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4.4.1 Classication Pipelines and Performance Measures

Each simulated signal is filtered with a bandpass 3rd order Butterworth filter between 0.1 and 20Hz, and decimated by a factor of 4. It is then segmented into

0.6 second trials Xistarting from stimulus offset. We present the performances of

three classification method, each one corresponding to one of the transfer learning

methods described in chapter3, section3.3. Each classification method is trained

on the source dataset and tested on each one of the target datasets.

The first classification method is a Riemannian classification algorithm known as the Minimum Distance to Riemannian Mean (MDRM). Presented by Barachant

et al. in [Barachant et al.,2010] to classify features in Motor Imagery based BCI,

this method uses the sample covariance matrix Σi of a trial Xi as a feature, and

estimates the centroid of each class in the training set by calculating the Riemannian mean of all the class features. For each new feature, its Riemannian distance to all centroids is calculated, and the smallest among these distances defines the winning class. Since we have simulated a P300 experiment, we use the extended covariance

matrix ˜Σi as a feature, presented in chapter3, section3.3.1and call this method

EC-Rie.

The second classification method, labeled OT, is based on Optimal Transporta- tion theory. Initially, we train a Linear Discriminant Analysis (LDA) classifier over the source dataset using spatiotemporal features. Then, for each target dataset, we compute the transport plan using a squared Euclidean cost between the target and

sourcedomains and transport the target feature vectors onto the source domain. The

entropic regularization parameter is equal to λ = 0.001; it is chosen to be as small as possible, so that the transport plan γ is sparse. Our preliminary experiments (not displayed here) showed that the results of OT are robust with respect to the value of the second regularization parameter, which is set equal to η = 0.1. The transported feature vectors are classified with the trained LDA classifier.

(a)Sourceand target simulations use the same for-

ward model. (b)

Sourceand target simulations use a different

forward model.

Figure 4.4: Performances of the three proposed transfer learning classifiers and the LDA

classifier as we increase peak amplitude trial-to-trial variability. Each classification method is denoted by a different color. For each method, the different lines correspond to different average amplitudes, which is how we model cross-session variability.

tiotemporal features. We create 50 bootstrap samples from the source dataset and train 50 LDA classifiers. For comparison purposes, we also train a single LDA classifier over the entire source dataset.

Since the classes in each dataset are unbalance, we evaluate the outcome of each method using Cohen’s kappa as a performance metric, as proposed by Thomas

et al. in [Thomas et al.,2013]. Cohen’s kappa is defined as k = 1 −1−acc

1−pch, where

accis the classification accuracy, and p_chis the hypothetical probability of chance

agreement. For a binary classification problem, pch = _I12((T P +F N )(T P +F P )+

(T N + F P )(T N + F N )), where I denotes the total amount of trials in the target dataset and T P, T N, F P, and F P denote the true positives, true negatives, false positives and false negatives respectively. Cohen’s kappa takes values between -1 and 1, with 0 being the chance level.

4.4.2 Amplitude variability

Figure4.4displays the results obtained when we modulate amplitude variability.

On figure4.4a, we can see that, for the same head model, the most robust methods

are OT, Ens and the simple LDA classifier. Since the SNR in these experiments is high, the Ens and LDA have an almost identical performance. EC-Rie also

Evaluation on Simulated Experiments 53

(a)Sourceand target simulations use the same for-

ward model. (b)

Sourceand target simulations use a different

forward model.

Figure 4.5: Performances of the three proposed transfer learning classifiers and the LDA

classifier as we increase peak latency trial-to-trial variability. Each classification method is denoted by a different color. For each method, the different lines correspond to different average latencies, which is how we model cross-session variability.

performance decrease for higher amplitude standard deviations can be attributed to the fact that amplitude variability transforms only one of the two responses, i.e. the target response. Therefore the invariance property does not hold any longer.

For the second forward model, the performance of all classifiers except for OT and EC-Rie are greatly changed. The simple LDA classifier only works well for high mean amplitude values, a behavior which is also reflected in the performance of the bagging classifier. This is due to the fact that we only change the mean amplitude of the target class, therefore the LDA features end up producing classes with a higher separability. When the amplitude is the same for both target and

sourcedomains, both methods classify every trial as a nontarget trial, which is why

the classification performance is equal to the chance level.

4.4.3 Latency variability

On figure4.5we present the results of our experiments when we modulate the

average peak latency np and the trial-to-trial variability through parameter σlat.

Concerning the results of the experiments when the forward model between source

and target is the same, we can see a performance deterioration on figure4.5afor

all classification methods as the trial-to-trial peak latency variability increases. As expected, the EC-Rie method performs less well than all others, since it mostly de-

(a)Sourceand target simulations use the same forward model.

(b)Sourceand target simulations use a different forward model.

Figure 4.6: Performances of the three proposed transfer learning classifiers and the LDA

classifier as we increase the noise. On the left, we show the effect of increasing the signal energy of the pink noise process that simulates background activity. On the right, we display the classification performances as a function of the SNR, which is decreased as we increase the standard deviation of the white additive noise. Each classification method is denoted by a different color.

pends on the correlation of each trial to the archetype target and nontarget responses.

For a different forward model, we can see on figure4.5bthat only OT performs well,

and its performance deteriorates as the trial-to-trial latency variability increases.

4.4.4 Background activity and noise variability

On figure4.6, we can see the results of the experiments in which we modulate

the background activity Nb and those in which we modulate the additive noise

N_a. Increases in the energy of the pink noise greatly affects OT for both the same

forward model and for a different forward model. On the other hand, OT seems not at all affected by decreases in the SNR that originate from additive white

Evaluation on Simulated Experiments 55

noise, which seems to mostly affect the EC-Rie method. While the LDA and the Bagging classifiers have a similar performance when the pink noise energy increases, the bagging classifier is more robust to additive white noise. When the forward model is different between source and target, the Ens and LDA classifiers seem to surprisingly perform better as the pink noise energy increases and as the SNR decreases. This is discussed in the next section.