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Table 3 Set of features extracted to test the proposed scheme performance

From: Identifying smartphone users based on how they interact with their phones

TimeArithmetic mean\(\bar{s} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} s_{i}\)
TimeMinimum amplitude\(s_{min} = min\left( {s_{i} } \right)\)
TimeMaximum amplitude\(s_{max} = max\left( {s_{i} } \right)\)
TimeStandard deviation\(std\left( s \right) = \sigma = \sqrt {\frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {s_{i} - \overline{s} } \right)^{2} }\)
Timekurtosis\(kurtosis\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{4} }}{{N\sigma^{4} }}\)
TimeSkewness\(skewness\left( s \right) = \mathop \sum \limits_{i}^{N} \frac{{\left( {s_{i} - \overline{s} } \right)^{3} }}{{N\sigma^{3} }}\)
TimeSignal magnitude area\(sma\left( s \right) = \frac{1}{3}\mathop \sum \limits_{i = 1}^{3} \mathop \sum \limits_{j = 1}^{N} \left| {s_{i,j} } \right|\)
TimeMedian absolute deviation\(mad\left( s \right) = median_{i} \left( {\left| {s_{i} - median_{{j\left( {s_{j} } \right)}} } \right|} \right)\)
TimeInterquartile range\(iqr\left( s \right) = Q3\left( s \right) - Q1\left( s \right)\)
TimeAutoregression\(a=arburg\left( s,4 \right), \, \!\! \!\! \, a\epsilon {{\mathbb{R}}^{4}}\)
TimeSum vector magnitude\(\left| s \right| = \sqrt {s_{i, x}^{2} + s_{i, y}^{2} + s_{i, z}^{2} }\)
TimeAngle between z-axis and vertical\(\theta 1 = atan2\left( {\sqrt {s_{i,x}^{2} + s_{i,y}^{2} } ,s_{i, z} } \right)\)
TimeOrientation of a person’s trunk\(\theta 2 = {\text{atan}}\left( {\sqrt {s_{i, x}^{2} + s_{i, y}^{2} } /s_{i, z} } \right)\)
TimeAngle between device and ground\(\theta 3 = \sin \left( s \right)\)
FrequencyMaximum frequency index\(maxFreqInd\left( S \right) = arg \,max_{i} \left( {S_{i} } \right)\)
FrequencyMean frequency\(mean\,freq\left( S \right) = \mathop \sum \limits_{i = 1}^{N} \left( {iS_{i} } \right)/\mathop \sum \limits_{j = 1}^{N} S_{j}\)
FrequencyEnergy\(E_{f} = \sum \left| {S\left( f \right)} \right|^{2}\)
FrequencyEntropy\(H\left( {S\left( f \right)} \right) = - \mathop \sum \limits_{i = 1}^{N} p_{i} \left( {S\left( f \right)} \right) \log_{2} p_{i} \left( {S\left( f \right)} \right)\)
  1. *Here \(s\). represents a 3D signal, \(i\) and \(j\) signify the signal index, \(s_{i, x}\)., \(s_{i, y}\), and \(s_{i, z}\) denote the signal value along x, y, and z-axis of the sensor, respectively,\(Q1\) and \(Q3\) represent the first and third signal quartile, \(N\) is the total number of samples in a data chunk, \(S\) is the Fourier transform of signal \(s\), and \(p\) is the probability