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Table 3 Features extracted from the compiled datasets

From: Animal-borne behaviour classification for sheep (Dohne Merino) and Rhinoceros (Ceratotherium simum and Diceros bicornis)

Feature Equation
Average signal magnitude \(\frac{1}{N}\sum\nolimits _{i=1}^{N}\sqrt{x_i^2 + y_i^2 + z_i^2}\)
Maximum value \({\text {max}}({\mathbf {x}})\)
Minimum value \({\text {min}}({\mathbf {x}})\)
Mean (\(\bar{x}\)) \(\frac{1}{N} \sum\nolimits _{i=1}^{N} x_i\)
Standard deviation (\(\sigma _x\)) \(\sqrt{ \frac{1}{N} \sum\nolimits _{i=1}^{N}(x_i - \bar{x})^2}\)
Variance \(\sigma^2_x\)
Skewness \(\frac{\frac{1}{N} \sum \nolimits_{i=1}^{N} (x_i - \bar{x})^3}{\sigma^3_x}\)
Kurtosis \(\frac{\frac{1}{N} \sum\nolimits _{i=1}^{N} (x_i - \bar{x})^4}{\sigma^4_x}\)
Energy \(\frac{1}{N} \sum\nolimits _{i=1}^{N} |X_i|^2\)
Spectral entropy \(\sum\nolimits _{i=1}^{N} P(x_i) \log \frac{1}{P(x_i)}\)
Pairwise correlation between the axes \(\frac{{\hbox {cov}}({{\mathbf {x}}}, {{\mathbf {y}}})}{\sigma_x \sigma_y}\)
  1. Each frame consists of N sequential samples, and x denotes a vector of these samples for each accelerometer axis, x, y and z. The FFT of x is denoted by X and the normalised power spectrum of x by \(P({\mathbf {x}})\). Cross-correlation is calculated for each axis pair (xy), (xz), and (yz). All features except average signal magnitude provide three values: one per axis