Tree Centroid Properties Clarification

Clarification

A new Initial Centroid finding Method based on Dissimilarity Tree for K-means Algorithm

—Cluster analysis is one of the primary data analysis technique in data mining and K-means is one of the commonly used partitioning clustering algorithm. In K-means algorithm, resulting set of clusters depend on the choice of initial centroids. If we can find initial centroids which are coherent with the arrangement of data, the better set of clusters can be obtained. This paper proposes a meth...

Subtle and Ineffable Tree Properties

Now it is obvious from the usual definitions that an inaccessible κ is subtle iff every κ-tree T satisfies STP(T ), for which we shall just write κ-STP, iff the complete binary tree 2<κ satisfies STP(2<κ), and similarly for ineffability (and one can take this as a definition if unfamiliar with the concepts). By [Mit73] one can collapse a weakly compact (a Mahlo) cardinal onto ω2 such that in th...

Decidable Properties of Tree Languages

The first part of the thesis concerns problems related to the question: " when can a regular tree language be defined in first-order logic? " Characterizations in terms of automata of first-order logic and the related chain logic are presented. A decidable property of tree automata called confusion is introduced; it is conjectured that a regular tree language can be defined in chain logic if an...

Properties of tree convex constraints

It is known that a tree convex network is globally consistent if it is path consistent. However, if a tree convex network is not path consistent, enforcing path consistency on it may not make it globally consistent. In this paper, we investigate the properties of some tree convex constraints under intersection and composition. As a result, we identify a sub-class of tree convex networks that ar...