Formation of Resemblance Measures Among Sets
Formación de Medidas de Equivalencia entre Conjuntos
Otar Verulava, Ramaz Khurodze and Lasha Verulava.
Artificial Intelligence Departament
University of GTU
Georgia, Tbilisi ]]>
verulava@gtu.ge
Article received on February 2, 2005; accepted on June 22, 2005
Abstract
In this paper it is described a method to compute the distance between sets, that implies the formation of distance functions different from Hausdorff metric. Two functions with metric properties, which describe quantitatively distances between sets, are formed. First function can be used for sets arbitrary situated from each other. Second distance is more suited for sets clustered by rank links. For reconstructing the metric functions, we define the so–called boundary points between sets. This allows to defining the minimal and the maximal distances between them, which represents the arguments for the formed metric functions. This also allows quantitatively estimate in amore complete way the isolation degree between given sets.
Keywords: Clusterization, Metric Functions, Pattern Recognition.
Resumen
En este artículo se describe un método para el cálculo de la lejanía entre conjuntos. Esto implica la formación de funciones distancia pero diferentes a la métrica de Hausdorff. Se forman dos clases de funciones con propiedades métricas, que describen cualitativamente distancias entre conjuntos. La primera función puede ser usada para conjuntos arbitrariamente situados entre ellos. La segunda función es más aplicable para conjuntos que pueden ser acumulados a través del método de "Rank Links". Para re–construir las funciones métricas, se definen los llamados puntos de la frontera entre conjuntos. Esto permite definir distancias mínimas y máximas entre ellos, lo que representa sus argumentos. También, esto permite estimar cuánticamente de firma más completa el índice de separación entre ellos.
]]> Palabras clave: Clusterización, Funciones de medida, Reconocimiento de patrones.
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References
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