Developing Criteria for Measuring Space Distortion in Combinatorial Cluster Analysis and Methods for Controlling the Distortion

Space Distortion and Monotone Admissibility in Agglomerative Clustering

“…On the other hand, we believe space distortion and monotonicity should be defined depending on both the algorithm selected and the data to be analyzed. Yadohisa et al (1999) proposed space distortion criteria, which they call the "distortion ratio at stage m" and the "total distortion ratio." and which are defined depending on both the algorithm selected and the data to be analyzed.…”

“…Space Distortion Ratio Yadohisa et al (1999) defined several new space distortion criteria, not just for the clustering algorithms but for each combination of objects. Each criterion is represented by a numerical value that allows its use in selecting a particular clustering algorithm in applications.…”

“…Each criterion is represented by a numerical value that allows its use in selecting a particular clustering algorithm in applications. In this section, we introduce the combined distance at stage m and the distortion measures proposed by Yadohisa et al (1999).…”

“…Yadohisa et al (1999) proposed two criteria for space distortion. The two criteria measure space distortion at each stage and in the entire clustering, respec tively.…”

“…Large values of j, r1 J make the ratio sensitive to differences between the combined distance and the standard distance. Yadohisa et al (1999) recommend that K = 1 and 71 = 0. Then, we can judge the monotonicity from the magnitude positivity of (2.2) and can understand the distortion by comparing (2.2) with unity.…”