An Objective for Hierarchical Clustering in Euclidean Space and Its Connection to Bisecting K-means

This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree being a ½ approximation if the distances form a metric. This shows the objective does not make a significant distinction between a good and poor hierarchical clustering in metric spaces.Motivated by this, the paper develops a new global objective for hierarchical clustering in Euclidean space. The objective captures the criterion that has motivated the use of divisive clustering algorithms: that when a split happens, points in the same cluster should be more similar than points in different clusters. Moreover, this objective gives reasonable results on ground-truth inputs for hierarchical clustering.The paper builds a theoretical connection between this objective and the bisecting k-means algorithm. This paper proves that the optimal 2-means solution results in a constant approximation for the objective. This is the first paper to show the bisecting k-means algorithm optimizes a natural global objective over the entire tree.

Cuckoo Search and M-Tree based Multicast Ad hoc On-demand Distance Vector Protocol for MANET

The proposed work, Cuckoo Search (CS) and M-Tree based Multicast Ad hoc On-demand Distance Vector (MAODV), is a two-step process, which involves M-Tree construction and optimal multicast route selection. Divisional based Cluster (DIVC), a technique of clustering inspired from Divisive clustering, builts the M-Tree using three constraints, destination flag, path-inclusion factor, and multi-factor. This paper aims to provide optimal multicasting with multiple objectives, such as energy, link lifetime, distance and delay

High-Throughput Single-Molecule Analysis via Divisive Segmentation and Clustering

ABSTRACTSingle-molecule approaches provide insight into the dynamics of biomolecules, yet analysis methods have not scaled with the growing size of data sets acquired in high-throughput experiments. We present a new analysis platform (DISC) that uses divisive clustering to accelerate unsupervised analysis of single-molecule trajectories by up to three orders of magnitude with improved accuracy. Using DISC, we reveal an inherent lack of cooperativity between cyclic nucleotide binding domains from HCN pacemaker ion channels embedded in nanophotonic zero-mode waveguides.