Probabilistic D-Clustering

Abstract

Clustering, Probabilistic clustering, Mahalanobis distance, Harmonic mean, Joint distance function, Weiszfeld method, Similarity matrix,

Probabilistic Distance Clustering Adjusted for Cluster Size

“…A method for probabilistic clustering of data, proposed by the authors [1], is based on the assumption that the probability of a point belongimg to a cluster is inversely proportional to its distance from the cluster center. The resulting clustering algorithm is fast and efficient and works best if the cluster sizes are about equal.…”

Probabilistic Distance Clustering

“…Indeed, the Lagrangian of this problem is 10) and zeroing the partials ∂L/∂p i gives the principle (4.2).…”

“…For Q = I, the identity matrix, (2.9) gives the Euclidean distance (2.6). Another common choice is Q = Σ −1 , where Σ is the covariance matrix of the data in question, in which case (2.9) gives 10) that is used commonly in multivariate statistics.…”

“…There are several ways to model the relationship between distances and probabilities [10], see chapter 3. The following assumption is our basic principle.…”

“…A method for probabilistic clustering of data, proposed in [10], is based on the assumption that the probability of a point belonging to a cluster is inversely proportional to its distance from the cluster center. The resulting clustering algorithm is fast and efficient, and works best if the cluster sizes are about equal.…”