Features computed from physical exercises measurements

The data represents time series features from an accelerometer and gyroscope extracted from Physical Exercise Measurements with Accelerometer and Gyroscope (zenodo.org). The data consists of 5 feature sets.

Description of feature sets:

1.     RQA features set

• "RR" - Recurrence rate• "DET" - Determinism, count recurrence points in diagonal lines of length >= lmin• "RATIO" - DET/RR• "AVG" - average length of diagonal lines of length >= lmin• "MAX" - maximal length of diagonal lines of length >= lmin• "DIV" - Divergence, 1/MAX• "LAM" - Laminarity, VLRP/TR• "TT" - Trapping time, average length of vertical lines of length >= lmin• "MAX_V" - maximal length of vertical lines of length >= lmin• "TR" - Total number of recurrence points• "DLRP" - Recurrence points on the diagonal lines of length of length >= lmin• "DLC" - Count of diagonal lines of length of length >= lmin• "VLRP" - Recurrence points on the vertical lines of length of length >= lmin• "VLC" - Count of vertical lines of length of length >= lmin

Was calculated by Chaos01 R package.

https://CRAN.R-project.org/package=Chaos01

The parameters were chosen so that the embedding will create a vector of one value of each axis of the accelerometer/gyroscope measurements. Therefore the used parameters were:

Function argument
Value

embedding dimension (dim)
3

embedding lag (lag)
time series length

Minimal length of recurrence line (lmin)
20

For Chaos01 we change eps argument and calculated it by following formula:

# Calculate eps for acc and gyro Chaos 01----

get_eps <- function(input_data, scale = 1) {

  # Calculate eps for acc and gyro

  eps_a <-

    purrr::map_dbl(input_data$data,

                   ~ .x |>

                     select(Ax, Ay, Az) |>

                                              as.matrix() |>

                                              as.vector() |>

                                               sd()) |>

                                               mean() * scale

  eps_g <-

    purrr::map_dbl(input_data$data,

                   ~ .x |>

                                             select(Gx, Gy, Gz) |> 

                                              as.matrix()

                                             as.vector() |>

                                              sd()) |>

                                              mean() * scale

return(list(a = eps_a, g = eps_g))

}

"TREND" - Trend of the number of recurrent points depending on the distance to the main diagonal.

Was calculated by nonlinearTseries R package.

 https://CRAN.R-project.org/package=nonlinearTseries

All following feature sets was calculated by Python package

https://tsfresh.readthedocs.io/en/latest/index.html

The used dictionary is included in file named tsfresh_autocorr_spectral_features.py.

2.     Autocorrelation features set

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.autocorrelation

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.agg_autocorrelation

3.     Spectral features set

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.fft_aggregated

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.approximate_entropy

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.fft_coefficient

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.fourier_entropy

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.spkt_welch_density

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html#tsfresh.feature_extraction.feature_calculators.ar_coefficient

4.     Mix RQA/Spectral/Autocorrelation features set

5.     Tsfresh all features set

#https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html

Versions of the software:

Python (version 3.8.10)

tsfresh = 0.20.2

R (version 4.3.2)

Chaos01 = Version 1.2.1

nonlinearTseries = 0.3.0