r.change.info - GRASS GIS manual

NAME

r.change.info - Landscape change assessment

KEYWORDS

raster, statistics, change detection, landscape structure

SYNOPSIS

r.change.info

r.change.info --help

r.change.info [-ac] input=name[,name,...] output=name[,name,...] [method=string[,string,...]] [size=integer] [step=integer] [alpha=float] [--overwrite] [--help] [--verbose] [--quiet] [--ui]

Flags:

-a: Do not align input region with input maps
-c: Use circular mask
--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:

input=name[,name,...] [required]: Name of input raster map(s)
output=name[,name,...] [required]: Name for output raster map(s)
method=string[,string,...]: Change assessment; Options: pc, gain1, gain2, gain3, ratio1, ratio2, ratio3, gini1, gini2, gini3, dist1, dist2, dist3, chisq1, chisq2, chisq3; Default: ratio3; pc: proportion of changes; gain1: Information gain for category distributions; gain2: Information gain for size distributions; gain3: Information gain for category and size distributions; ratio1: Information gain ratio for category distributions; ratio2: Information gain ratio for size distributions; ratio3: Information gain ratio for category and size distributions; gini1: Gini impurity for category distributions; gini2: Gini impurity for size distributions; gini3: Gini impurity for category and size distributions; dist1: Statistical distance for category distributions; dist2: Statistical distance for size distributions; dist3: Statistical distance for category and size distributions; chisq1: CHI-square for category distributions; chisq2: CHI-square for size distributions; chisq3: CHI-square for category and size distributions
size=integer: Window size (cells); Default: 40
step=integer: Processing step (cells); Default: 40
alpha=float: Alpha for general entropy; Default = 1 for Shannon Entropy; Default: 1

DESCRIPTION
- Cell-based change assessment
- Landscape structure change assessment
NOTES
- Shannon's entropy
- Rényi's entropy
EXAMPLES
SEE ALSO
REFERENCES
AUTHOR

DESCRIPTION

r.change.info calculates landscape change assessment for a series of categorical maps, e.g. land cover/land use, with different measures based on information theory and machine learning. More than two input maps can be specified.

r.change.info moves a processing window over the input maps. This processing window is the current landscape under consideration. The size of the window is defined with size. Change assessment is done for each processing window (landscape) separately. The centers of the processing windows are step cells apart and the output maps will have a resolution of step input cells. step should not be larger than size, otherwise some cells will be skipped. If step is half of size , the moving windows will overlap by 50%. The overlap increases when step becomes smaller. A smaller step and/or a larger size will require longer processing time.

The measures information gain, information gain ratio, CHI-square and Gini-impurity are commonly used in decision tree modelling (Quinlan 1986) to compare distributions. These measures as well as the statistical distance are based on landscape structure and are calculated for the distributions of patch categories and/or patch sizes. A patch is a contiguous block of cells with the same category (class), for example a forest fragment. The proportion of changes is based on cell changes in the current landscape.

Cell-based change assessment

The method pc calculates the proportion of changes as the actual number of cell changes in the current landscape divided by the theoretical maximum number of changes (number of cells in the processing window x (number of input maps - 1)).

Landscape structure change assessment

Landscape structure

For each processing window, the number of cells per category are counted and patches are identified. The size and category of each patch is recorded. From these cell and patch statistics, three kinds of patterns (distributions) are calculated:

1. Distributions over categories (e.g land cover class): This provides information about changes in categories (e.g land cover class), e.g. if one category becomes more prominent. This detects changes in category composition.
2. Distributions over size classes: This provides information about fragmentation, e.g. if a few large fragments are broken up into many small fragments. This detects changes in fragmentation.
3. Distributions over categories and size classes.: This provides information about whether particular combinations of category and size class changed between input maps. This detects changes in the general landscape structure.

The latter is obtained from the category and size of each patch, i.e. each unique category - size class combination becomes a separate class.

The numbers indicate which distribtution will be used for the selected method (see below).

A low change in category distributions and a high change in size distributions means that the frequency of categories did not change much whereas the size of patches did change.

Information gain

The methods gain1, gain2 and gain3 calculate the information gain after Quinlan (1986). The information gain is the difference between the entropy of the combined distribution and the average entropy of the observed distributions (conditional entropy). A larger value means larger differences between input maps.

Information gain indicates the absolute amount of information gained (to be precise, reduced uncertainty) when considering the individual input maps instead of their combination. When cells and patches are distributed over a large number of categories and a large number of size classes, information gain tends to over-estimate changes.

The information gain can be zero even if all cells changed, but the distributions (frequencies of occurrence) remained identical. The square root of the information gain is sometimes used as a distance measure and it is closely related to Fisher's information metric.

Information gain ratio

The methods ratio1, ratio2 and ratio3 calculate the information gain ratio that changes occurred, estimated with the ratio of the average entropy of the observed distributions to the entropy of the combined distribution. In other words, the ratio is equivalent to the ratio of actual change to maximum possible change (in uncertainty). The gain ratio is better suited than absolute information gain when the cells are distributed over a large number of categories and a large number of size classes. The gain ratio here follows the same rationale as the gain ratio of Quinlan (1986), but is calculated differently.

The gain ratio is always in the range (0, 1). A larger value means larger differences between input maps.

CHI-square

The methods chisq1, chisq2 and chisq3 calculate CHI square after Quinlan (1986) to estimate the relevance of the different input maps. If the input maps are identical, the relevance measured as CHI-square is zero, i.e. no change occurred. If the input maps differ from each other substantially, major changes occurred and the relevance measured as CHI-square is large.

Gini impurity

The methods gini1, gini2 and gini3 calculate the Gini impurity, which is 1 - Simpson's index, or 1 - 1 / diversity, or 1 - 1 / 2^entropy for alpha = 1. The Gini impurity can thus be regarded as a modified measure of the diversity of a distribution. Changes occurred when the diversity of the combined distribution is larger than the average diversity of the observed distributions, thus a larger value means larger differences between input maps.

The Gini impurity is always in the range (0, 1) and calculated with

G = 1 - ∑ p_i²

The methods information gain and CHI square are the most sensitive measures, but also the most susceptible to noise. The information gain ratio is less sensitive, but more robust against noise. The Gini impurity is the least sensitive and detects only drastic changes.

Distance

The methods dist1, dist2 and dist3 calculate the statistical distance from the absolute differences between the average distribution and the observed distributions. The distance is always in the range (0, 1). A larger value means larger differences between input maps.

Methods using the category or size class distributions (gain1, gain2, ratio1, ratio2 gini1, gini2, dist1, dist2) are less sensitive than methods using the combined category and size class distributions (gain3, ratio3, gini3, dist3).

For a thorough change assessment it is recommended to calculate different change assessment measures (at least information gain and information gain ratio) and investigate the differences between these change assessments.

NOTES

Shannon's entropy

Entropies for information gain and its ratio are by default Shannon entropies H, calculated with

H = ∑ p_i * log₂(p_i)

The entropies are here calculated with base 2 logarithms. The upper bound of information gain is thus log₂(number of classes). Classes can be categories, size classes, or unique combinations of categories and size classes.

Rényi's entropy

The alpha option can be used to calculate general entropies H_α after Rényi (1961) with the formula

H_α = 1 / (1 - α) * log₂ (∑ p_i^α)

An alpha < 1 gives higher weight to small frequencies, whereas an alpha > 1 gives higher weight to large frequencies. This is useful for noisy input data such as the MODIS land cover/land use products MCD12*. These data often differ only in single-cell patches. These differences can be due to the applied classification procedure. Moreover, the probabilities that a cell has been assigned to class A or class B are often very similar, i.e. different classes are confused by the applied classification procedure. In such cases an alpha > 1, e.g. 2, will give less weight to small changes and more weight to large changes, to a degree alleviating the problem of class confusion.

EXAMPLES

Assuming there is a time series of the MODIS land cover/land use product MCD12Q1, land cover type 1, available, and the raster maps have the names

MCD12Q1.A2001.Land_Cover_Type_1
MCD12Q1.A2002.Land_Cover_Type_1
MCD12Q1.A2003.Land_Cover_Type_1
...

then a change assessment can be done with

r.change.info in=`g.list type=rast pat=MCD12Q1.A*.Land_Cover_Type_1 sep=,` \
	      method=pc,gain1,gain2,ratio1,ratio2,dist1,dist2 
	      out=MCD12Q1.pc,MCD12Q1.gain1,MCD12Q1.gain2,MCD12Q1.ratio1,MCD12Q1.ratio2,MCD12Q1.dist1,MCD12Q1.dist2 \
	      radius=20 step=40 alpha=2

REFERENCES

Quinlan, J.R. 1986. Induction of decision trees. Machine Learning 1: 81-106. DOI:10.1007/BF00116251
Rényi, A. 1961. On measures of information and entropy. Proceedings of the fourth Berkeley Symposium on Mathematics, Statistics and Probability 1960: 547-561.
Shannon, C.E. 1948. A Mathematical Theory of Communication. Bell System Technical Journal 27(3): 379-423. DOI:10.1002/j.1538-7305.1948.tb01338.x

AUTHOR

Markus Metz

SOURCE CODE

Available at: r.change.info source code (history)