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--- determine_weights_of_evidence_ranges [2012/01/21 12:43]
admin [Inputs]
+++ determine_weights_of_evidence_ranges [2026/08/28 03:17] (current)
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 ====== Determine Weights Of Evidence Ranges ======
 ===== Description =====
-This container defines the best ranges or intervals employed to categorize continuous gray-tone variables.
+This container defines the best ranges, or intervals, used to categorize continuous gray-tone spatial variables before their Weights of Evidence coefficients are calculated by [[Determine Weights Of Evidence Coefficients]]. For each variable, the range of values is divided into a sequence of increasingly large buffers, and a breakpoint-finding algorithm is applied to the resulting curve to choose a small number of ranges that still preserve the shape of the underlying relationship between the variable and the modeled transition.
+This container accepts one or more [[Name Map]] hooks nested inside it, each assigning a name to a map. These named maps supply the values for the spatial variables referenced by Skeleton.
 ===== Inputs =====
-^ Name ^ Type ^ Description ^
+^ Name  ^ Type  ^ Description  ^
-| Initial Landscape  | [[Categorical Map Type|Categorical Map]]  | Initial map of land use and cover classes.  |
+| Initial Landscape  | [[Categorical Map Type]]  | Initial map of land use and cover classes.  |
-| Final Landscape  | [[Categorical Map Type|Categorical Map]]  | Final map of land use and cover classes.  |
+| Final Landscape  | [[Categorical Map Type]]  | Final map of land use and cover classes.  |
-| Skeleton  | [[Weights Of Evidence Skeleton Type|Weights Of Evidence Skeleton]]  | Spatial variables selected and their types - Category or continuous gray-tone -, and the parameters specified for range definitions, such as increment, maximum and minimum deltas, and tolerance angle.  |
+| Skeleton  | [[Weights Of Evidence Skeleton Type]]  | Selected spatial variables and their types (category or continuous gray-tone), along with the parameters used to define ranges for each continuous variable, such as increment, minimum and maximum deltas, and tolerance angle.  |
 ===== Optional Inputs =====
+^ Name  ^ Type  ^ Description  ^ Default Value  ^
+| Fix Abnormal Weights  | [[Boolean Value Type]]  | If true, recalculates weights that would otherwise result in abnormal values, such as those arising from a division by zero. If false, those abnormal values are assumed to be zero. This is an advanced port.  | No  |
+| Potential Transition Criteria  | [[Boolean Value Type]]  | Affects how a possible but unexecuted transition from class C to class P is identified. If true, any cell that transitions from C to some other class X (different from P) is considered a case where the C to P transition was possible but did not happen. If false, only a cell that stays in class C is considered such a case. This affects the analysis of concurrent transitions, and is an advanced port.  | Yes  |
 ===== Outputs =====
-^ Name ^ Type ^ Description ^
+^ Name  ^ Type  ^ Description  ^
-| Ranges  | [[Weights Type| Weights]]  | Intervals defined for continuous gray-tone variable.  |
+| Ranges  | [[Weights Type]]  | Ranges defined for each continuous gray-tone variable.  |
 ===== Group =====
-[[Functor List#Calibration  | Calibration]]
+[[Functor List#Calibration | Calibration]]
 ===== Notes =====
-The Weights of Evidence calculations, which employ binary patterns, can be extended to multiple category maps, by treating in each case
+For each continuous variable, a sequence of nested buffers is built by incrementing a minimum delta over the variable's range. The number of cells in each buffer, and the number of occurrences of the modeled transition within it, are used to calculate a weight for that buffer. A breakpoint-finding algorithm, using the same criteria as MicroStation's line-generalizing algorithm, is then applied to the resulting curve to choose a small set of ranges: a new range boundary is placed whenever consecutive points are farther apart than the maximum delta, and no boundary is placed between points closer than the minimum delta, unless the angle between them exceeds the tolerance angle.
-one category versus all other categories combined, whose areas are added to represent (<m>overline{B}</m>). Agterberg & BonhamCarter (1990) also present an extension of this method to gray-tone maps (e.g., a map of distances to road), by defining intervals for these maps.
-A key issue to any categorization process concerns the preservation of the data structure. The present method adapted from Agterberg & BonhamCarter (1990), calculates ranges according to the data structure by first establishing a minimum delta (//Dx//) for a continuous gray-tone variable x that is used to build n incremental buffers (//Nx//) comprising intervals from //x<sub>minimum</sub>// to //x<sub>minimum</sub>// + //nDx//. Each n defines a threshold that divides the map into two classes: (//Nx//) and (<m>overline{Nx}</m>). //An// is the number of cells for a buffer (//Nx//) multiple of //n// and //dn// is the number of occurrences for the modeled event (//D//) within this buffer. The quantities //An// and //dn// are obtained for an ordered sequence of buffers //N(x<sub>minimum</sub> + nDx)//. Subsequently, values of //W<sup>+</sup>//, //C//, and //S<sup>2</sup>// for each buffer are calculated using equations 2 to 8.
+Reports an error if a spatial variable named in Skeleton is not provided by a nested Name Map hook.
-A sequence of quantities //An// is plotted against <m>An*exp(W^+)</m>. Thereafter breaking points for this graph are determined by applying a
+Reports an error if a spatial variable is categorized as a category variable but its map has cells of type Unsigned 32 Bit Integer or Floating Point (32 Bit).
-line-generalizing algorithm (Intergraph, 1991) that contains three parameters:
-  - minimum distance interval along //x//, //mindx//,
+This method was adapted from Agterberg & Bonham-Carter (1990).
-  - maximum distance interval along //x//, //maxdx//, and
-  - tolerance angle //ft//.
-For //dx// (a distance between two points along //x//) greater than //mindx// or lesser than //maxdx//, a new breaking point is placed whenever //dx > maxdx// or //f// (an angle between //v// and //v’// - vectors linking the current to the last point and the last point to its antecedent, respectively) exceeds the tolerance angle //ft//. Thus, the number of ranges decreases as a function of //ft//. The ranges are finally defined by linking the breaking points with straight lines. Note that //An// is practically error-free whereas //dn// is subject to a considerable amount of uncertainty because it is regarded as the realization of a random variable. Since small //An// can generate noisy values for //W<sup>+</sup>//, Goodacre et al. (1993) suggest that, instead of calculating by employing equations 2 and 4, one should estimate //W<sup>+</sup>// for each defined range through the following expression:
+**References**
-<m>W^+ = ln({y_{n=k}-y_{n=k-1}}/{A_{n=k}-A_{n=k-1}})</m> (10)
+Agterberg, F.P. and Bonham-Carter, G.F., 1990: Deriving weights of evidence from geoscience contour maps for the prediction of discrete events. XXII Int. Symposium AP-COM, 381-395.
-where <m>y_n=An*exp(W^+)</m> and //k// represents the breakpoints defined for the n increments of //Dx//.
+Intergraph Corporation, 1991. Intergraph Microstation PC, Version 4 User's Guide. Bentley Systems, Inc. and Intergraph Corporation, 333 pp.
-[{{ :weightsofevidenceranges004.gif?nolink& |(a) Plot of //An// against for the variable "distance to all roads". The best-fitting curve can be approximated by a series of straight-line segments by using a line-generalizing algorithm as explained in the text. This approach is used to define the breaking points for this curve and subsequently category intervals for a continuous variable (b).}}]
+===== Internal Name =====
-In sum, the application of Weights of Evidence in a change analysis aims at selecting the most important variables as well as quantifying their influences on each type of transition. Weights of evidence are assigned for each range or category of a variable represented by its cartographic layer and a post-probability map is obtained from the integration of these weights of evidence. This map points out the most favorable areas for a
+DetermineWeightsOfEvidenceRanges
-transition, thus it can be interpreted as a map of spatial transition probability. As a result, this empirical relationship, determined by Weights of Evidence, can be used to parameterize and calibrate spatial simulation models such as Dinamica EGO. Although Weights of Evidence can be classified as a local operator, because it only computes values from overlapping map locations (x,y), the use of chorographic variables, like distance to a geographic feature, ensures the capture of the neighborhood effect in this calculation.
-==== References ====
+===== Usage examples =====
-Agterberg, F.P. and Bonham-Carter, G.F., 1990: Deriving weights of evidence from geoscience contour maps for the prediction of discrete
+See practical examples of this functor in [[lesson_18|Lesson 18: Building a land-use and land-cover change simulation model]]
-events. XXII Int. Symposium AP-COM, 381-395.
-Intergraph Corporation, 1991. Intergraph Microstation PC, Version 4 User’s Guide. Bentley Systems, Inc. and Intergraph Corporation, 333
-pp.
-===== Internal Name =====
-DetermineWeightsOfEvidenceRanges