# A CSI-Based Multi-Environment Human Activity Recognition Framework
## 2 Materials and Methods
### Data Pre-Processing
#### 2.4.5 Feature Selection
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Set of Features** & **Feature** & **Description** \\ \hline \multirow{4}{*}{Distribution tests} & Anderson-Darling test & The test result at a 0.05 level and the \(p\)-value \\  & chi-square test & The test result at a 0.05 level and the \(p\)-value \\  & Durbin-Watson test & The \(p\)-value \\  & Jarque-Bera test & The test result at a 0.05 level and the \(p\)-value \\  & Kolmogorov-Smirnov test & The test result at a 0.05 level and the \(p\)-value \\  & Lilliefors composite test & The test result at a 0.05 level and the \(p\)-value \\  & Runs test for randomness & The test result at a 0.05 level \\ \hline \multirow{4}{*}{Location tests} & Wilcoxon rank sum test for equal & The test result at a 0.05 level and the \(p\)-value \\  & Wilcoxon rank sum test for zero medians & The test result at a 0.05 level and the \(p\)-value \\  & Sign test for zero medians & The test result at a 0.05 level and the \(p\)-value \\  & One-sample and paired-sample \(t\)-test & The test result at a 0.05 level and the \(p\)-value \\  & two-sample \(t\)-test & The test result at a 0.05 level and the \(p\)-value \\ \hline \multirow{4}{*}{Sationary tests} & Ansari-Bradley two-sample test & The test result at a 0.05 level and the \(p\)-value \\  & two-sample F test & The test result at a 0.05 level and the \(p\)-value \\ \hline \multirow{4}{*}{Sationary tests} & Augmented Tukey-Fuller test & The test result at a 0.05 level and the \(p\)-value \\  & KPS test & The test result at a 0.05 level and the \(p\)-value \\  & Leybourne-McCabe test & The test result at a 0.05 level and the \(p\)-value \\  & Phillips-Perron test & The test result at a 0.05 level and the \(p\)-value \\  & Variance ratio test & The test result at a 0.05 level and the \(p\)-value \\  & Paired integration/stationarity tests & The test result at a 0.05 level and the \(p\)-value for both the signal and the signal differences. \\ \hline \multirow{4}{*}{Correlation} & Auto-correlation & Extract the time-series features from the auto-correlation sample signal \\  & Partial auto-correlation & Extract the time-series features from the partial auto-correlation sample signal \\  & Cross-correlation & Extract the time-series features from the cross-correlation between the first and \\  & Linear-correlation & Linear-correlation between the first and second halves of the signal \\  & Ljung-Box Q-test & The test result at a 0.05 level and the \(p\)-value \\  & [PERSON] collinearity diagnostics test & Strength of collinearity in the first and second halves of the signal \\ \hline Causation test & Granger causality tests & The test result at a 0.05 level and the \(p\)-value \\ \hline Heteroscedasticity & Engle test & The test result at a 0.05 level and the \(p\)-value \\ \hline \multirow{4}{*}{Cointegration} & Engle-Granger cointegration test & The test result at a 0.05 level and the \(p\)-value \\  & [PERSON] cointegration test & The test result at a 0.05 level and the \(p\)-value for the first and second halves of \\  & Instantaneous frequency & The signal \\ \hline \multirow{2}{*}{Spectral entropy} & Instantaneous frequency & Extract the time-series features from the temporal derivative of the oscillation \\  & & phase divided by \(2\pi\) \\ \hline Spectral entropy & Spectral entropy & Extract the time-series features from the spectral entropy of the signal \\ \hline \multirow{4}{*}{Audio features} & Spectral Centroid & Extract the time-series features from the spectral centroid of the signal \\  & Spectral Crest & Extract the time-series features from the spectral crest of the signal \\  & Spectral Decrease & Extract the time-series features from the spectral degrees of the signal \\  & Spectral Entropy & Extract the time-series features from the spectral entropy of the signal \\  & Spectral Flatness & Extract the time-series features from the spectral flatness of the signal \\  & Spectral Flux & Extract the time-series features from the spectral flux of the signal \\  & Spectral Kurtosis & Extract the time-series features from the spectral kurtosis of the signal \\  & Spectral Rolloff & Extract the time-series features from the spectral rolloff of the signal \\  & Spectral Skewness & Extract the time-series features from the spectral skewness of the signal \\  & Spectral Slop & Extract the time-series features from the spectral slope of the signal \\  & Spectral Spread & Extract the time-series features from the spectral spread of the signal \\  & MLR Spectrum & Extract the time-series features from the MEL spectrum of the signal \\  & Estimation of the fundamental frequency & Extract the time-series features from the fundamental frequency of the signal \\  & Signal loudness & Total loudness of the signal \\ \hline \hline \end{tabular}
\end{table}