*1.5.3. Support vector machine (SVM)*

*w*(*s*, *τ*) = ∫

94 Evolving BCI Therapy - Engaging Brain State Dynamics

*1.4.5. Hilbert-Huang transform (HHT)*

**1.5. Feature classification**

*1.5.1. Bayesian classifier*

k-nearest neighbor (k-NNC) [31, 36].

*1.5.2. Linear discriminant classifier (LDA)*

−∞ ∞

where cross variance is calculated for the signal and some predefined waveform [26].

for tracing out the site of high frequency SSVEP components [17].

where, ψ\*(t) is the complex conjugate wavelet function, x(t) is the particular function and w(s,τ) is the wavelet coefficient corresponding to frequency related with scale s and time τ of the involved wavelet function. CWT works like template matching just like matched filter

Zhang et al. established the use of CWT technique for extracting features and classifying them in SSVEP-based BCI [16]. Kumari et al. transformed the CWT coefficients into feature vectors

HHT is a self-adaptive data analysis technique comprising empirical mode decomposition (EMD) and Hilbert spectral analysis (HAS) [27]. It can opt stationary and non-stationary signals analysis. An intrinsic mode function (IMF) is an oscillator function with time-varying

Huang et al. identified high frequency SSVEP signals using HHT in SSVEP-based BCI [18].

The classification algorithms designate boundaries between various targets in the feature space on the basis of feature vectors involved considering the as independent variables.

The classification methods for SSVEP signals are heterogeneous in nature, like Bayesian classifier [14], linear discriminant classifier (LDA) [29–31], support vector machine (SVM) [32–35],

Bayesian statistical classifier obtains the posterior probability P(y|x) as per prior probability of a feature vector for belonging to some particular class. The class that has got the maximum

LDA or Fisher's LDA (FLDA) classifies the data into various classes using hyper planes [36]. This classifier is successfully applied in BCI community despite of high computational time involvement. This classifier traces out an optimal projection that maximizes the distance

frequencies capable of depicting the local properties of non-stationary signals [28].

HHT remodeled the original signals into 11-order IMF with the help of EMD.

probability is the one to which the particular feature vector belongs.

P(y|x) <sup>=</sup> P(y)P(x|y) \_\_\_\_\_\_\_\_\_

*x*(*t*)*ψ* ∗ (*t*)*dt* (2)

P(x) (3)

SVM classifies the feature vectors into various classes by the concept of construction of one or more hyper planes. This classifier differs from LDA, as in this, the decision boundary or hyper plane escalates the margins that implies, the distance between the decision boundary and the training sample nearest to it [38]. While the hyper plane separates the training data set with maximal margin, it also maps them to a higher dimensional space [39]. The decision boundary followed up in SVM may be linear as well as non-linear depending upon the choice of kernel function (linear, cubic, polynomial, Gaussian or radial basis (RBF)) [40].

### **1.6. k-Nearest neighbor (k-NNC)**

The classification principle of k-NNC is that the features belonging to different classes get flocked up in different clusters while keeping the adjacent neighbors in one cluster. It considers k metric distances between the testing dataset features and those of the nearest classes for classifying a test feature vector. Although classification with k-NNC reduces the error probability in the decision but still it is not so commonly used in BCI community [41].
