## NAME

r.kappa - Calculates error matrix and kappa parameter for accuracy assessment of classification result.

## KEYWORDS

raster, statistics, classification

## SYNOPSIS

r.kappa
r.kappa --help
r.kappa [-whm] classification=name reference=name [output=name] [title=string] format=string [--overwrite] [--help] [--verbose] [--quiet] [--ui]

### Flags:

-w
  Wide report
  132 columns (default: 80)
-h
  No header in the report
-m
  Print Matrix only
--overwrite
  Allow output files to overwrite existing files
--help
  Print usage summary
--verbose
  Verbose module output
--quiet
  Quiet module output
--ui
  Force launching GUI dialog

### Parameters:

classification=name [required]
  Name of raster map containing classification result
reference=name [required]
  Name of raster map containing reference classes
output=name
  Name for output file containing error matrix and kappa
  If not given write to standard output
title=string
  Title for error matrix and kappa
  Default: ACCURACY ASSESSMENT
format=string [required]
  Output format
  Options: plain, json
  Default: plain
  plain: Plain text output
  json: JSON (JavaScript Object Notation)

## DESCRIPTION

r.kappa tabulates the error matrix of classification result by crossing classified map layer with respect to reference map layer. Both overall kappa (accompanied by its variance) and conditional kappa values are calculated. This analysis program respects the current geographic region and mask settings.

r.kappa calculates the error matrix of the two map layers and prepares the table from which the report is to be created. kappa values for overall and each classes are computed along with their variances. Also percent of commission and omission error, total correct classified result by pixel counts, total area in pixel counts and percentage of overall correctly classified pixels are tabulated.

The report will be written to an output file which is in plain text format and named by user at prompt of running the program. To obtain machine readable version, specify a json output format.

The body of the report is arranged in panels. The classified result map layer categories is arranged along the vertical axis of the table, while the reference map layer categories along the horizontal axis. Each panel has a maximum of 5 categories (9 if wide format) across the top. In addition, the last column of the last panel reflects a cross total of each column for each row. All of the categories of the map layer arranged along the vertical axis, i.e., the reference map layer, are included in each panel. There is a total at the bottom of each column representing the sum of all the rows in that column.

## OUTPUT VARIABLES

All output variables (except kappa variance) have been validated to produce correct values in accordance to formulas given by Rossiter, D.G., 2004. "Technical Note: Statistical methods for accuracy assessment of classified thematic maps".

Observations
  Overall count of observed cells (sum of both correct and incorrect ones).
Correct
  Overall count of correct cells (cells with equal value in reference and classification maps).
Overall accuracy
  Number of correct cells divided by overall cell count (expressed in percent).
User's accuracy
  Share of correctly classified cells out of all cells classified as belonging to specified class (expressed in percent). Inverse of commission error.
Commission
  Commission error = 100 - user's accuracy.
Producer's accuracy
  Share of correctly classified cells out of all cells known to belong to specified class (expressed in percent). Inverse of omission error.
Omission
  Omission error = 100 - producer's accuracy.
Kappa
  Choen's kappa index value.
Kappa variance
  Variance of kappa index. Correctness needs to be validated.
Conditional kappa
  Conditional user's kappa for specified class.
MCC
  Matthews (Mattheus) Correlation Coefficient is implemented according to Grandini, M., Bagli, E., Visani, G. 2020. "Metrics for multi-class classification: An overview."

## NOTES

It is recommended to reclassify categories of classified result map layer into a more manageable number before running r.kappa on the classified raster map layer. Because r.kappa calculates and then reports information for each and every category.

NA's in output mean it was not possible to calculate the value (e.g. calculation would involve division by zero). In JSON output NA's are represented with value null. If there is no overlap between both maps, a warning is printed and output values are set to 0 or null respectively.

The Estimated kappa value in r.kappa is the value only for one class, i.e. the observed agreement between the classifications for those observations that have been classified by classifier 1 into the class i. In other words, here the choice of reference is important.

It is calculated as:

kpp[i] = (pii[i] - pi[i] * pj[i]) / (pi[i] - pi[i] * pj[i]);

where=

- pii[i] is the probability of agreement (i.e. number of pixels for which there is agreement divided by total number of assessed pixels)
- Pi[i] is the probability of classification i having classified the point as i
- Pj[i] is the probability of classification j having classified the point as i.

Some of reported values (overall accuracy, Choen's kappa, MCC) can be misleading if cell count among classes is not balanced. See e.g. Powers, D.M.W., 2012. "The Problem with Kappa"; Zhu, Q., 2020. "On the performance of Matthews correlation coefficient (MCC) for imbalanced dataset".

## EXAMPLE

Example for North Carolina sample dataset:

    g.region raster=landclass96 -p
    r.kappa -w classification=landuse96_28m reference=landclass96

    # export Kappa matrix as CSV file "kappa.csv"
    r.kappa classification=landuse96_28m reference=landclass96 output=kappa.csv -m -h

Verification of classified LANDSAT scene against training areas:

    r.kappa -w classification=lsat7_2002_classes reference=training

## SEE ALSO

g.region, r.category, r.mask, r.reclass, r.report, r.stats

## AUTHORS

Tao Wen, University of Illinois at Urbana-Champaign, Illinois
Maris Nartiss, University of Latvia (JSON output, MCC)

## SOURCE CODE

Available at: r.kappa source code (history)

Accessed: Friday Jul 14 13:01:25 2023

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