S-MOUNTAIN METHOD FOR OBTAINING FOCUS POINTS FROM DATA
We introduce a variation of the Mountain Method called the S-Mountain Method, an algorithm for finding focus points from data points based on the similarity of a focus point with the data points. An important aspect of this algorithm is the association of energy levels with the data points and the reduction of these energy levels as we discover focus points. The rate of reduction of the energy level at a data point is related to its similarity with the recently discovered focus point. We provide a general form for this reduction operation using the t-norm operators. We show how this S-Mountain algorithm can be used to discover focus elements that are granular objects such as fuzzy subsets. Finally we extend the S-Mountain method to environments where our similarities are drawn from an ordinal scale. Here we discuss the interesting question of comparing objects consisting of collections of ordinal values.
similarity t-norm operators aggregation data mining