Feature Statistics

 

The features in this group are oscillation characteristics and are meaningful for oscillating time series. Each oscillation can be roughly, but often sufficiently, described by four features, the peak (local maximum) and trough (local minimum) of the oscillation, the time duration of the oscillation (e.g. from one peak to the next) and the time from peak to trough (or equivalently from trough to peak). A fifth feature that can be useful at cases, especially in the presence of drifts in the time series, is formed by the difference of the peaks from the corresponding troughs. The first two features constitute the turning points of the time series and have been used in the analysis of other non-oscillating time series, e.g. in finance.

For the computation of the features the turning points have to be identified first. A sample point of the time series is a turning point, i.e. local minimum (maximum), if it is the smallest (largest) of the samples of the time series in a data window centered in this sample point. The data window size is given as 2w+1 for a given offset value w. For noisy time series, smoothing prior to the turning point detection is suggested and this is implemented here with a moving average filter of a given order. Standard descriptive statistics are given as measures from each of the five oscillating features.

The use of statistics of oscillating features as measures of time series analysis is rather new and it has been suggested in

Kugiumtzis D., Papana A., Tsimpiris A., Vlachos I. and Larsson P.G. (2006), Time Series Feature Evaluation in Discriminating Preictal EEG States, Lecture Notes in Computer Science, Vol 4345, pp 298-310.

Kugiumtzis D., Vlachos I., Papana A. and Larsson, P.G. (2007), Assessment of Measures of Scalar Time Series Analysis in Discriminating Preictal States, International Journal of Bioelectromagnetism, Vol 9, No 3, 134-145.

The measure names for the 5 features are

Local Maxima (LocalMaxim)

Local Minima (LocalMinim)

Minimum to Maximum Time  (MinMaxTime)

Minimum to Minimum Time (MaxMaxTime)

Difference Minimum from Maximum (DiffMinMax)

The following parameter can be specified for all five features:

- moving average filter order (a): any valid matlab format denoting an array of positive integers or a single positive integer. The default is '1' meaning that no filter is applied as there is only the target point in the moving window for averaging. The moving average filter runs through the time series (forward direction), then the filtered time series is reversed and the same moving average filter runs through it (backward direction). In this way, there is no phase distortion. Note that a change of the value of a in the first feature of Local Maxima is passed to the parameter a of the other four features.

- offset for local window (w): any valid matlab format denoting an array of positive integers or a single positive integer. The default is '1' meaning that the local window is comprised of the target sample point in the center, the preceding sample point and the succeeding sample point. The length of the local window is 2w+1. A sample point xi is a local maximum (minimum) if it is the maximum (minimum) of the samples {xi-w,...,xi,...,xi+w}. Note that a change of the value of w in the first feature of Local Maxima is passed to the parameter w of the other four features.

The following statistics can be selected for each of the five features: mean, median, standard deviation and inter-quartile range. If none of the four statistics is selected, then all statistics of the feature are considered as measures. Note that if a statistic is activated or deactivated for the first feature of Local Maxima the status for this statistic is passed to the same statistic of the other four features.

Example: If the user selects the measure Local Maxima by activating the check box in the beginning of the measure line and sets for moving average filter order (a) '3 5', for offset for local window (w) '2 4 6', and checks only median, then the median of Local Maxima is computed for the combinations of the 2 values of a and the 3 values of w and in the measure list the following measure names will appear 

LocalMaximMEDIANa3w2
LocalMaximMEDIANa3w4
LocalMaximMEDIANa3w6
LocalMaximMEDIANa5w2
LocalMaximMEDIANa5w4
LocalMaximMEDIANa5w6