Clustering objects with weighted attributes

I want to cluster a set of objects which have multiple attributes and开发者_如何转开发 some attributes are more important than others is there a simple way to give these specific attributes a heavy weight in a way to give them more importance then the others?

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Look - every instance of objects from your set might been represented as multidimensional vector (each attribute of your object is a component of vector). So, you might use distance-based clustering (distance between similar vectors is very small), such as k-means. You need to define your own distance function between vectors.

For example if your objects has 3 attributes (X Y Z), also that each attribute has its weight (importance) (wx wy wz). According to this, for example, you might define distance function between two vectors (X1 Y1 Z1) and (X2 Y2 Z2) in such way (cosinus distance):

                         (wx^2*X1*X2+wy^2*Y1*Y2+wz^2*Z1*Z2)
dist= -----------------------------------------------------------------------
       [(wx^2*X1^2+wy^2*Y1^2+wz^2*Z1^2)*(wx^2*X2^2+wy^2*Y2^2+wz^2*Z2^2)]^0,5