**5.2 Performance of features**

To further estimate the performance of proposed ANFIS time-series prediction method and MFFV features, ANFIS time-series prediction method combined with power spectra features is used for comparison in Table 2. The average classification accuracy for ANFIS time-series prediction method combined with power spectra features is 82.8%, while MFFV features under ANFIS time-series prediction method obtain 91.0 in the average classification accuracy.


Table 2. Comparison of performance between power spectra and MFFV features under the use of ANFIS time-series prediction

#### **5.3 Statistical analysis**

Two-way analysis of variance (ANOVA) and multiple comparison tests [40] are performed in the experiments. The statistical analyses with two-way ANOVA are used to evaluate that the difference is significant or not for the two factors, methods and subjects. After analyzing with the two-way ANOVA, multiple comparison tests are used to estimate the *p*-values and significance of each pair of methods. The results of tests will be discussed in detail in the next section.

### **6. Discussion**

#### **6.1 Statistical evaluation of prediction methods**

ANFIS combines the advantage of NN with that of FIS. Moreover, the training of ANFIS is fast and it can generally converge from small data sets. These attractive properties are suitable for the prediction of non-stationary EEG signals. Table 1 lists the comparisons of performance among different prediction frameworks using power spectra features. In addition, two-way ANOVA and multiple comparison tests are performed to verify if the prediction methods are significantly different or not. The results indicate that AAR timeseries prediction method is much better than AAR parameter approach in classification accuracy (*p*-value 0.0007) that is improved by 10.7% on average, while ANFIS time-series prediction method is slightly better than AAR prediction method (*p*-value 0.0195). The classification accuracy increases by 5.1%. Accordingly, ANFIS time-series prediction has the best performance in classification accuracy among these three methods. The results deduce that ANFIS time-series prediction is the best prediction framework in MI classification.

#### **6.2 Statistical evaluation of features**

308 Fuzzy Inference System – Theory and Applications

ANFIS time-series prediction method are replaced by left and right AAR models. The lengths of windows for the AAR-parameter approach and AAR time-series prediction are all

The comparison results of classification accuracy among different time-series prediction using power spectra features are listed in Table 1. The average classification accuracy of AAR-parameter approach is 67.0%, while AAR time-series prediction is 77.7% in the average classification accuracy. ANFIS time-series prediction obtains the best average classification

To further estimate the performance of proposed ANFIS time-series prediction method and MFFV features, ANFIS time-series prediction method combined with power spectra features is used for comparison in Table 2. The average classification accuracy for ANFIS time-series prediction method combined with power spectra features is 82.8%, while MFFV features under ANFIS time-series prediction method obtain 91.0 in the average

Accuracy [%] Power Spectra MFFV S1 86.9 92.8 S2 84.2 88.5 S3 77.2 90.3 S4 88.6 93.9 S5 80.1 88.2 S6 79.8 92.0 Average 82.8 91.0 Table 2. Comparison of performance between power spectra and MFFV features under the

Two-way analysis of variance (ANOVA) and multiple comparison tests [40] are performed in the experiments. The statistical analyses with two-way ANOVA are used to evaluate that the difference is significant or not for the two factors, methods and subjects. After analyzing with the two-way ANOVA, multiple comparison tests are used to estimate the *p*-values and significance of each pair of methods. The results of tests will be

ANFIS combines the advantage of NN with that of FIS. Moreover, the training of ANFIS is fast and it can generally converge from small data sets. These attractive properties are

1-s windows, which are the same as that for the ANFIS time-series prediction.

accuracy (82.8%).

**5.2 Performance of features** 

classification accuracy.

Classification

use of ANFIS time-series prediction

discussed in detail in the next section.

**6.1 Statistical evaluation of prediction methods** 

**5.3 Statistical analysis** 

**6. Discussion** 

Wavelet-fractal features are extracted from wavelet data by modified fractal dimension. MFFVs are utilized to describe the characteristic of fractal features in different wavelet scales, which are greatly beneficial for the analysis of EEG data. The comparison of performance between power spectra and MFFV features under the use of ANFIS time-series prediction is listed in Table 2. In addition, two-way ANOVA and multiple comparison tests are performed again to validate whether the two features are significantly different. The results indicate that MFFV features are significantly better than power spectra features in classification accuracy (*p*-value 0.0030), which is improved by 8.2% on average. The results indicate that MFFV features are better. These two results also suggest that ANFIS prediction framework together with MFFV features is a good combination in BCI applications.

#### **6.3 Advantage of proposed method**

The proposed ANFIS prediction framework combined with MFFV features provides a good potential for EEG-based MI classification. Furthermore, the proposed method has other potential advantages as follows: Firstly, the MFFV features really improve the separability of MI data, because the power spectra feature extracted from the predicted signals results in poorer performance. Secondly, the MFFV features can effectively reduce the degradation of noise. In other words, the MFFV features are extracted by DWT and modified fractal dimension. The former obtains multiscale information of EEG signals while the latter decreases the effect of noise. It is because the calculation of an improved DBC method is proposed and applied to modified fractal dimension.
