# Automating Stimulation Frequency Selection for SSVEP-Based Brain-Computer Interfaces
## 5 Experimental Evaluation
### Pre-Processing and Descriptive Statistics
As can be seen from the figure above, subject 3 demonstrated the most stable threshold overcoming response at photostimuli frequencies from 13 to 18 Hz, as well as at 21 and 24 Hz, according to the \(K_{o}\) coefficient, calculated for the fundamental frequency (O2 and Oz leads). Although the level of his response in terms of the reaction _speed_ criterion \(K_{sp}\) at the fundamental frequency was high enough from the stimulus frequency of 13 Hz to 25 Hz (Figure 3), the coefficient \(K_{o}\) showed that not all of these photostimulus frequencies were able to produce a _stable_ response. It can also be noted that while the \(K_{sp}\) coefficient, calculated for the second harmonic, (Figure 3) identified photostimuli frequencies from 6 to 9 Hz as acceptable in terms of reaction _speed_, the \(K_{o}\) coefficient showed that only the stimulus frequency at 9 Hz from the mentioned range was able to produce a _stable_ response at the second harmonic of photostimulus (O1, O2, and Oz leads). This example demonstrates that if one photostimulus frequency may be acceptable under one criterion, it does not mean that it will be acceptable under another criterion. Tables 3 and 4 contain the results of calculating the \(K_{o}\) coefficient in the Oz lead for all subjects who participated in the experiment. Figure 4: Threshold overcoming coefficient values for subject 3.  
results obtained for the \(K_{o}\) coefficient values remain very low, except for the 13-16 Hz photostimulus frequencies for the \(K_{o}\) coefficient calculated at the fundamental frequency and the 22 Hz photostimulus frequency for the \(K_{o}\) coefficient calculated for the second harmonic (44 Hz in Table 4). The results of calculating the \(K_{fa}\) coefficient for subject 3 are shown in Figure 5. According to the \(K_{fa}\) coefficient formula (Equation (5)), the values close to one correspond to the photostimuli frequencies that evoke the fastest and most stable SSVEP potentials. Thus, this coefficient integrates both \(K_{sp}\) and \(K_{o}\) coefficients and provides an indication of the frequency optimality according to two criteria at once. Thus, in the case of subject 3, the photostimuli frequencies at 13, 15-18, 21, and 24 Hz correspond to high-enough (at least 0.95) values of the coefficient \(K_{fa}\), calculated for the fundamental frequency (O2 and Oz leads). At the same time, for the \(K_{fa}\) coefficient calculated for the second harmonic, the photostimuli frequencies of 9, 13, 15, and 17 Hz correspond to values exactly equal to one (O1, O2, and Oz leads). It should be noted that for this participant, the photostimulus frequencies of 13, 15, and 17 Hz have maximum values of the \(K_{fa}\) coefficient at the second harmonic. This further validates the relevance of evaluating the response not only at the fundamental frequency but also at its harmonics. The \(K_{fa}\) coefficient values calculated for all other subjects are presented in Tables 5 and 6. Due to the fact that the \(K_{fa}\) coefficient takes into account both \(K_{sp}\) and \(K_{o}\) coefficients, it can be used as an indicator of frequency optimality in terms of response speed and stability. For example, subject 7 demonstrated equal-to-one values for the \(K_{fa}\) coefficient calculated for fundamental frequency (Table 5) in the photostimuli frequency range from 7 to 24 Hz because of high values for \(K_{sp}\) (Table 1) and \(K_{o}\) (Table 3) coefficients. Similar values of the \(K_{fa}\) coefficient calculated for the second harmonic are achieved for this subject in the first half of the used frequency range (Table 6). Analyzing the \(K_{fa}\) coefficient values for subject 3, who previously demonstrated very low values of \(K_{sp}\) (Tables 1 and 2) and \(K_{o}\) (Tables 3 and 4) coefficients, the corresponding results can be seen. Thus, according to Table 5, the subject only has 3 values of the \(K_{fa}\) coefficient calculated for the fundamental frequency, namely, for 13, 15, and 16 Hz, which are close enough to one.