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calc_reciprocal_similarity_map [2013/07/23 17:53] admin |
calc_reciprocal_similarity_map [2015/10/11 21:26] admin |
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^ Name ^ Type ^ Description ^ | ^ Name ^ Type ^ Description ^ | ||
- | | First Map | [[Categorical Map Type|Categorical Map ]] | A map consisting of classes or categories. | | + | | First Map | [[Categorical Map Type|Categorical Map]] | A map consisting of classes or categories. | |
- | | Second Map | [[Categorical Map Type|Categorical Map ]] | A map consisting of classes or categories. | | + | | Second Map | [[Categorical Map Type|Categorical Map]] | A map consisting of classes or categories. | |
===== Optional Inputs ===== | ===== Optional Inputs ===== | ||
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| Cell Type | [[Cell Type Type|Cell Type]] | Data cell type. | Signed 8 Bit Integer | | | Cell Type | [[Cell Type Type|Cell Type]] | Data cell type. | Signed 8 Bit Integer | | ||
| Null Value | [[Null Value Type|Null Value]] | Null value. | -128 | | | Null Value | [[Null Value Type|Null Value]] | Null value. | -128 | | ||
- | | Exponential Decay Divisor | [[Double Type|Double]] | Value used to attenuate the distance in the exponential decay function. | 2 | | + | | Exponential Decay Divisor | [[Real Value Type|Real Value]] | Value used to attenuate the distance in the exponential decay function. This value must be increased when the "Use Exponential Decay" is greater the 11.((See the [[calc_reciprocal_similarity_map#exponential_decay_function|exponential decay function documentation]] for more details.)) | 2 | |
===== Output ===== | ===== Output ===== | ||
^ Name ^ Type ^ Description ^ | ^ Name ^ Type ^ Description ^ | ||
- | | First Similarity | [[Map Type|Map ]] | Map showing the degree of spatial match from the first to the second input map. Similarity varies from zero (no match) to 1 (perfect match) within the specified window size. | | + | | First Similarity | [[Map Type|Map]] | Map showing the degree of spatial match from the first to the second input map. Similarity varies from zero (no match) to 1 (perfect match) within the specified window size. | |
- | | Second Similarity | [[Map Type|Map ]] | Map showing the degree of spatial match from the second to the first input map. Similarity varies from zero (no match) to 1 (perfect match) within the specified window size. | | + | | Second Similarity | [[Map Type|Map]] | Map showing the degree of spatial match from the second to the first input map. Similarity varies from zero (no match) to 1 (perfect match) within the specified window size. | |
- | | First Mean | [[Double Type|Double ]] | The mean similarity index for the given window size comparing the first map to the second. | | + | | First Mean | [[Real Value Type|Real Value]] | The mean similarity index for the given window size comparing the first map to the second. | |
- | | Second Mean | [[Double Type|Double ]] | The mean similarity index for the given window size comparing the second map to the first. | | + | | Second Mean | [[Real Value Type|Real Value]] | The mean similarity index for the given window size comparing the second map to the first. | |
===== Group ===== | ===== Group ===== | ||
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The overall similarity of a pair of maps can be calculated by averaging the two-way similarity values for all map cells. As random maps tend to score higher, it is recommended picking up the minimum fit value from the two-way comparison. | The overall similarity of a pair of maps can be calculated by averaging the two-way similarity values for all map cells. As random maps tend to score higher, it is recommended picking up the minimum fit value from the two-way comparison. | ||
+ | |||
+ | ==== Exponential Decay Function ==== | ||
+ | |||
+ | The exponential decay function used to calculate similarity can be seen below: | ||
+ | |||
+ | <m>S=1/2^(d/A)</m> | ||
+ | where //d// is the distance from the window center and //A// is the attenuation factor [Exponential Decay Divisor]. | ||
+ | |||
+ | The attenuation parameter can be used to control how fast the exponential function value decreases. The graphs below illustrates: | ||
+ | |||
+ | [ {{:exponential_decay_function_x_1.png?direct&450|Exponential Decay Function with A=1}} ] | ||
+ | |||
+ | [ {{:exponential_decay_function_x_2.png?direct&450|Exponential Decay Function with A=2}} ] | ||
+ | |||
+ | [ {{:exponential_decay_function_x_4.png?direct&450|Exponential Decay Function with A=4}} ] | ||
+ | |||
+ | [ {{:exponential_decay_function_x_10.png?direct&450|Exponential Decay Function with A=10}} ] | ||
==== References ==== | ==== References ==== |