Table 1.

Handcrafted features used for autism spectrum disorder/typically developing (ASD/TD) classification.

Features	Formulation
1. Peak-Peak Mean (PPM)	PPM $=\frac{1}{H}\sum _{i=1}^H(x(P_i)-x(T_i))$ Where, Pi and Ti are the time indexes of peak and trough, respectively.
2. Mean Square Value (MSV)	MSV $=\frac{1}{N}\sum _{n=0}^{N-1}{x(n)}^2$
3. Variance (VAR)	VAR $={\sigma }^2=\frac{1}{N}\sum _{n=0}^{N-1}{\left[x(n)-\overline{x}\right]}^2$, $\overline{x}=\frac{1}{N}\sum _{n=0}^{N-1}x(n)$
	DFT (Discrete Fourier Transform): X$(k)=\sum _{n=0}^{N-1}x(n)e^{\frac{-j2\pi nk}{N}}\mathrm{\text{ k}}=0,\dots ,\mathrm{\text{N}}-1$
4. Power Spectral Sum (PSS)	PSS $=\sum _{k=0}^{N-1}\frac{1}{N}|\text{X}(\text{k}){|}^2$
5. Maximum Power Spectral Frequency (MPSF)	MPSF $=arg\underset{k}{max}\frac{1}{N}|\text{X}(\text{k}){|}^2$
6. Maximum Power Spectral Density (MPSD)	MPSD $=\underset{k}{max}\frac{1}{N}|\text{X}(\text{k}){|}^2$
	$m_n=\underset{-\infty }{\overset{\infty }{\int }}{\omega }^{n}X(\omega )d\omega$
7. Hjorth Parameter: Activity	Activity = m0
8. Hjorth Parameter: Mobility	Mobility $={(\frac{m_2}{m_0})}^{1/2}$
9. Hjorth Parameter: Complexity	Complexity $=\frac{{(\frac{m_4}{m_2})}^{1/2}}{{(\frac{m_2}{m_0})}^{1/2}}$
	Y $={\left[{\xi }_i,\dots ,{\xi }_N\right]}^T{\xi }_i=(x(t_i),x(t_i+\tau ),\dots ,x(t_i+(\text{m }-1)\tau ))$
10. Correlation Dimension (CD)	CD $=\underset{r\to 0}{\mathrm{\text{lim}}}\frac{log\text{C}(m,r)}{logr}$ $C(m,r)=\frac{1}{m^2}\sum _{i,j=1}^m\theta (r-|{\xi }_i-{\xi }_j|)$ Where, θ is a Heaviside step function; r is threshold of similarity.
11. Kolmogorov Entropy (KE)	KE $=\frac{1}{\tau }ln\frac{C(m,r)}{C(m+1,r)}$
12. Approximate Entropy (AE)	AE = Φm(r)−Φm+1(r) ${\Phi }^m(r)=\frac{1}{N-m+1}\sum _{i=1}^{N-m+1}\text{In}{C}_i^m(r)$ $C_i^m(r)=\frac{No.of{\xi }_j\left|\underset{j}{max}\right|{\xi }_i-{\xi }_j|\le r}{N-m+1}$ j ∈ [1, N − m + 1]
13. Sample Entropy (SaE)	SaE = −ln(Ψm+1(r)/Ψm(r)) ${\text{Ψ}}^m(r)=\frac{1}{N-m+1}\sum _{i=1}^{N-m+1}{C}_i^m(r)$ $C_i^m(r)=\frac{No.of{\xi }_j\left|\underset{j}{max}\right|{\xi }_i-{\xi }_j|\le r}{N-m}$ j ∈ [1, N − m + 1], j ≠ i
14. Lyapunov Exponent (LE)	$LE(i)=\underset{z\to \infty }{\mathrm{\text{lim}}}\frac{1}{z}{log}_2\frac{\left|\right|\delta {\xi }_i(z)\left|\right|}{\left|\right|\delta {\xi }_i(0)\left|\right|}$ Where, ||δξi(z)|| is the distance of two neighboring points in the i-th direction at time z.
15. Singular Spectrum Entropy (SSE)	SSE $=-\sum _j{p}_j(\text{s})log(p_j(s))$ Where, {pj(s)} is the probability distribution of singular spectrum value $\frac{s_m}{\sum _m{s}_m}$; sm is the eigenvalue of Y.
16. Permutation Entropy (PE)	PE $=-\sum _{i=1}^{m!}{p}_i(\pi )ln(p_i(\pi ))/\text{ln}(m!)$ Where, π is the order pattern; {pi(π)} is the probability distribution of π.
17. C0 Complexity	C0 $=\frac{\sum _{n=0}^{N-1}|x(n)-y(n){|}^2}{\sum _{n=0}^{N-1}|x(n){|}^2},$ $y(\text{n})=\frac{1}{N}\sum _{k=0}^{N-1}\text{Y}(k)e^{\frac{j2k\pi n}{N}}$ $\text{Y}\left(\text{k}\right)\text{=}\left\{\begin{array}{l}\text{X(k), }{\text{|X(k)|}}^2>\text{ PSS}\\ 0,{\text{|X(k)|}}^2\ge \text{ PSS}\end{array}\right\}$
18. Shannon Entropy (SE)	SE $=-\sum _i{p}_i(\text{x}(\text{n}))log(p_i(\text{x}(\text{n})))$ Where, {pi(x(n))} is the probability distribution of x(n).
19. Power Spectral Entropy (PSE)	PSE $=-\sum _i{p}_i(\text{PS})log(p_i(\text{PSS}))$ Where, {pi(PSS)} is the probability distribution of power spectral sum.
20. Differential Entropy (DE)	DE $=\frac{1}{2}log(2\pi e{\sigma }^2)$ Where, σ is the standard deviation of x(n).