Ubuntu Manpage: math::changepoint - Change point detection methods

NAME

       math::changepoint - Change point detection methods

SYNOPSIS

       package require Tcl  8.6

       package require TclOO

       package require math::statistics

       package require math::changepoint  ?0.1?

       ::math::changepoint::cusum-detect data ?args?

       ::math::changepoint::cusum-online ?args?

       $cusumObj examine value

       $cusumObj reset

       ::math::changepoint::binary-segmentation data ?args?

________________________________________________________________________________________________________________

DESCRIPTION

The math::changepoint package implements a number of well-known methods to determine if a series of data
contains a shift in the mean or not. Note that these methods only indicate if a shift in the mean is
probably. Due to the stochastic nature of the data that will be analysed, false positives are possible.
The CUSUM method is implemented in both an "offline" and an "online" version, so that it can be used
either for a complete data series or for detecting changes in data that come in one by one. The
implementation has been based on these websites mostly:

• https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc323.htm

• https://en.wikipedia.org/wiki/CUSUM

Basically, the deviation of the data from a given target value is accumulated and when the total
deviation becomes too large, a change point is reported. A second method, binary segmentation, is
implemented only as an "offline" method, as it needs to examine the data series as a whole. In the
variant contained here the following ideas have been used:

• The segments in which the data series may be separated shold not be too short, otherwise the
ultimate result could be segments of only one data point long. So a minimum length is used.

• To make the segmentation worthwhile there should be a minimum gain in reducing the cost function
(the sum of the squared deviations from the mean for each segment).

This may not be in agreement with the descriptions of the method found in various publications, but it is
simple to understand and intuitive. One publication that provides more information on the method in
general is "Selective review of offline change point detection methods" by Truong et al.
https://arxiv.org/abs/1801.00718.

PROCEDURES

       The package defines the following public procedures:

       ::math::changepoint::cusum-detect data ?args?
              Examine a given data series and return the location of the first change (if any)

              double data
                     Series of data to be examined

              list args
                     Optional list of key-value pairs:

                     -target value
                            The target (or mean) for the time series

                     -tolerance value
                            The tolerated standard deviation

                     -kfactor value
                            The  factor  by which to multiply the standard deviation (defaults to 0.5, typically
                            between 0.5 and 1.0)

                     -hfactor value
                            The factor determining the limits betweem which the "cusum"  statistic  is  accepted
                            (typicaly 3.0-5.0, default 4.0)

       ::math::changepoint::cusum-online ?args?
              Class  to  examine  data  passed in against expected properties. At least the keywords -target and
              -tolerance must be given.

              list args
                     List of key-value pairs:

                     -target value
                            The target (or mean) for the time series

                     -tolerance value
                            The tolerated standard deviation

                     -kfactor value
                            The factor by which to multiply the standard deviation (defaults to  0.5,  typically
                            between 0.5 and 1.0)

                     -hfactor value
                            The  factor  determining  the limits betweem which the "cusum" statistic is accepted
                            (typicaly 3.0-5.0, default 4.0)

       $cusumObj examine value
              Pass a value to the cusum-online object and examine it. If, with this new  value,  the  cumulative
              sum remains within the bounds, zero (0) is returned, otherwise one (1) is returned.

              double value
                     The new value

       $cusumObj reset
              Reset the cumulative sum, so that the examination can start afresh.

       ::math::changepoint::binary-segmentation data ?args?
              Apply  the binary segmentation method recursively to find change points. Returns a list of indices
              of potential change points

              list data
                     Data to be examined

              list args
                     Optional key-value pairs:

                     -minlength number
                            Minimum number of points in each segment (default: 5)

                     -threshold value
                            Factor applied to the standard deviation functioning as a  threshold  for  accepting
                            the change in cost function as an improvement (default: 1.0)

KEYWORDS

       control, statistics

COPYRIGHT