'\"
'\" Generated from file 'changepoint\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2020 by Arjen Markus
'\"
.TH "math::changepoint" 3tcl 0\&.1 tcllib "Tcl Math Library"
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.SH NAME
math::changepoint \- Change point detection methods
.SH SYNOPSIS
package require \fBTcl  8\&.6\fR
.sp
package require \fBTclOO \fR
.sp
package require \fBmath::statistics \fR
.sp
package require \fBmath::changepoint  ?0\&.1?\fR
.sp
\fB::math::changepoint::cusum-detect\fR \fIdata\fR ?args?
.sp
\fB::math::changepoint::cusum-online\fR ?args?
.sp
\fB$cusumObj\fR examine \fIvalue\fR
.sp
\fB$cusumObj\fR reset
.sp
\fB::math::changepoint::binary-segmentation\fR \fIdata\fR ?args?
.sp
.BE
.SH DESCRIPTION
.PP
The \fBmath::changepoint\fR 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:
.IP \(bu
\fIhttps://www\&.itl\&.nist\&.gov/div898/handbook/pmc/section3/pmc323\&.htm\fR
.IP \(bu
\fIhttps://en\&.wikipedia\&.org/wiki/CUSUM\fR
.PP
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:
.IP \(bu
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\&.
.IP \(bu
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)\&.
.PP
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\&. \fIhttps://arxiv\&.org/abs/1801\&.00718\fR\&.
.SH PROCEDURES
The package defines the following public procedures:
.TP
\fB::math::changepoint::cusum-detect\fR \fIdata\fR ?args?
Examine a given data series and return the location of the first change (if any)
.RS
.TP
double \fIdata\fR
Series of data to be examined
.TP
list \fIargs\fR
Optional list of key-value pairs:
.RS
.TP
\fB-target\fR \fIvalue\fR
The target (or mean) for the time series
.TP
\fB-tolerance\fR \fIvalue\fR
The tolerated standard deviation
.TP
\fB-kfactor\fR \fIvalue\fR
The factor by which to multiply the standard deviation (defaults to 0\&.5, typically between 0\&.5 and 1\&.0)
.TP
\fB-hfactor\fR \fIvalue\fR
The factor determining the limits betweem which the "cusum" statistic is accepted (typicaly 3\&.0-5\&.0, default 4\&.0)
.RE
.RE
.TP
\fB::math::changepoint::cusum-online\fR ?args?
Class to examine data passed in against expected properties\&. At least the keywords \fI-target\fR and \fI-tolerance\fR must be given\&.
.RS
.TP
list \fIargs\fR
List of key-value pairs:
.RS
.TP
\fB-target\fR \fIvalue\fR
The target (or mean) for the time series
.TP
\fB-tolerance\fR \fIvalue\fR
The tolerated standard deviation
.TP
\fB-kfactor\fR \fIvalue\fR
The factor by which to multiply the standard deviation (defaults to 0\&.5, typically between 0\&.5 and 1\&.0)
.TP
\fB-hfactor\fR \fIvalue\fR
The factor determining the limits betweem which the "cusum" statistic is accepted (typicaly 3\&.0-5\&.0, default 4\&.0)
.RE
.RE
.TP
\fB$cusumObj\fR examine \fIvalue\fR
Pass a value to the \fIcusum-online\fR object and examine it\&. If, with this new value, the cumulative sum remains within the bounds,
zero (0) is returned, otherwise one (1) is returned\&.
.RS
.TP
double \fIvalue\fR
The new value
.RE
.TP
\fB$cusumObj\fR reset
Reset the cumulative sum, so that the examination can start afresh\&.
.TP
\fB::math::changepoint::binary-segmentation\fR \fIdata\fR ?args?
Apply the binary segmentation method recursively to find change points\&. Returns a list of indices of potential change points
.RS
.TP
list \fIdata\fR
Data to be examined
.TP
list \fIargs\fR
Optional key-value pairs:
.RS
.TP
\fB-minlength\fR \fInumber\fR
Minimum number of points in each segment (default: 5)
.TP
\fB-threshold\fR \fIvalue\fR
Factor applied to the standard deviation functioning as a threshold for accepting the change in cost function as an improvement (default: 1\&.0)
.RE
.RE
.PP
.SH KEYWORDS
control, statistics
.SH CATEGORY
Mathematics
.SH COPYRIGHT
.nf
Copyright (c) 2020 by Arjen Markus

.fi