Table 3 Set of features extracted to test the proposed scheme performance
From: Identifying smartphone users based on how they interact with their phones
Domain | Feature | Equation* |
|---|---|---|
Time | Arithmetic mean | \(\bar{s} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} s_{i}\) |
Time | Minimum amplitude | \(s_{min} = min\left( {s_{i} } \right)\) |
Time | Maximum amplitude | \(s_{max} = max\left( {s_{i} } \right)\) |
Time | Standard deviation | \(std\left( s \right) = \sigma = \sqrt {\frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {s_{i} - \overline{s} } \right)^{2} }\) |
Time | kurtosis | \(kurtosis\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{4} }}{{N\sigma^{4} }}\) |
Time | Skewness | \(skewness\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{3} }}{{N\sigma^{3} }}\) |
Time | Signal magnitude area | \(sma\left( s \right) = \frac{1}{3}\mathop \sum \limits_{i = 1}^{3} \mathop \sum \limits_{j = 1}^{N} \left| {s_{i,j} } \right|\) |
Time | Median absolute deviation | \(mad\left( s \right) = median_{i} \left( {\left| {s_{i} - median_{{j\left( {s_{j} } \right)}} } \right|} \right)\) |
Time | Interquartile range | \(iqr\left( s \right) = Q3\left( s \right) - Q1\left( s \right)\) |
Time | Autoregression | \(a=arburg\left( s,4 \right), \, \!\! \!\! \, a\epsilon {{\mathbb{R}}^{4}}\) |
Time | Sum vector magnitude | \(\left| s \right| = \sqrt {s_{i, x}^{2} + s_{i, y}^{2} + s_{i, z}^{2} }\) |
Time | Angle between z-axis and vertical | \(\theta 1 = atan2\left( {\sqrt {s_{i,x}^{2} + s_{i,y}^{2} } ,s_{i, z} } \right)\) |
Time | Orientation of a person’s trunk | \(\theta 2 = {\text{atan}}\left( {\sqrt {s_{i, x}^{2} + s_{i, y}^{2} } /s_{i, z} } \right)\) |
Time | Angle between device and ground | \(\theta 3 = \sin \left( s \right)\) |
Frequency | Maximum frequency index | \(maxFreqInd\left( S \right) = arg \,max_{i} \left( {S_{i} } \right)\) |
Frequency | Mean frequency | \(mean\,freq\left( S \right) = \mathop \sum \limits_{i = 1}^{N} \left( {iS_{i} } \right)/\mathop \sum \limits_{j = 1}^{N} S_{j}\) |
Frequency | Energy | \(E_{f} = \sum \left| {S\left( f \right)} \right|^{2}\) |
Frequency | Entropy | \(H\left( {S\left( f \right)} \right) = - \mathop \sum \limits_{i = 1}^{N} p_{i} \left( {S\left( f \right)} \right) \log_{2} p_{i} \left( {S\left( f \right)} \right)\) |