Feature Overview Table

A high-level summary table of all catch22 features.

Note: All catch22 features are statistical properties of the z-scored time series - they aim to focus on the properties of the time-ordering of the data and are insensitive to the raw values in the time series.

In the following table, we give the original feature name (from the Lubba et al. (2019) paper), and a shorter name more suitable for use in feature descriptions. Features are also (loosely) categorised into broader conceptual groupings.

Each feature is listed according to the order in which it, along with its associated value, is returned by catch22 e.g., the first feature returned (i.e., #1) is always DN_HistogramMode_5.

#	Feature name	Short name	Category	Description
1	DN_HistogramMode_5	mode_5	Distribution shape	5-bin histogram mode
2	DN_HistogramMode_10	mode_10	Distribution shape	10-bin histogram mode
3	DN_OutlierInclude_p_001_mdrmd	outlier_timing_pos	Extreme event timing	Positive outlier timing
4	DN_OutlierInclude_n_001_mdrmd	outlier_timing_neg	Extreme event timing	Negative outlier timing
5	first1e_acf_tau	acf_timescale	Linear autocorrelation	First $1/e$ crossing of the ACF
6	firstMin_acf	acf_first_min	Linear autocorrelation	First minimum of the ACF
7	SP_Summaries_welch_rect_area_5_1	low_freq_power	Linear autocorrelation	Power in lowest 20% frequencies
8	SP_Summaries_welch_rect_centroid	centroid_freq	Linear autocorrelation	Centroid frequency
9	FC_LocalSimple_mean3_stderr	forecast_error	Simple forecasting	Error of 3-point rolling mean forecast
10	FC_LocalSimple_mean1_tauresrat	whiten_timescale	Incremental differences	Change in autocorrelation timescale after incremental differencing
11	MD_hrv_classic_pnn40	high_fluctuation	Incremental differences	Proportion of high incremental changes in the series
12	SB_BinaryStats_mean_longstretch1	stretch_high	Symbolic	Longest stretch of above-mean values
13	SB_BinaryStats_diff_longstretch0	stretch_decreasing	Symbolic	Longest stretch of decreasing values
14	SB_MotifThree_quantile_hh	entropy_pairs	Symbolic	Entropy of successive pairs in symbolized series
15	CO_HistogramAMI_even_2_5	ami2	Nonlinear autocorrelation	Histogram-based automutual information (lag 2, 5 bins)
16	CO_trev_1_num	trev	Nonlinear autocorrelation	Time reversibility
17	IN_AutoMutualInfoStats_40_gaussian_fmmi	ami_timescale	Linear autocorrelation structure	First minimum of the AMI function
18	SB_TransitionMatrix_3ac_sumdiagcov	transition_variance	Symbolic	Transition matrix column variance
19	PD_PeriodicityWang_th001	periodicity	Linear autocorrelation structure	Wang's periodicity metric
20	CO_Embed2_Dist_tau_d_expfit_meandiff	embedding_dist	Other	Goodness of exponential fit to embedding distance distribution
21	SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1	rs_range	Self-affine scaling	Rescaled range fluctuation analysis (low-scale scaling)
22	SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1	dfa	Self-affine scaling	Detrended fluctuation analysis (low-scale scaling)

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Catch24 (Catch22 + Mean + Std)

In some cases, in which scale and spread of the raw time-series values may be relevant to class differences, the two simple distributional moment features (using the catch24 flag in the software implementations) can be added. This will result in 24 features being calculated: the catch22 features in addition to the mean and standard deviation.

#	Feature name	Short name	Description
23	DN_Mean	mean	Mean
24	DN_Spread_Std	std	Standard deviation

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Feature Dependencies

Although the selection framework used to generate the catch22 feature set included a step to reduce redundancy, it was not designed to generate an independent set of features.

Pairwise Spearman Correlations

Below is an example of the generic non-independence of features. We have plotted the Spearman correlation coefficient between all pairs of features, quantifying the similarity of their outputs across a diverse range of 1000 empirical time series:

• We find a large cluster of features sensitive to the autocorrelation of a time series.

• We also find a small cluster of two highly correlated features, DN_HistogramMode_5 and DN_HistogramMode_10, which measure the mode of the z-scired time-series distribution using different numbers of bins.

This dependency structure should be taken in mind when interpreting the result of catch22 analyses: Does your dataset exhibit any of these generic dependencies, or some unique dependencies?

PC Loadings

Below is a similar plot, but with colour overlayed according to the weights onto the first three principal components:

Broadly,

• The first two principal components capture different aspects of the autocorrelation structure.

• The third principal component captures different aspects of the distribution symmetry.

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