## 2 Materials and Methods
### Data  
The steps described in this section include our procedures for data collection, noise reduction, feature extraction and normalization. This processing flow is illustrated in Figure 2. Our pipeline starts with data collection, then the data is preprocessed, and we perform feature extraction on the preprocessed data in the time, frequency, wavelet, statistical, and information-theoretic domains. Additionally, we added a normalization operation after the feature extraction step. The extracted features are classified using selected models.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature** & **Description** & **Formula** \\ \hline Lempel–Ziv Complexity (\(C_{\text{LZ}}\)) & The complexity–predictability of the signal [53; 60; 63; 64] & \(C_{\text{LZ}}=\frac{S(X)}{\log_{2}N}\) where \(S(X)\) is the number of unique patterns in sequence \(X\), and \(N\) is the sequence length. \\ \hline Entropy Rate (H(X)) & The uncertainty measure of the signal, representing the regularity of a signal when consecutive data points are related [53; 54; 55; 56] & \(H(X)=-\sum p(x)\log_{2}p(x)\) where \(p(x)\) represents the probability distribution of the signal values. \\ \hline \hline \end{tabular} Notes: In the Lempel–Ziv formula, \(S(X)\) denotes the number of unique patterns in sequence \(X\), and \(N\) is the sequence length. In the entropy rate, \(p(x)\) is the estimated probability distribution of signal values. Both features capture the signal’s complexity or unpredictability over time.  
\end{table}
Table 6: Information-Theoretic Features.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Feature** & **Description** & **Formula** \\ \hline Zeroth-Lag Cross-Correlation Coefficient (\(\rho_{xy}\)) & The agreement or similarity between two directional acceleration signals [53] & \(\rho_{xy}=\frac{\sum(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum(x_{i}-\bar{x})^ {2}\sum(y_{i}-\bar{y})^{2}}}\) \\ \hline Kurtosis (\(K\)) & The extent to which the distribution of signal amplitudes lies predominantly on the left of the mean amplitude [39; 53; 61] & \(K=\frac{\sum(x_{i}-\bar{x})^{4}}{N\cdot\sigma^{4}}\) \\ \hline Standard Deviation (\(\sigma\)) & Measure for signal spreading, defined as the square root of variance [53; 54] & \(\sigma=\sqrt{\frac{1}{N}\sum(x_{i}-\bar{x})^{2}}\) \\ \hline \hline \end{tabular} Notes: \(x_{i},y_{i}\) are the values of the signals \(x\) and \(y\); \(\bar{x},\bar{y}\) are their means. \(\sigma\) is the standard deviation. \(N\) is the total number of samples. The cross-correlation coefficient measures the similarity between two time series.  
\end{table}
Table 5: Statistical Features.  
Data Collection and Dataset Summary  
[PERSON] et al. [65] conducted a 5-week study collecting gait data from 24 participants using the MATLAB version 9.0 (R2016a) mobile app to sample accelerometer and gyroscope data from smartphones during walking. Intoxication simulation was achieved by having participants wear special goggles designed to simulate different BAC levels. The resulting data, including timestamps, was saved in CSV files for further analysis. This work focuses on signal processing features extracted from accelerometer data, excluding gyroscope data, with measurements represented in the x, y, and z axes. Nine subjects were excluded due to unreliable or insufficient data. Each subject performed 60 walking trials, with 5 segments corresponding to BAC levels of 0, 0.05, 0.12, 0.2, and 0.3, and with each segment lasting a minimum of 5 s. It is instructive to note that the study was approved by the university's IRB. All participants gave their informed consent, and no actual alcohol was consumed; intoxication was simulated using certified drunk goggles/busters. A synthetic version of our dataset can be found in Supplementary Materials