Selection of the optimal channel configuration for implementing wearable EEG devices for the diagnosis of mild cognitive impairment

Table 2 List of EEG features evaluated in this study

Feature	Mathematical expression
Absolute power spectrum density (APSD)^a	\(\frac{1}{N}\sum\limits_{n=1}^Nx(n){e}^{-i2\pi fn/N}\)
Relative power spectrum density (RPSD)	Absolute PSD of specific band/absolute PSD of total band
Differential asymmetry (DASM) [32]	Difference between absolute PSDs of inter-hemispheric electrode pairs
Rational asymmetry (RASM) [32]	Ratio between absolute PSDs of inter-hemispheric electrode pairs
Phase-amplitude coupling (PAC)^b[38]	\({\textrm{coherence}}_{fph}\left({X}_{ph},{\overset{\sim }{A}}_{ph}\right)\)
Shannon entropy (SE) [39]	\(-\sum\limits_{i=1}^Np\left({x}_i\right)\ln p\left({x}_i\right),\textrm{where}\sum\limits_{i=1}^Np\left({x}_i\right)=1\)
Hjorth parameters (HP)^c[40]	\(\textbf{Activity}\left(\boldsymbol{x}\right)=\frac{1}{N}\sum\limits_{i=1}^N{\left({x}_i-{\mu}_i\right)}^2\) \(\textbf{Mobility}\left(\boldsymbol{x}\right)=\sqrt{\frac{\upsigma \left({\textrm{x}}^{\prime}\right)}{\upsigma \left(\textrm{x}\right)}}\) \(\textbf{Complexity}\left(\boldsymbol{x}\right)=\frac{\textrm{Mobility}\left({\textrm{x}}^{\prime}\right)}{\textrm{Mobility}\left(\textrm{x}\right)}\)
Lyapunov exponent (LE)^d[41]	\(\lambda (i)=\frac{1}{i\Delta t}\frac{1}{K}\sum\limits_{\textrm{j}=1}^K\ln \frac{d_j(i)}{d_j(0)}\)
Hurst exponent (HE)^e[42]	log(R/S)/ log(N)
Kolmogorov complexity^f(KC) [43]	c(n)/b(n)

x represents the EEG time-series data and ^aN indicates the length of the data. ^b The coherence here is the coherence at frequency fph between the time-varying energy of the high-frequency signal (\({\overset{\sim }{A}}_{ph}\)) and the unfiltered raw signal believed to contain the modulating frequency (X_ph), ^cμ_i represents the mean of x, x^′ represents the derivative of x, and σ(x) represents the standard deviation of x. ^d ∆t is the sampling period of the EEG time series, K is the embedding dimension, d_j(0) is the initial distance from the jth point to its nearest neighbor, and d_j(i) is the distance between the jth pair of nearest neighbors after i discrete time steps. ^eN is the length of the data sample, R is the difference between the maximum deviation from the mean and the minimum deviation from the mean, and S is the standard deviation. ^fn is the length of the time-series data, c(n) reflects the relative complexity of the data, and b(n) is the ratio between n and log(n). The details are described in the Supplementary Material

ISSN: 1758-9193