Distribution shape

The DN_HistogramMode features measure properties of the shape of the distribution of time-series values.

catch22 contains two features involving the DN_HistogramMode function in hctsa:

• mode_5 (the hctsa feature DN_HistogramMode_5)

• mode_10 (the hctsa feature DN_HistogramMode_10)

Note: The C implementation of these features (in catch22) does not map perfectly onto the hctsa implementation, due to slight differences in how the histogram bins are constructed. But the trends are similar.

What it does

These functions involve computing the mode of the z-scored time-series through the following steps:

1. z-score the input time series.

2. Compute a histogram using a given number of (linearly spaced) bins, e.g., 5 bins for mode_5 and 10 bins for mode_10.

3. Return the location of the bin with the most counts.

What these features measure

Being distributional properties, these features are completely insensitive to the time-ordering of values in the time series. Instead, they capture how the most probable time-series values are positioned relative to the mean.

Example 1: Gaussian-distributed noise

Time series with a symmetric distribution, with a central peak, will have a mode near the center, and value close to zero. Here is an example of Gaussian-distributed noise:

Feature output: -0.36

Example 2: Chirikov Map

Time series with a symmetric distribution but with density far from the origin, like this Chirikov map obtain high (positive or negative) values:

Feature output: 1.26

Example 3: Beta-distributed noise

Time series with positively skewed distributions, like this example of beta-distributed noise obtain negative values as shown below:

Feature output: -0.805

Similarly, a negatively skewed distribution will yield positive values.