On a Minimal Spanning Tree Approach in the Cluster Validation Problem

On a Minimal Spanning Tree Approach in the Cluster Validation Problem

In this paper, a method for the study of cluster stability is purposed. We draw pairs of samples from the data, according to two sampling distributions. The first distribution corresponds to the high density zones of data-elements distribution. Thus it is associated with the clusters cores. The second one, associated with the cluster margins, is related to the low density zones. The samples are...

On the bicriterion - minimal cost/minimal label - spanning tree problem

We deal with a bicriterion spanning tree problem relevant in some application fields such as telecommunication networks or electric networks. Each edge is assigned with a cost value and a label (such as a color). The first criterion intends to minimize the total cost of the spanning tree (the summation of its edge costs), while the second intends to get the solution with a minimum number of dif...

Estimating the Cluster Tree of a Density by Analyzing the Minimal Spanning Tree of a Sample

We present runt pruning, a new clustering method that attempts to find modes of a density by analyzing the minimal spanning tree of a sample. The method exploits the connection between the minimal spanning tree and nearest neighbor density estimation. It does not rely on assumptions about the specific form of the data density (e.g., normal mixture) or about the geometric shapes of the clusters,...

A Metaheuristic Algorithm for the Minimum Routing Cost Spanning Tree Problem

The routing cost of a spanning tree in a weighted and connected graph is defined as the total length of paths between all pairs of vertices. The objective of the minimum routing cost spanning tree problem is to find a spanning tree such that its routing cost is minimum. This is an NP-Hard problem that we present a GRASP with path-relinking metaheuristic algorithm for it. GRASP is a multi-start ...

On the Minimum Label Spanning Tree Problem