_{1}

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The assessment of emotions with fractal dimensions of EEG signals has been attempted before, but the quantification of the intensity and duration of sudden and short emotions remains a challenge. This paper suggests a method for this purpose, by using a new fractal dimension algorithm and by adjusting the amplitude of the EEG signal in order to obtain maximal separation of high and low fractal dimensions. The emotion was induced by embedding a scary image at 20 seconds in landscape videos of 60 seconds length. The new method did not only detect the onset of the emotion correctly, but also revealed its duration and intensity. The intensity is based on the magnitude and impulse of the fractal dimension signal. It is also shown that Higuchi’s method does not always detect emotion spikes correctly; on the contrary, the region of the expected emotional response can be represented by fractal dimensions smaller than the rest of the signal, whereas the new method directly reveals distinct spikes. The duration of these spikes was 10 - 11 seconds. The magnitude of these spikes varied across the EEG channels. The build-up and cool-down of the emotions can occur with steep and flat gradients.

The assessment of emotions with fractal dimensions of EEG signals has been proposed in several studies [

The knowledge gap is therefore whether “acute” or sudden emotions or emotional changes can be determined with fractal dimensions of EEG signals and quantified in terms of intensity and duration. Furthermore it is of interest how quickly emotions build up and cool down. Acute emotions can be triggered with a startle reaction that involves little or no movement reflex. For example a startle reaction induced acoustically generates a movement reflex action and is therefore not considered an emotion per se [

Fuss [_{0})

where i and l are counters,

and

where f_{0} is the sampling frequency; y is the signal amplitude; and m is the amplitude multiplier.

The fractal dimension of the modified signal, FD, results from

where FD is the gradient and I is the intercept.

The aim of this research is to trigger a sudden emotion with a startle reaction by using a video method, and by applying a new fractal dimension processing method [

The EEG signals were recorded with the Mindset 24 EEG system (24 channels, Nolan Computer Systems, Conifer CO, USA) and an electro-cap (Electro-Cap International, Eaton OH, USA) for 60 s when a test person was watching three different screamer videos (prank videos). The videos showed landscape scenes for 60 seconds, and after 20 s a scary image (

The amplitude of the EEG signal (in mV) was converted to absolute values and filtered with a running average filter (sliding window filter, 1^{st} order Savitzky-Golay filter) with a window width of 2 s for identifying regions of higher amplitude.

The raw EEG signal was processed with Fuss’ method [

high and low fractal dimensions. This was achieved by identifying potential regions with high fractal dimensions from the running average filter, and expected regions with low fractal dimensions from 0 to 20 s (before the scary image), and after the high dimension regions. The entire 60 s signal was processed with a window width of 1 s (255 data), and the average fractal dimension was calculated for high and low dimension regions as well as of the entire signal. For this purpose, and according to Fuss’ method [_{max}, FD_{avg}, FD_{min}, were plotted against the decadic logarithm of the multiplier m. In order to find the optimal multiplier m, the following differentials and ratio were calculated:

The peak effect of Equations (5)-(7) can also be achieved when applying the following equation

Plotting z against m delivers the maximum z at the optimal m. The differentials are intended to maximize the difference between high and low FD; the ratio suppresses the low FD and enhances the high FD.

Subsequently, 24 EEG channels were processed per video experiment with multipliers m of 0.3, 0.03, 0.003, 0.0003, and 0.00003, in order to find the FD differences of different multipliers. The fractal dimension intensity or impulse I_{FD} of the spikes related to the emotion caused by the scary image was calculated from

where t denotes the duration of the spike.

In channel F8, the average absolute amplitude exceeded 5.5 mV within a time period from 24.5 s to 31 s; within this time period, the fractal dimensions were expected to be at a maximum. From

When calculating the average fractal dimensions of the time periods of the expected high and low fractal

dimensions with different amplitude multipliers m (

that the fractal dimension derived from the actual raw EEG signal with Fuss’ method [

As there were two options for the multiplier m, i.e. m = 0.003 (maximum differentials) and m < 0.0003 or 0.00003 (maximum ratio), multipliers from m = 0.3 to 0.00003 were evaluated in terms of changes to the fractal dimensions of the two channels (F3 and F8).

As the signal did not change anymore in terms of shape from m = 0.0003 to m = 0.00003, the universal amplitude multiplier was set to m = 0.0003 for further analyses. It has to be noted that the amplitude of the fractal dimension dropped when decreasing m, and approached zero (

Other channels of the EEG signal related to video 1 have smaller FD than channel F8 (

Comparing all 3 videos (^{nd} peak, whereas cool-down was very sharp and two-fold, interrupted by the 3^{rd} peak. In videos 2 and 3, the sharp onset was very steep (1 s) followed by a sharp cool down, some fluctuation, and finally a slow cool down phase. The duration of all three emotional phases (of videos 1 - 3) was about 10 - 11 s. The highest peak was found in video 3 and the smallest in video 2 (

Data | Videos | ||
---|---|---|---|

Video 1 | Video 2 | Video 3 | |

Maximum fractal dimension | 1.0401 | 1.0379 | 1.0503 |

Average fractal dimension | 1.0198 | 1.0132 | 1.0204 |

Standard deviation of the average | 0.0111 | 0.0086 | 0.0096 |

Impulse of the fractal dimension over 10.5 s | 0.2074 | 0.1390 | 0.2139 |

Fuss’ method or Modified Amplitude Fractal Dimension Method (MAFDM [

The optimization methods suggested by Fuss [

The method used in this paper, and described in detail in [

・ by adjusting the amplitude of the EEG signal with an optimal multiplier m, a maximal separation of high and low fractal dimensions can be achieved (

・ smaller amplitude multipliers filter the noise of the fractal dimension signal (cf. top and bottom subfigures of

・ smaller amplitude multipliers change the shape of the fractal dimension signal, reveal hidden chaotic behavior of an EEG signal, and enhance the fractal dimension of these signal segments.

It is suggested in this paper to quantify the emotional pressure with integrating the fractal dimension with time, in order to determine the fractal dimension impulse or intensity of emotion index, according to Equation (10). In order to standardize the method, it is proposed to process the EEG data (sampled with a frequency of 256 Hz) with an amplitude multiplier m of 0.0003 and a window width of 1 s (255 data). Changing the multiplier and the window width affects the fractal dimensions in terms of amplitude and shape. The correlation of this impulse with the actual subjective feeling of the affected person has to be validated in further studies.

This paper suggests a method for assessment of the intensity of emotions by calculating the fractal dimension of an EEG signal. This is achieved with a new fractal dimension algorithm, by adjusting the amplitude of the EEG signal in order to obtain maximal separation of high and low fractal dimensions. The algorithm returns Higuchi’s fractal dimension if the implemented amplitude multiplier m is sufficiently high (between 1 and infinity for EEG signals recorded in mV). It is shown in this paper that the best separation of high and low fractal dimensions is actually achieved on the other side of the multiplier spectrum, i.e. with extremely small multipliers (close to zero). In addition to the separation of fractal dimensions, small amplitude multipliers result in a filter effect by reducing the noise of the fractal dimension signal, as well as can provoke a shape change of the fractal dimension signal.

The emotion was induced by embedding a scary image at 20 seconds in landscape videos of 60 seconds length. The new method did not only detect the onset of the emotion correctly, but also revealed its duration and intensity. The intensity is based on the magnitude and impulse of the FD signal. The impulse resulted from integrating the FD signal over time. The duration of the emotions measured from the FD signal was 10 - 11 seconds. The build-up and cool-down of the emotions can occur with steep and flat gradients.

Franz KonstantinFuss, (2016) A Method for Quantifying the Emotional Intensity and Duration of a Startle Reaction with Customized Fractal Dimensions of EEG Signals. Applied Mathematics,07,355-364. doi: 10.4236/am.2016.74033