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本数据集涵盖从《Physical Exercise Measurements with Accelerometer and Gyroscope》（zenodo.org）中提取的加速度计与陀螺仪时间序列特征，共包含5组特征集。 ### 特征集说明 1. 递归量化分析（Recurrence Quantification Analysis，简称RQA）特征集 • "RR" - 复发率（Recurrence rate） • "DET" - 确定性（Determinism），即长度≥lmin的对角线上的复发点总数 • "RATIO" - 确定性与复发率的比值（DET/RR） • "AVG" - 长度≥lmin的对角线的平均长度 • "MAX" - 长度≥lmin的对角线的最大长度 • "DIV" - 离散度（Divergence），即1/MAX • "LAM" - 层流性（Laminarity），即VLRP/TR • "TT" - 捕获时间（Trapping time），即长度≥lmin的垂直线的平均长度 • "MAX_V" - 长度≥lmin的垂直线的最大长度 • "TR" - 复发点总数量 • "DLRP" - 长度≥lmin的对角线上的复发点 • "DLC" - 长度≥lmin的对角线的总条数 • "VLRP" - 长度≥lmin的垂直线上的复发点 • "VLC" - 长度≥lmin的垂直线的总条数 该特征集通过Chaos01 R包计算得到，包链接：https://CRAN.R-project.org/package=Chaos01 本次计算选用的参数可使嵌入过程为加速度计/陀螺仪的每个轴生成单值向量，具体参数设置如下： | 函数参数 | 参数取值 | | ---- | ---- | | 嵌入维度（embedding dimension, dim） | 3 | | 嵌入延迟（embedding lag, lag） | 时间序列长度 | | 复发线最小长度（Minimal length of recurrence line, lmin） | 20 | 针对Chaos01工具，我们通过以下自定义函数计算eps参数： r # 为加速度计与陀螺仪计算Chaos01所需的eps参数 ---- get_eps <- function(input_data, scale = 1) { # 计算加速度计三轴数据的eps值 eps_a <- purrr::map_dbl(input_data$data, ~ .x |> select(Ax, Ay, Az) |> as.matrix() |> as.vector() |> sd()) |> mean() * scale # 计算陀螺仪三轴数据的eps值 eps_g <- purrr::map_dbl(input_data$data, ~ .x |> select(Gx, Gy, Gz) |> as.matrix() |> as.vector() |> sd()) |> mean() * scale return(list(a = eps_a, g = eps_g)) } 此外，"TREND"特征表示复发点数量随到主对角线距离变化的趋势，该特征通过nonlinearTseries R包计算得到，包链接：https://CRAN.R-project.org/package=nonlinearTseries ### 其余特征集说明 其余所有特征集均通过Python包tsfresh计算得到，官方文档地址：https://tsfresh.readthedocs.io/en/latest/index.html 本次使用的特征字典包含在名为`tsfresh_autocorr_spectral_features.py`的文件中。 2. 自相关特征集 > 相关计算接口参考： > 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. 频谱特征集 > 相关计算接口参考： > 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. RQA/频谱/自相关混合特征集 5. tsfresh全特征集 > 相关计算接口参考：https://tsfresh.readthedocs.io/en/latest/api/tsfresh.feature_extraction.html ### 所用软件版本 Python（版本3.8.10） tsfresh = 0.20.2 R（版本4.3.2） Chaos01 = 1.2.1版 nonlinearTseries = 0.3.0版