Filtering and normalizing
The first step in analyzing a dataset involves processing the data matrix, which can be done using TS_normalize. This involves filtering out operations or time series that produced many errors or special-valued outputs, and then normalizing of the output of all operations, which is typically done in-sample, according to an outlier-robust sigmoidal transform (although other normalizing transformations can be selected). Both of these tasks are performed using the function TS_normalize. The TS_normalize function writes the new, filtered, normalized matrix to a local file called HCTSA_N.mat. This contains normalized, and trimmed versions of the information in HCTSA.mat.
Example usage is as follows:
TS_normalize('scaledRobustSigmoid',[0.8,1.0]);
The first input controls the normalization method, in this case a scaled, outlier-robust sigmoidal transformation, specified with 'scaledRobustSigmoid'. The second input controls the filtering of time series and operations based on minimum thresholds for good values in the corresponding rows (corresponding to time series; filtered first) and columns (corresponding to operations; filtered second) of the data matrix.
In the example above, time series (rows of the data matrix) with more than 20% special values (specifying 0.8) are first filtered out, and then operations (columns of the data matrix) containing any special values (specifying 1.0) are removed. Columns with approximately constant values are also filtered out. After filtering the data matrix, the outlier-robust ‘scaledRobustSigmoid’ sigmoidal transformation is applied to all remaining operations (columns). The filtered, normalized matrix is saved to the file HCTSA_N.mat.
Details about what normalization is saved to the HCTSA_N.mat file as normalizationInfo, a structure that contains the normalization function, filtering options used, and the corresponding TS_normalize code that can be used to re-run the normalization.
It makes sense to weight each operation equally for the purposes of dimensionality reduction, and thus normalize all operations to the same range using a transformation like ‘scaledRobustSigmoid’, ‘scaledSigmoid’, or ‘mixedSigmoid’. For the case of calculating mutual information distances between operations, however, one would rather not distort the distributions and perform no normalization, using ‘raw’ or a linear transformation like ‘zscore’, for example. The full list of implemented normalization transformations are listed in the function BF_NormalizeMatrix.
Note that the 'scaledRobustSigmoid' transformation does not tolerate distributions with an interquartile range of zero, which will be filtered out; 'mixedSigmoid' will treat these distributions in terms of their standard deviation (rather than interquartile range).
Filtering parameters depend on the application. Some applications can allow the filtering thresholds to be relaxed. For example, setting [0.7,0.9], removes time series with less than 70% good values, and then removes operations with less than 90% good values. Some applications can tolerate some special-valued outputs from operations (like some clustering methods, where distances are simply calculated using those operations that are did not produce special-valued outputs for each pair of objects), but others cannot (like Principal Components Analysis); the filtering parameters should be specified accordingly.
Analysis can be performed on the data contained in HCTSA_N.mat in the knowledge that different settings for filtering and normalizing the results can be applied at any time by simply rerunning TS_normalize, which will overwrite the existing HCTSA_N.mat with the results of the new normalization and filtration settings.