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calc_kernel_map [2015/10/12 00:47]
admin 		calc_kernel_map [2026/08/28 03:11] (current)
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-====== Calc Kernel Map ====== ​+====== Calc Kernel Map ======
  
 ===== Description ===== ===== Description =====
  
-This functor calculates ​[[wp>​Multivariate_kernel_density_estimation|kernel density]] of an event map representing a point pattern.+This functor calculates ​the kernel density of an event map representing a point pattern.
  
 ===== Inputs ===== ===== Inputs =====
  
 ^ Name  ^ Type  ^ Description ​ ^ ^ Name  ^ Type  ^ Description ​ ^
-| Events ​ | [[Map Type]] ​ | Map showing the events ​location. Events are represented by non null cells, indicating the number of occurrences on the cell. Cell values must be positive integer; otherwise an error will be reported. ​| +| Events ​ | [[Map Type]] ​ | Map showing the location ​of events. Events are represented by non-null cells, indicating the number of occurrences on the cell.  | 
-| Bandwidth | [[Real Value Type]] ​ | The bandwidth is the radius (in meters) of a disc centered on each cell within which events ​will contribute to the Kernel ​estimate. ​ |+| Bandwidth ​ | [[Real Value Type]] ​ | Radius, ​in meters, of the disc centered on each cell within which events contribute to the kernel ​estimate. ​ |
  
 ===== Optional Inputs ===== ===== Optional Inputs =====
  
 ^ Name  ^ Type  ^ Description ​ ^ Default Value  ^ ^ Name  ^ Type  ^ Description ​ ^ Default Value  ^
-| Mask  | [[Map Type]] ​ | A map used to mask the distance ​calculation ​on its null cell areas. Data cell type of this map must be &​quot;​Signed 32 Bit Integer&​quot;​ or an error will be reported.  | None  | +| Mask  | [[Map Type]] ​ | Map whose null cells mask the kernel ​calculation. ​ | .none  | 
-| Null Value | [[Integer ​Value Type]] ​ | The bandwidth is the radius (in meters) ​of a disc centered on each cell within which events will contribute to the Kernel estimate.  | -9999  |+| Null Value  | [[Null Value Type]] ​ | Null value of the calculated kernel map.  | .default ​ |
  
-===== Output ​=====+===== Outputs ​=====
  
 ^ Name  ^ Type  ^ Description ​ ^ ^ Name  ^ Type  ^ Description ​ ^
-| Kernel ​Density ​Map  | [[Map Type]] ​ | Output map showing the kernel density estimate for each cell.  |+| Kernel Map  | [[Map Type]] ​ | Map showing the kernel density estimate for each cell.  |
  
 ===== Group ===== ===== Group =====
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 ===== Notes ===== ===== Notes =====
  
-Typically, the objective of point pattern analysis is to identify the spatial distribution of the events in a region, in particular cluster patterns. In this case, visual inspection of the events may be tricky, as superimposition of points may confuse the identification of high density areas. ​Kernel density estimation produces continuous ​estimates ​of the spatial intensity of a point pattern ​(Silverman, 1986), hence it allows exploration of the spatial ​distribution of points ​and identification of hotspots. Basically, it is a non parametric statistical method that returns event density weighted by a kernel function that is based on the distance between each one of the events, located within a radius, and the center of the cell.+Kernel density estimation produces ​a continuous ​estimate ​of the spatial intensity of a point pattern, ​making ​it possible to explore hotspots and other patterns in the distribution of events even when overlapping ​points ​would make visual inspection misleading.
  
-The effect of increasing ​the radius (bandwidth) is to stretch the region ​around ​the cluster ​center, in a manner that for large radii the density ​will appear flat and local features ​will be obscured; on the other hand, if the radius is small, density will tend to show local patterns ​of hotspots.+Increasing Bandwidth spreads ​the density estimate over a wider area around ​each cluster: with a large bandwidth ​the density ​appears flatter ​and local features ​are obscured, ​while a small bandwidth reveals ​local hotspot ​patterns ​more sharply.
  
-The technical aspects of the algorithm that calculates ​kernel ​density was extracted from Bailey & Gatrell (1995) and uses the quartic ​Kernel ​function. ​+The kernel ​function used is the quartic function ​k(h) = (3/​PI)*(1-h^2)^2.
  
-==== Referências ====+**References**
  
 Bailey, T. and Gatrell, A., 1995: Interactive Spatial Data Analysis. Longman, Harlow. Bailey, T. and Gatrell, A., 1995: Interactive Spatial Data Analysis. Longman, Harlow.