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Feature Descriptions

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Ben Fulcher edited this page Feb 1, 2023 · 2 revisions

Short descriptions of each feature are provided here, but more detailed descriptions with visual depictions of the behavior of these features is on this GitBooks website. More information can be found by inspecting the C code (or inspecting the original implementation in hctsa).

Distribution

Properties of the data distribution (that ignore the time-ordering of values in the time series).

  • DN_HistogramMode_5: Mode of the z-scored distribution estimated using a 5-bin histogram.
  • DN_HistogramMode_10: Mode of the z-scored distribution estimated using a 10-bin histogram.

Extreme events

How extreme events are temporally distributed across the time series.

  • DN_OutlierInclude_p_001_mdrmd: Time intervals between successive extreme events above the mean.
  • DN_OutlierInclude_n_001_mdrmd: Time intervals between successive extreme events below the mean.

Symbolic

Features that involve symbolic transformations of a real-valued time series to a set of discrete symbols.

  • SB_BinaryStats_mean_longstretch1: Longest period of consecutive values above the mean.
  • SB_BinaryStats_diff_longstretch0: Longest period of successive incremental decreases.
  • SB_MotifThree_quantile_hh: Shannon entropy of two successive letters in an equiprobable 3-letter symbolization of the time series.
  • SB_TransitionMatrix_3ac_sumdiagcov: The trace of the covariance of the transition matrix between symbols in 3-letter alphabet.

Linear autocorrelation and periodicity

Statistics extracted from the linear autocorrelation properties of the time series (e.g., from the autocorrelation function or Fourier power spectrum).

  • CO_f1ecac: First 1/e crossing of the autocorrelation function.
  • CO_FirstMin_ac: First minimum of the autocorrelation function.
  • SP_Summaries_welch_rect_area_5_1: Total power in the lowest fifth of frequencies in the Fourier power spectrum.
  • SP_Summaries_welch_rect_centroid: Centroid of the Fourier power spectrum.
  • FC_LocalSimple_mean3_stderr: Mean error from a rolling 3-sample mean forecasting.
  • PD_PeriodicityWang_th0_01: Periodicity measure of Wang et al. (2007).

Nonlinear autocorrelation

Statistics involving nonlinear transformations of the time series and its past.

  • CO_trev_1_num: Time-reversibility statistic, ⟨(x_{t+1}−x_t)^3⟩_t.
  • CO_HistogramAMI_even_2_5: Automutual information, m = 2, τ = 5.
  • IN_AutoMutualInfoStats_40_gaussian_fmmi: First minimum of the automutual information function.

Successive differences

Statistics of the first derivative of the time series (the time series of incremental differences).

  • MD_hrv_classic_pnn40: Proportion of successive differences exceeding 0.04σ.
  • FC_LocalSimple_mean1_tauresrat: Change in correlation length after iterative differencing.
  • CO_Embed2_Dist_tau_d_expfit_meandiff: Exponential fit to successive distances in 2-dimensional embedding space.

Fluctuation analysis

Statistics of the long-range (self-affine) scaling of temporal fluctuations.

  • SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1: Proportion of slower timescale fluctuations that scale with DFA (50% sampling).
  • SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1: Proportion of slower timescale fluctuations that scale with linearly rescaled range fits.
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