A Polynomial fitting And KNN Based Approach For Improving Classification

A Polynomial fitting And K-NN Based Approach For Improving Classification Of Motor Imagery BCI Data:

A Polynomial fitting And K-NN Based Approach For Improving Classification Of Motor Imagery BCI Data By: Raed T. Aldahdooh Supervise: Prof. Ibrahim S. Abuhaiba

What is an EEG?:

An electroencephalogram is a measure of the brain's voltage fluctuations as detected from scalp electrodes. It is an approximation of the cumulative electrical activity of neurons. What is an EEG?

What is a BCI?:

BCIs read electrical signals or other manifestations of brain activity and translate them into a digital form that computers can understand, process, and convert into actions of some kind, such as moving a cursor or turning on a TV. BCI can help people with inabilities to control computers, wheelchairs , televisions, or other devices with brain activity. What is a BCI?

BCI … cont.:

BCI competitions have been organized to provide objective formal evaluation and comparison of alternative methods for EEG data taken under different imagery tasks. Many methods in the last decade have been reported to yield impressive results when applied to BCI data. speed and accuracy are the major issues that current research is attempting to solve in order to create realistic BCI systems in the near future. BCI … cont.

Motor imagery:

Motor imagery can be defined as a dynamic state during which an individual mentally simulates a given action. This type of phenomenal experience implies that the subject feels herself/himself performing the action . It corresponds to the so called internal imagery (or first person perspective) of sport psychologists. Motor imagery

Section 2 Materials and methods:

Section 2 Materials and methods

2.1. Data set description:

BCI competition 2003 data set Ia Datasets provided by University of Tuebingen, Germany. Description of Experiments : The datasets taken from a healthy subject. The subject was asked to move a cursor up (class 0) and down ( class1 ) on a computer screen, while his/her slow cortical potentials (SCPs ) were recorded. The subject received visual feedback of his/her SCPs, which were corrected for vertical eye movements. 2.1. Data set description

BCI competition 2003 data set Ia:

Brain activity was recorded from six different channels with sampling frequency of 256 Hz. BCI competition 2003 data set Ia Channel 1: A1 (left mastoid). Channel 2: A2 (right mastoid). Channel 3: FC3 (2 cm frontal of C3). Channel 4: CP3 (2 cm parietal of C3). Channel 5: FC4 (2 cm frontal of C4 ). Channel 6: CP4 (2 cm parietal of C4).

BCI competition data set Ia:

BCI competition data set Ia Every 896 column represent data from one channel. Number of column =6 ”channel ” * 896 = 5377 2-D Matrix data of 135 trials belonging to class 0 2-D Matrix data of 133 trials belonging to class 1 2-D Matrix has the dimension 293x5376 and contains 293 trials of test data

Curve fitting :

Curve fitting is the process of constructing a curve. Curve fitting, also known as regression analysis, is used to find the "best fit" line or curve for a series of data points . Curve fit will produce an equation that can be used to find points anywhere along the curve . Curve fitting

Least Squares Curve Fits:

Least Squares minimizes the square of the error between the original data and the values predicted by the equation . The major weakness of the Least Squared method is its sensitivity to outliers in the data. Least Squares Curve Fits

Fitting lines and polynomial curves to data points::

A first degree polynomial equation: line with slope a . a first degree polynomial equation is an exact fit through any two points. A second degree polynomial equation: a, b, and c are Coefficient. Fitting lines and polynomial curves to data points:

Channel 1 Curve Pattern:

S ignals of Channel 1 of class 0 reveal an upward curve pattern, whereas those of class 1 reveal a downward curve pattern, generally. Channel 1 Curve Pattern

2.2. Polynomial fitting:

Based on channel 1 curve observation , a feature extraction algorithm developed. For each of the trial signals of Channel 1, a second order polynomial is fitted directly to the raw signal of the trial. We denote the second order polynomial fitted to the trial signal by where a, b, and c are coefficients of the polynomial .. 2.2. Polynomial fitting

2.3. Feature extraction:

After estimating the coefficients a, b, and c Maximum value of downward shaped or Minimum value of upward shaped is computed as follows: values of b are generally negative for class 0 and positive for class 1 trials. The values of h for class 0 trials are generally greater than those of class 1 trials. 2.3. Feature extraction

Figs. 3a and 3b display the values of b and h estimated from the training dataset of Channel 1:

Figs. 3a and 3b display the values of b and h estimated from the training dataset of Channel 1 Based on these strong clues, they considered b and h values to be selected as features to classify two tasks.

Fig. 4 shows entire feature vectors extracted from the training set and the test set.:

Fig. 4 shows entire feature vectors extracted from the training set and the test set.

Validation Motivation:

Validation techniques are motivated by two fundamental problems in pattern recognition: model selection and performance estimation. Model selection Almost invariably, all pattern recognition techniques have one or more free parameters The number of neighbors in a kNN classification rule The network size, learning parameters and weights in MLPs Performance estimation Once we have chosen a model, how do we estimate its performance ? Validation Motivation

2.4. Validation procedure:

Speeding up classification algorithms depend on very small number of training signals . accuracy is a major concern when dealing with a limited number of trials for the training session . Cross-validation is the practice of partitioning the available training data into multiple subsets such that one or more of the subsets are used to estimate optimal values . Various cross-validation methods such as repeated random sub-sampling validation , K-fold cross-validation, and leave-one-out cross-validation. 2.4. Validation procedure

Validation …cont.:

Based on the repeated random sub-sampling validation technique we developed a classification procedure for the optimum choice of classification parameter(s ). They split the training set into a smaller training set sub-training set , a validation set , and a holdout set . Validation …cont.

2.5. Classification algorithms:

k-NN classification SVM classification MLP “ Multilayer perceptron's ” classification 2.5. Classification algorithms

Nearest Neighbour Rule:

Nearest Neighbour Rule Non-parametric pattern classification. Consider a two class problem where each sample consists of two measurements ( x,y ). k = 1 k = 3 For a given query point q, assign the class of the nearest neighbour. Compute the k nearest neighbours and assign the class by majority vote.

K Nearest Neighbors:

The key issues involved in training this model includes setting the variable K Validation techniques (ex. Cross validation) the type of distant metric Euclidean measure K Nearest Neighbors

Section 3 Results:

Section 3 Results

Result:

Accuracy may be influenced by the size of the training segment. For this purpose, they generated training segments with sizes of 2M = 40, 60, 100, 160, 220 and 268 . Totally 268 trials, the sizes of the corresponding holdout sets are 228, 208, 168, 108, 48 and 0. Training segment excludes the holdout set. Three segments were generated in order to observe the stability of the method. Result

Results of k-NN classification:

Based on the empirical work of Loftsgaarden and Quesenberry (1965 ), it was observed that a value of k near the square root number of the trials in the training set appears to give good results . The best k value of each splitting is searched in intervals between 50% and 200% of (M)^.5 , N is selected as 30. The test classification accuracy was defined as the percentage of the number of trials classified correctly in the test set over the total trials . Results of k-NN classification

Results of k-NN classification:

Results of k-NN classification The averages of the classification accuracies are in range between 87.7% and 90.6%. Using all trial and setting k equal to 16 (round of square 268). In this case the proposed method achieved 92.15% test accuracy.

Results of SVM classification:

SVM algorithm with Gaussian radial basis function. This kernel function is specified by the scaling factor The regularization parameter was set to its default value C = 1. The best r value of each splitting is searched in interval between 0.1 and 2.0, with step size of 0.1 . Procedure was applied N = 30 times for each splitting. Results of SVM classification

Results of SVM classification:

Results of SVM classification SVM algorithm achieved training accuracy in range between 79.8% and 85.3% The average values of testing accuracy are in range between 84.0% and 88.6%.

Results of MLP classification:

MLP with one hidden layer consisting of two nodes reveal best performance on the validation set . The results of training accuracy for three different training segments with sizes of 2M = 40, 60, 100, 160, 220 and 268 Results of MLP classification average values of the training accuracy in range between 79.8% and 89.4%.

Results of MLP classification:

Results of MLP classification MLP achieved testing accuracy in the range between 82.6% and 88.7%.

Results of the data set Ib:

Applying the similar steps of feature extraction and classification procedures to data set Ib. k-NN algorithm provided 57.2% whereas the ensemble classification provided 58.9 % test accuracy. Results of the data set Ib Compared to the results given in table1 , the ensembling two channels yielded slight improvement. Results of ensembling two channels

Performance comparison:

Performance comparison

conclusion:

The method is suitable for two-class signals reveali ng upward/downward curve behavior . Another good attribute of the proposed method is its simplicity in the feature extraction procedure. k-NN algorithm achieved much better performance than the SVM and the MLP algorithms in terms of not only classification accuracy but also speed . conclusion Reducing training and testing times and effort in designing BCI systems.