Hello everyone,

I noticed that Two-Step Clustering was using Log-Likelihood Distance measure to cluster the object which can handle both continuous and categorical variable well. Thus, I want to calculate the pairwise distance for my cluster object using Log-Likelihood distance but I come across some problem when checking through the document regarding this distance measures written in Two Step Cluster document.

There were 2 formulas which are slightly difference in the attached SPSS document and I need help to explain how to implement this measure correctly in SPSS. The first formula showed was including the log of the variance of kth feature of cluster and adjusted parameter of variance of kth feature of total samples. However, the second formula showed in Section 5.4.1 does not has the adjusted parameter and changed to Δk = 0.01 to account for degeneration problem of natural logarithm for value equal to zero.

Additionally, The log-likelihood distance between cluster j and cluster s was showed as:
d(i,j) = ξ(i) + ξ(j) - ξ(i,j). In the case of distance between same cluster, the resulting formula will return ξ(i) given that ξ(i) = ξ(j) = ξ(i,j) which are not zero, isn't the distance to itself should be zero instead?

Looking forward for your help, thank you!

Attachment(s)

Two Step Cluster.pdf   13.35 MB 1 version