Structure of the hctsa framework

Overview

The hctsa framework consists of three basic objects containing relevant metadata:

1. Master Operations specify pieces of code (Matlab functions) and their inputs to be computed. Taking in a single time series, master operations can generate a large number of outputs as a Matlab structure, each of which can be identified with a single operation (or 'feature').

2. Operations (or 'features') are a single number summarizing some measure of structure in a time series. In hctsa, each operation links to an output from a piece of evaluated code (a master operation).

3. Time series are univariate and uniformly sampled time-ordered measurements.

These three different objects are summarized below:

	Master Operation	Operation	Time Series
Summary:	Code and inputs to execute	Single feature	Univariate data
Example:	CO_AutoCorr(x,1:5,'TimeDomain')	AC_1	[1.2, 33.7, -0.1, ...]

In the example above, a master operation specifies the code to run, CO_AutoCorr(x,1:5,'TimeDomain'), which outputs the autocorrelation of the input time series (x) at lags 1, 2, ..., 5. Each operation (or 'feature') is a single number that draws on this set of outputs, for example, the autocorrelation at lag 1, which is named AC_1, for example.

In the hctsa framework, master operations, operations, and time series are stored as tables that contain all of their associated keywords and metadata (and actual time-series data in the case of time series).

For a given hctsa analysis, the user must specify a set of code to evaluate (master operations), their associated individual outputs to measure (operations), and a set of time series to evaluate the features on (time series).

We provide a default library of over 7700 operations (derived from approximately 1000 unique master operations). This can be customized, and additional pieces of code can also be added to the repository.

The results of a hctsa analysis

Having specified a set of master operations, operations, and time series, the results of computing these functions in the time series data are stored in three matrices:

• TS_DataMat is an n x m data matrix containing the results of applying m operations to the n time series.

• TS_Quality is an n x m matrix containing quality labels for each operation output (coding different outputs such as errors or NaNs). Quality labels are described in the section below.

• TS_CalcTime is an n x m matrix containing calculation times for each operation output. Note that the calculation time stored is for the corresponding master operation.

HCTSA .mat files

Each HCTSA*.mat file includes the tables described above: for TimeSeries (corresponding to the rows of the TS_ matrices), Operations (corresponding to columns of the TS_ matrices), and MasterOperations, corresponding to the code evaluated to compute the operations. In addition, the results are stored as above: TS_DataMat, TS_Quality, and TS_CalcTime.

Quality labels

Quality labels are used to indicate when operations take non-real values, or when fatal errors were encountered. Quality labels are stored in the Quality column of the Results table in the mySQL database, and in local Matlab files as the TS_Quality matrix.

When the quality label is nonzero, this indicates that a special-valued output occurred. In this case, the output value of the operation is set to zero, as a convention, and the quality label codes the special output value:

Quality label	Description
0	No problems with calculation. Output was a real number.
1	A fatal error was encountered.
2	Output of the code was NaN.
3	Output of the code was Inf.
4	Output of the code was -Inf
5	Output had a non-zero imaginary component
6	Output was empty (e.g., [])
7	Field specified for this operation did not exist in the master operation output structure