_FB031,1.416091472001396
S01_Sess01_FB032,1.5787232415641164
S01_Sess01_FB033,1.3154707104120789
S01_Sess01_FB034,1.6115708196328655
S01_Sess01_FB035,1.4191579763800672
S01_Sess01_FB036,1.1288989117714738
S01_Sess01_FB037,1.2841743521980329
S01_Sess01_FB038,1.3672865371151697
S01_Sess01_FB039,1.4713128693161266
S01_Sess01_FB040,1.1224992416836825
S01_Sess01_FB041,1.4334581400677893
S01_Sess01_FB042,1.1647252771805916
S01_Sess01_FB043,1.4234464136768614
S01_Sess01_FB044,1.0945925732661583
S01_Sess01_FB045,1.081517226652839
S01_Sess01_FB046,1.5696025927334079
S01_Sess01_FB047,1.3554872610990727
S01_Sess01_FB048,1.1614066383070667
S01_Sess01_FB049,0.8375081012411557
S01_Sess01_FB050,1.2654498288072142
S01_Sess01_FB051,1.5067441249070992
S01_Sess01_FB052,1.2966301738190324
S01_Sess01_FB053,1.2874728117225134
S01_Sess01_FB054,1.3536866546536204
S01_Sess01_FB055,1.3154304305854616
S01_Sess01_FB056,1.494400888275429
S01_Sess01_FB057,1.5997942931224345
S01_Sess01_FB058,1.2753062181720942
S01_Sess01_FB059,1.3565626667949235
S01_Sess01_FB060,1.6425262322247356
S01_Sess02_FB001,1.3219609603693978
S01_Sess02_FB002,1.2739395290357374
S01_Sess02_FB003,1.1167288185029394
S01_Sess02_FB004,1.3539543263349951
S01_Sess02_FB005,1.3394195779008888
S01_Sess02_FB006,1.353748879565011
S01_Sess02_FB007,1.326798063392144
S01_Sess02_FB008,1.458672892688564
S01_Sess02_FB009,1.4467605258988576
S01_Sess02_FB010,1.5987525697627687
S01_Sess02_FB011,1.344586059191054
S01_Sess02_FB012,1.3741086704638716
S01_Sess02_FB013,1.2495944666597971
S01_Sess02_FB014,1.3557101472777613
S01_Sess02_FB015,1.314768780202082
S01_Sess02_FB016,1.5717001421975398
S01_Sess02_FB017,1.17635252165007
S01_Sess02_FB018,1.086488672155768
S01_Sess02_FB019,1.1630996178090562
S01_Sess02_FB020,1.4139877725943428
S01_Sess02_FB021,1.4532408955649352
S01_Sess02_FB022,1.1699681859422904
S01_Sess02_FB023,1.2140005091771933
S01_Sess02_FB024,1.2582368122293934
S01_Sess02_FB025,1.2456744525291208
S01_Sess02_FB026,1.3180224444180122
S01_Sess02_FB027,1.3973283267252252
S01_Sess02_FB028,1.2576778958224852
S01_Sess02_FB029,1.176778889226786
S01_Sess02_FB030,1.3644119651637645
S01_Sess02_FB031,1.2718548363411162
S01_Sess02_FB032,1.2371186304290644
S01_Sess02_FB033,1.4974155478391926
S01_Sess02_FB034,1.4980353732018776
S01_Sess02_FB035,1.2525364170920534
S01_Sess02_FB036,1.4722545401150784
S01_Sess02_FB037,1.2079538428915244
S01_Sess02_FB038,1.1781383950282127
S01_Sess02_FB039,1.2926636543436216
S01_Sess02_FB040,1.51426242426898
S01_Sess02_FB041,1.5230087210839889
S01_Sess02_FB042,1.2475006677231426
S01_Sess02_FB043,1.186874596809318
S01_Sess02_FB044,1.6321149755699742
S01_Sess02_FB045,1.403796870972211
S01_Sess02_FB046,1.1635938112753461
S01_Sess02_FB047,1.4775107831033447
S01_Sess02_FB048,0.9702922287091957
S01_Sess02_FB049,1.5853690384575359
S01_Sess02_FB050,1.1289298250513076
S01_Sess02_FB051,1.4330309349905594
S01_Sess02_FB052,1.3096995868700283
S01_Sess02_FB053,1.420675350206787
S01_Sess02_FB054,1.3684049696138638
S01_Sess02_FB055,1.3645639199100925
S01_Sess02_FB056,1.4154124117935019
S01_Sess02_FB057,1.4686943304295688
S01_Sess02_FB058,1.0397439685522618
S01_Sess02_FB059,1.3975405583991345
S01_Sess02_FB060,1.3802513596799133
S01_Sess03_FB001,1.1439959038105916
S01_Sess03_FB002,1.3274838184147133
S01_Sess03_FB003,1.29860694431013
S01_Sess03_FB004,1.0819433536339842
S01_Sess03_FB005,1.3878147988913976
S01_Sess03_FB006,1.103742182989239
S01_Sess03_FB007,1.6350747903776193
S01_Sess03_FB008,1.3833667254845663
S01_Sess03_FB009,1.2138529856206746
S01_Sess03_FB010,1.1601163091112152
S01_Sess03_FB011,1.1748500227793972
S01_Sess03_FB012,1.272549522355753
S01_Sess03_FB013,1.1436159461997237
S01_Sess03_FB014,1.2497204612202581
S01_Sess03_FB015,1.1016106857881844
S01_Sess03_FB016,1.4898649028104598
S01_Sess03_FB017,1.5832349374432004
S01_Sess03_FB018,1.3700646134543426
S01_Sess03_FB019,1.296143756689304
S01_Sess03_FB020,1.2164407661591712
S01_Sess03_FB021,1.5898363187701299
S01_Sess03_FB022,1.533475807721569
S01_Sess03_FB023,1.668929272327559
S01_Sess03_FB024,1.662489017149066
S01_Sess03_FB025,1.3541252672939703
S01_Sess03_FB026,1.585897874010787
S01_Sess03_FB027,1.3933957231267695
S01_Sess03_FB028,1.4826668677485726
S01_Sess03_FB029,1.5719479692642282
S01_Sess03_FB030,1.2437254340174981
S01_Sess03_FB031,1.2117099425828666
S01_Sess03_FB032,1.5495113835876122
S01_Sess03_FB033,1.374669783315491
S01_Sess03_FB034,1.3221757386913575
S01_Sess03_FB035,1.5361628605647195
S01_Sess03_FB036,1.2995408618475857
S01_Sess03_FB037,1.3876086325626058
S01_Sess03_FB038,1.1960903796598599
S01_Sess03_FB039,1.264453526069453
S01_Sess03_FB040,1.4194505965267221
S01_Sess03_FB041,1.5150047392323986
S01_Sess03_FB042,1.4365023039251965
S01_Sess03_FB043,1.4672015951212853
S01_Sess03_FB044,1.361734047893874
S01_Sess03_FB045,1.3497546240421516
S01_Sess03_FB046,1.2271854432437241
S01_Sess03_FB047,1.615370037922939
S01_Sess03_FB048,1.5769048296611157
S01_Sess03_FB049,1.2936323027138243
S01_Sess03_FB050,1.362992082351193
S01_Sess03_FB051,1.1363034896338444
S01_Sess03_FB052,1.3742897437174404
S01_Sess03_FB053,1.2587988006630382
S01_Sess03_FB054,1.1248537238547682
S01_Sess03_FB055,1.6260485397104247
S01_Sess03_FB056,1.2451066586085484
S01_Sess03_FB057,1.215694862047924
S01_Sess03_FB058,1.3767450729953348
S01_Sess03_FB059,0.9973822395043495
S01_Sess03_FB060,1.508211292294999
S01_Sess04_FB001,1.355820221338711
S01_Sess04_FB002,1.400550861960112
S01_Sess04_FB003,1.2420543759685032
S01_Sess04_FB004,1.364723377058973
S01_Sess04_FB005,1.3732484731041283
S01_Sess04_FB006,1.3340383692575153
S01_Sess04_FB007,1.4359820735282076
S01_Sess04_FB008,1.2823667503529115
S01_Sess04_FB009,1.3724462003537923
S01_Sess04_FB010,1.3366027702488839
S01_Sess04_FB011,1.3319795670232577
S01_Sess04_FB012,1.0535594848821765
S01_Sess04_FB013,1.1685573565575034
S01_Sess04_FB014,1.311382009960981
S01_Sess04_FB015,1.4592168817821154
S01_Sess04_FB016,1.2973887714184997
S01_Sess04_FB017,1.2384592216002597
S01_Sess04_FB018,1.5698264626123297
S01_Sess04_FB019,1.2000808956140612
S01_Sess04_FB020,1.2446354752862803
S01_Sess04_FB021,1.360447571963002
S01_Sess04_FB022,1.6394890225571488
S01_Sess04_FB023,1.1906959268284583
S01_Sess04_FB024,1.3177701343216666
S01_Sess04_FB025,1.430518458655147
S01_Sess04_FB026,1.4156973980926157
S01_Sess04_FB027,1.2629048914230192
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S25_Sess05_FB047,1.238039403720892
S25_Sess05_FB048,0.7889756779322918
S25_Sess05_FB049,1.1873319683848527
S25_Sess05_FB050,1.1845948203576127
S25_Sess05_FB051,1.157424611135223
S25_Sess05_FB052,1.0377273552757642
S25_Sess05_FB053,0.9138044632727502
S25_Sess05_FB054,0.8701570676999104
S25_Sess05_FB055,0.6325653017632253
S25_Sess05_FB056,1.2426379123548137
S25_Sess05_FB057,0.8853829983114158
S25_Sess05_FB058,1.05366468111378
S25_Sess05_FB059,0.9667185311450056
S25_Sess05_FB060,1.0675675788311922
S25_Sess05_FB061,0.9042974261671158
S25_Sess05_FB062,0.8789636372126186
S25_Sess05_FB063,1.1255484082532838
S25_Sess05_FB064,0.8715280581613722
S25_Sess05_FB065,0.7857750937675297
S25_Sess05_FB066,0.934258130021773
S25_Sess05_FB067,1.0753473083363092
S25_Sess05_FB068,1.005712803838469
S25_Sess05_FB069,1.2489510516311317
S25_Sess05_FB070,1.3526436080031208
S25_Sess05_FB071,0.8091600677582859
S25_Sess05_FB072,1.166811829632001
S25_Sess05_FB073,1.2035123678300068
S25_Sess05_FB074,1.0203376040244052
S25_Sess05_FB075,1.454625752561037
S25_Sess05_FB076,1.2258938848197616
S25_Sess05_FB077,1.2499957903035548
S25_Sess05_FB078,1.156788638943761
S25_Sess05_FB079,1.1007077142895554
S25_Sess05_FB080,1.0043615177901353
S25_Sess05_FB081,0.6884622511372517
S25_Sess05_FB082,1.1808591168235938
S25_Sess05_FB083,0.8557838696969904
S25_Sess05_FB084,1.0440631759757664
S25_Sess05_FB085,1.2088779202197293
S25_Sess05_FB086,1.255171929383939
S25_Sess05_FB087,1.240876480225578
S25_Sess05_FB088,0.8284312203135662
S25_Sess05_FB089,0.7903546428799781
S25_Sess05_FB090,1.0284009343143121
S25_Sess05_FB091,1.375574762211854
S25_Sess05_FB092,1.3200013307723073
S25_Sess05_FB093,0.5071146335487996
S25_Sess05_FB094,1.244009959803691
S25_Sess05_FB095,0.9799319612402674
S25_Sess05_FB096,1.2328178568400117
S25_Sess05_FB097,0.9726798976091469
S25_Sess05_FB098,1.1945322723360947
S25_Sess05_FB099,1.350204650063937
S25_Sess05_FB100,0.908224665311704


================================================
FILE: results/submission_noLeak.csv
================================================
IdFeedBack,Prediction
S01_Sess01_FB001,0.5702150564299729
S01_Sess01_FB002,0.7821556815268756
S01_Sess01_FB003,0.5102936634746882
S01_Sess01_FB004,0.5151231254940448
S01_Sess01_FB005,0.6130136973870566
S01_Sess01_FB006,0.6942077625290399
S01_Sess01_FB007,0.6588219690797088
S01_Sess01_FB008,0.5443986478663876
S01_Sess01_FB009,0.6043584134370728
S01_Sess01_FB010,0.5275316252626667
S01_Sess01_FB011,0.8300329904025211
S01_Sess01_FB012,0.9652985755346953
S01_Sess01_FB013,0.7214914943912117
S01_Sess01_FB014,0.7926568848454579
S01_Sess01_FB015,0.8035687521779842
S01_Sess01_FB016,0.5960250575340728
S01_Sess01_FB017,0.9112582514458315
S01_Sess01_FB018,0.918796604319069
S01_Sess01_FB019,0.6671821694564348
S01_Sess01_FB020,0.6894420802535388
S01_Sess01_FB021,0.5709955884413173
S01_Sess01_FB022,0.7970237616000134
S01_Sess01_FB023,0.6601184613428869
S01_Sess01_FB024,0.6826453921276051
S01_Sess01_FB025,0.9373500724418258
S01_Sess01_FB026,0.6484877353128805
S01_Sess01_FB027,0.6313027646416984
S01_Sess01_FB028,0.3673126152703891
S01_Sess01_FB029,0.7345438063700757
S01_Sess01_FB030,0.42453126192288215
S01_Sess01_FB031,0.7850871390888785
S01_Sess01_FB032,0.9200224583431007
S01_Sess01_FB033,0.7368719497433085
S01_Sess01_FB034,0.959498508939947
S01_Sess01_FB035,0.8468939601142257
S01_Sess01_FB036,0.5141157786050651
S01_Sess01_FB037,0.6174360372409256
S01_Sess01_FB038,0.6696268197467888
S01_Sess01_FB039,0.7892226348879106
S01_Sess01_FB040,0.5523251619639666
S01_Sess01_FB041,0.7921110642227716
S01_Sess01_FB042,0.5563466915358165
S01_Sess01_FB043,0.7826463466411493
S01_Sess01_FB044,0.4783128340480781
S01_Sess01_FB045,0.5050474355352769
S01_Sess01_FB046,0.9310809225923509
S01_Sess01_FB047,0.7682196250701377
S01_Sess01_FB048,0.601569781854061
S01_Sess01_FB049,0.30519127786487277
S01_Sess01_FB050,0.6390517012834687
S01_Sess01_FB051,0.8508872817879695
S01_Sess01_FB052,0.6717526135412828
S01_Sess01_FB053,0.6691748948871263
S01_Sess01_FB054,0.716791629884055
S01_Sess01_FB055,0.675390364369885
S01_Sess01_FB056,0.8707811385729808
S01_Sess01_FB057,0.9976750339728295
S01_Sess01_FB058,0.6119105414335513
S01_Sess01_FB059,0.7210204563120035
S01_Sess01_FB060,1.0219557107549244
S01_Sess02_FB001,0.7295454560830642
S01_Sess02_FB002,0.6816564885888569
S01_Sess02_FB003,0.49098215546823265
S01_Sess02_FB004,0.7162283343664905
S01_Sess02_FB005,0.7014119691403626
S01_Sess02_FB006,0.728169624226656
S01_Sess02_FB007,0.7116467000157589
S01_Sess02_FB008,0.8035776927813914
S01_Sess02_FB009,0.7471722774403926
S01_Sess02_FB010,0.8746792649151981
S01_Sess02_FB011,0.7095337176615926
S01_Sess02_FB012,0.713353043921553
S01_Sess02_FB013,0.572435587432937
S01_Sess02_FB014,0.7827800568143997
S01_Sess02_FB015,0.6822442462644239
S01_Sess02_FB016,0.8763983440014622
S01_Sess02_FB017,0.541735379590119
S01_Sess02_FB018,0.49175348699904853
S01_Sess02_FB019,0.5868671917513678
S01_Sess02_FB020,0.7535177100119639
S01_Sess02_FB021,0.8105277594078785
S01_Sess02_FB022,0.5102278643874061
S01_Sess02_FB023,0.6341466771830965
S01_Sess02_FB024,0.639981653757688
S01_Sess02_FB025,0.578573433363628
S01_Sess02_FB026,0.6822649731341427
S01_Sess02_FB027,0.7317073079260208
S01_Sess02_FB028,0.5602163640690732
S01_Sess02_FB029,0.5403914160563815
S01_Sess02_FB030,0.6990542090108051
S01_Sess02_FB031,0.6246090503970604
S01_Sess02_FB032,0.6421000326320907
S01_Sess02_FB033,0.8873672652230937
S01_Sess02_FB034,0.7879616652074783
S01_Sess02_FB035,0.6097379956127652
S01_Sess02_FB036,0.7939063887409509
S01_Sess02_FB037,0.6254547033556666
S01_Sess02_FB038,0.5258604480481001
S01_Sess02_FB039,0.7145114915342711
S01_Sess02_FB040,0.7928909083912546
S01_Sess02_FB041,0.8741630768218569
S01_Sess02_FB042,0.6420123160969402
S01_Sess02_FB043,0.5564464697272095
S01_Sess02_FB044,0.9797494648701538
S01_Sess02_FB045,0.7553931297132068
S01_Sess02_FB046,0.590695669813416
S01_Sess02_FB047,0.8031618722125725
S01_Sess02_FB048,0.3324167458497452
S01_Sess02_FB049,0.8284511326446722
S01_Sess02_FB050,0.5382567331985915
S01_Sess02_FB051,0.7933249600484504
S01_Sess02_FB052,0.6758967138917339
S01_Sess02_FB053,0.8093749113028926
S01_Sess02_FB054,0.7501001280956983
S01_Sess02_FB055,0.6493774034923143
S01_Sess02_FB056,0.7701784390255698
S01_Sess02_FB057,0.8431794632705553
S01_Sess02_FB058,0.5157852183680347
S01_Sess02_FB059,0.710098988230139
S01_Sess02_FB060,0.6609674875072795
S01_Sess03_FB001,0.5753712120431596
S01_Sess03_FB002,0.682793370150589
S01_Sess03_FB003,0.6965122874344041
S01_Sess03_FB004,0.5585839240642232
S01_Sess03_FB005,0.8206196314126347
S01_Sess03_FB006,0.5403037716304803
S01_Sess03_FB007,0.9217270448262475
S01_Sess03_FB008,0.6839702829891314
S01_Sess03_FB009,0.6132609624152164
S01_Sess03_FB010,0.5623746541073441
S01_Sess03_FB011,0.5587707044456561
S01_Sess03_FB012,0.6283960206172731
S01_Sess03_FB013,0.5660192531178847
S01_Sess03_FB014,0.6166213960563597
S01_Sess03_FB015,0.511127290389623
S01_Sess03_FB016,0.7941359976999595
S01_Sess03_FB017,0.8732858042146976
S01_Sess03_FB018,0.7088423406595636
S01_Sess03_FB019,0.6727241362283516
S01_Sess03_FB020,0.7132469684848912
S01_Sess03_FB021,0.9475197743087882
S01_Sess03_FB022,0.8665070100765961
S01_Sess03_FB023,0.9709674962436656
S01_Sess03_FB024,1.0401938240375455
S01_Sess03_FB025,0.7526042948677023
S01_Sess03_FB026,0.9065241385126185
S01_Sess03_FB027,0.7478833146749313
S01_Sess03_FB028,0.8592026391402334
S01_Sess03_FB029,0.895572710300314
S01_Sess03_FB030,0.6036163810929873
S01_Sess03_FB031,0.6358264089264442
S01_Sess03_FB032,0.90705069568589
S01_Sess03_FB033,0.692431887778059
S01_Sess03_FB034,0.6843454281682316
S01_Sess03_FB035,0.8322218587534049
S01_Sess03_FB036,0.6121641340195679
S01_Sess03_FB037,0.7317155641751706
S01_Sess03_FB038,0.5687315058698625
S01_Sess03_FB039,0.5764686486813149
S01_Sess03_FB040,0.7350562481453384
S01_Sess03_FB041,0.8941492759447071
S01_Sess03_FB042,0.7879807987639819
S01_Sess03_FB043,0.7463405931332631
S01_Sess03_FB044,0.7142039824729348
S01_Sess03_FB045,0.7495647916442827
S01_Sess03_FB046,0.5937413126186014
S01_Sess03_FB047,0.9044747354190114
S01_Sess03_FB048,0.8470524111431057
S01_Sess03_FB049,0.5119621368094862
S01_Sess03_FB050,0.666745069640783
S01_Sess03_FB051,0.54292848443949
S01_Sess03_FB052,0.6985378941106842
S01_Sess03_FB053,0.5968705785171129
S01_Sess03_FB054,0.540655998636808
S01_Sess03_FB055,0.8646068377972257
S01_Sess03_FB056,0.6618666329817878
S01_Sess03_FB057,0.5605964367852357
S01_Sess03_FB058,0.73459029099299
S01_Sess03_FB059,0.43699254675320387
S01_Sess03_FB060,0.8377133459195095
S01_Sess04_FB001,0.7042615603110933
S01_Sess04_FB002,0.7178372248704129
S01_Sess04_FB003,0.5618745939329198
S01_Sess04_FB004,0.6506074056700907
S01_Sess04_FB005,0.7273972213484384
S01_Sess04_FB006,0.6953941004591547
S01_Sess04_FB007,0.743492001561779
S01_Sess04_FB008,0.6849449360146062
S01_Sess04_FB009,0.7503044131958306
S01_Sess04_FB010,0.6508167902450905
S01_Sess04_FB011,0.6295488768472335
S01_Sess04_FB012,0.5375569144751751
S01_Sess04_FB013,0.5535061030482632
S01_Sess04_FB014,0.6736064453318715
S01_Sess04_FB015,0.7396547246246439
S01_Sess04_FB016,0.6865411111387901
S01_Sess04_FB017,0.6477555031085787
S01_Sess04_FB018,0.8251220979618082
S01_Sess04_FB019,0.6408752051756735
S01_Sess04_FB020,0.5753692991724998
S01_Sess04_FB021,0.7345646552513277
S01_Sess04_FB022,0.9237763416254776
S01_Sess04_FB023,0.5394664435919323
S01_Sess04_FB024,0.7419456147043016
S01_Sess04_FB025,0.7497083582483356
S01_Sess04_FB026,0.6892964203061468
S01_Sess04_FB027,0.5573137163719345
S01_Sess04_FB028,0.5988662235687826
S01_Sess04_FB029,0.5628981748023628
S01_Sess04_FB030,0.6184069952646414
S01_Sess04_FB031,0.698686359250251
S01_Sess04_FB032,0.7292343507104626
S01_Sess04_FB033,0.63500073097425
S01_Sess04_FB034,0.40131598764111515
S01_Sess04_FB035,0.37015280118057386
S01_Sess04_FB036,0.6961432286659346
S01_Sess04_FB037,0.7709152307382806
S01_Sess04_FB038,0.6471764455872626
S01_Sess04_FB039,0.6526867075678641
S01_Sess04_FB040,0.7183265334735378
S01_Sess04_FB041,0.2991917673763331
S01_Sess04_FB042,0.6025561254983166
S01_Sess04_FB043,0.6907488497940695
S01_Sess04_FB044,0.6734004941077872
S01_Sess04_FB045,0.666056236787138
S01_Sess04_FB046,0.6173777077796319
S01_Sess04_FB047,0.7632464496394769
S01_Sess04_FB048,0.8052090445383346
S01_Sess04_FB049,0.7369745402630069
S01_Sess04_FB050,0.7088320387577163
S01_Sess04_FB051,0.5736087698391321
S01_Sess04_FB052,0.8283466585616678
S01_Sess04_FB053,0.7203730381733396
S01_Sess04_FB054,0.9054473470914014
S01_Sess04_FB055,0.711021709115731
S01_Sess04_FB056,0.7010075773689273
S01_Sess04_FB057,0.8327880516833565
S01_Sess04_FB058,0.8627961736776808
S01_Sess04_FB059,0.8481258150830124
S01_Sess04_FB060,0.7954985920750416
S01_Sess05_FB001,0.5009767601484126
S01_Sess05_FB002,0.5716644176745307
S01_Sess05_FB003,0.5319644780527967
S01_Sess05_FB004,0.6302884849372086
S01_Sess05_FB005,0.5882933699103566
S01_Sess05_FB006,0.5405596268959818
S01_Sess05_FB007,0.7228590010654251
S01_Sess05_FB008,0.6548007521834063
S01_Sess05_FB009,0.6599804564928262
S01_Sess05_FB010,0.5517201835915921
S01_Sess05_FB011,0.6432937924790675
S01_Sess05_FB012,0.5420344475690427
S01_Sess05_FB013,0.44943404228881895
S01_Sess05_FB014,0.5818560329021064
S01_Sess05_FB015,0.6105563790310187
S01_Sess05_FB016,0.6638568170145945
S01_Sess05_FB017,0.6629176856702961
S01_Sess05_FB018,0.8375104558855478
S01_Sess05_FB019,0.4910716896527304
S01_Sess05_FB020,0.8094830205325948
S01_Sess05_FB021,0.4580273929209639
S01_Sess05_FB022,0.682355831065595
S01_Sess05_FB023,0.5221833266154916
S01_Sess05_FB024,0.600700846264052
S01_Sess05_FB025,0.5982175761217413
S01_Sess05_FB026,0.7090345222730341
S01_Sess05_FB027,0.7944091501094594
S01_Sess05_FB028,0.5775669299513748
S01_Sess05_FB029,0.7802804353136207
S01_Sess05_FB030,0.5397721326930829
S01_Sess05_FB031,0.7645933644762591
S01_Sess05_FB032,0.7008239654575797
S01_Sess05_FB033,0.5975005396892684
S01_Sess05_FB034,0.7451498730008167
S01_Sess05_FB035,0.49401899711174757
S01_Sess05_FB036,0.7325287625683466
S01_Sess05_FB037,0.7094549062418757
S01_Sess05_FB038,0.5549502764267533
S01_Sess05_FB039,0.6436759272994612
S01_Sess05_FB040,0.5656045864936199
S01_Sess05_FB041,0.7934117447758552
S01_Sess05_FB042,0.7243347521981015
S01_Sess05_FB043,0.7152029474585937
S01_Sess05_FB044,0.6267366941519309
S01_Sess05_FB045,0.41124599827695085
S01_Sess05_FB046,0.7662918155191281
S01_Sess05_FB047,0.4857157708415977
S01_Sess05_FB048,0.6826677978069626
S01_Sess05_FB049,0.687020007023889
S01_Sess05_FB050,0.5834457011101899
S01_Sess05_FB051,0.6982897956030351
S01_Sess05_FB052,0.6878020384037229
S01_Sess05_FB053,0.5093301173276379
S01_Sess05_FB054,0.6311647486010599
S01_Sess05_FB055,0.7520938432250549
S01_Sess05_FB056,0.6180769298583693
S01_Sess05_FB057,0.6686685146814758
S01_Sess05_FB058,0.8377652309563947
S01_Sess05_FB059,0.5776732946841736
S01_Sess05_FB060,0.6583267552326785
S01_Sess05_FB061,0.5861871171578518
S01_Sess05_FB062,0.7168242840751972
S01_Sess05_FB063,0.7097359661849258
S01_Sess05_FB064,0.7643252620614271
S01_Sess05_FB065,0.39314051748254225
S01_Sess05_FB066,0.4344870684850393
S01_Sess05_FB067,0.7228126628260255
S01_Sess05_FB068,0.6737746588214539
S01_Sess05_FB069,0.6268810218129419
S01_Sess05_FB070,0.6753369964471504
S01_Sess05_FB071,0.9811003096245818
S01_Sess05_FB072,0.7310017077632217
S01_Sess05_FB073,0.5058522309958927
S01_Sess05_FB074,0.5839673525330783
S01_Sess05_FB075,0.59371156718645
S01_Sess05_FB076,0.5336032957835408
S01_Sess05_FB077,0.632314708590217
S01_Sess05_FB078,0.32364163691159575
S01_Sess05_FB079,0.6131172667528946
S01_Sess05_FB080,0.7287423144837911
S01_Sess05_FB081,0.6142206282799072
S01_Sess05_FB082,0.29678085615069766
S01_Sess05_FB083,0.6141736287444404
S01_Sess05_FB084,0.6729619320262712
S01_Sess05_FB085,0.34705126375179046
S01_Sess05_FB086,0.5309733707511984
S01_Sess05_FB087,0.6815282726051076
S01_Sess05_FB088,0.6647308995313178
S01_Sess05_FB089,0.5843148143619751
S01_Sess05_FB090,0.5445982731661035
S01_Sess05_FB091,0.6833125953181656
S01_Sess05_FB092,0.7903088957719394
S01_Sess05_FB093,0.502312580978289
S01_Sess05_FB094,0.5282232220587111
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================================================
FILE: riemann/__init__.py
================================================
from utils import *

================================================
FILE: riemann/utils.py
================================================
import numpy
from numpy import matrix, sqrt, diag, log, exp, mean, eye, triu_indices_from, zeros, cov, concatenate, triu
from numpy.linalg import norm, inv, eigvals
from numpy.linalg import eigh as eig
from scipy.linalg import eigvalsh

def sqrtm(Ci):
	D,V = eig(Ci)
	D = matrix(diag(sqrt(D)))
	V = matrix(V)
	Out = matrix(V*D*V.T)
	return Out

def logm(Ci):
    D,V = eig(Ci)
    Out = numpy.dot(numpy.multiply(V,log(D)),V.T)
    return Out
	
def expm(Ci):
	D,V = eig(Ci)
	D = matrix(diag(exp(D)))
	V = matrix(V)
	Out = matrix(V*D*V.T)
	return Out

def invsqrtm(Ci):
	D,V = eig(Ci)
	D = matrix(diag(1.0/sqrt(D)))
	V = matrix(V)
	Out = matrix(V*D*V.T)
	return Out

def powm(Ci,alpha):
	D,V = eig(Ci)
	D = matrix(diag(D**alpha))
	V = matrix(V)
	Out = matrix(V*D*V.T)
	return Out		
	
	
def distance(C0,C1):
    return sqrt((log(eigvalsh(C0,C1))**2).sum())
	
def geodesic(C0,C1,alpha):
    A = matrix(sqrtm(C0))
    B = matrix(invsqrtm(C0))
    C = B*C1*B
    D = matrix(powm(C,alpha))
    E = matrix(A*D*A)
    return E
	
def tangent_space(covmats,ref):
    Nt,Ne,Ne = covmats.shape
    Cm12 = invsqrtm(ref)
    idx = triu_indices_from(ref)
    T = zeros((Nt,Ne*(Ne+1)/2))
    coeffs = (sqrt(2)*triu(numpy.ones((Ne,Ne)),1) + numpy.eye(Ne))[idx]
    for index in range(Nt):
        tmp = numpy.dot(numpy.dot(Cm12,covmats[index,:,:]),Cm12)
        tmp = logm(tmp)
        T[index,:] = numpy.multiply(coeffs,tmp[idx])
    return T
 
#def untangent_space(T,ref):
#    Nt,Nd = T.shape
#    Ne = (sqrt(1+8*Nd)-1)/2
#    Cm12 = invsqrtm(ref)
#    idx = triu_indices_from(ref)
#    covmats = zeros((Nt,Ne,Ne))
#    for index in range(Nt):
#        tmp = logm(matrix(Cm12*covmats[index,:,:]*Cm12))
#        #fixme : not very efficient        
#        tmp = sqrt(2)*triu(tmp,1) + diag(diag(tmp))
#        T[index,:] = tmp[idx]
#    return T
 
def riemann_mean(covmats,tol=10e-9,maxiter=50):
    #init 
    Nt,Ne,Ne = covmats.shape
    C = numpy.mean(covmats,axis=0)
    k=0
    J = eye(2)
    nu = 1.0
    tau = 10e19
    crit = norm(J,ord='fro')
    # stop when J<10^-9 or max iteration = 50
    while (crit>tol) and (k<maxiter) and (nu>tol):
        k=k+1
        C12 = sqrtm(C)
        Cm12 = invsqrtm(C)
        T = zeros((Ne,Ne))
       
        for index in range(Nt):
            tmp =  numpy.dot(numpy.dot(Cm12,covmats[index,:,:]),Cm12)
            T += logm(matrix(tmp))
        
        #J = mean(T,axis=0)
        J = T/Nt        
        crit = norm(J,ord='fro')
        h = nu*crit
        if h < tau:            
            C = matrix(C12*expm(nu*J)*C12)
            nu = 0.95*nu
            tau = h
        else:
            print "bad"
            nu = 0.5*nu
        
    return C	
    
def logeuclid_mean(covmats):
    Nt,Ne,Ne = covmats.shape 
    T = zeros((Ne,Ne))
    for index in range(Nt):
        T+= logm(matrix(covmats[index,:,:]))
    C = expm(T/Nt)
    
    return C    

def logdet_mean(covmats,tol=10e-5,maxiter=50):
    #init 
    Nt,Ne,Ne = covmats.shape
    C = mean(covmats,axis=0)
    k=0
    J = eye(2)
    crit = norm(J,ord='fro')
    # stop when J<10^-9 or max iteration = 50
    while (crit>tol) and (k<maxiter) :
        k=k+1

        J = zeros((Ne,Ne))

        for Ci in covmats:
            J += inv(0.5*Ci + 0.5*C);
            
        J = J/Nt
        Cnew = inv(J)
        crit = norm(Cnew-C,ord='fro')
        C = Cnew
    #if k==maxiter:
    #    print 'Max iter reach'
    return C	

def euclid_mean(covmats):
    return mean(covmats,axis=0)    
    
def identity(covmats):    
    C = eye(covmats.shape[1])
    return C
    
def mean_covariance(covmats,metric='riemann',*args):
    options = {'riemann' : riemann_mean,
               'logeuclid': logeuclid_mean,
               'euclid' : euclid_mean,
               'identity' : identity,
               'logdet' : logdet_mean}
    C = options[metric](covmats,*args)
    return C
    
def covariances(X):
     Nt,Ne,Ns = X.shape
     covmats = zeros((Nt,Ne,Ne))
     for i in range(Nt):
         covmats[i,:,:] = cov(X[i,:,:])
     return covmats
     
def covariances_EP(X,P):
     Nt,Ne,Ns = X.shape
     Np,Ns = P.shape
     covmats = zeros((Nt,Ne+Np,Ne+Np))
     for i in range(Nt):
         covmats[i,:,:] = cov(concatenate((P,X[i,:,:]),axis=0))
     return covmats

def eegtocov(sig,window=128,overlapp=0.5,padding = True):
    X = []
    if padding:
        padd = numpy.zeros((int(window/2),sig.shape[1]))
        sig = numpy.concatenate((padd,sig,padd),axis=0)
        
    Ns,Ne = sig.shape
    jump = int(window*overlapp)
    ix = 0
    while (ix+window<Ns):
        X.append(cov(sig[ix:ix+window,:].T))
        ix = ix+jump
        
    return numpy.array(X)