Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

mdendro：一个用于扩展凝聚层次聚类的R包

mdendro: An R package for extended agglomerative hierarchical clustering

“mdendro”R包为凝聚层次聚类提供全面的连接方法，通过生成多重树状图解决数据结值导致的非唯一性问题，并包含多种加权及参数化方法与五个描述性度量。

Revisiting Agglomerative Clustering

An important issue in clustering concerns the avoidance of false positives while searching for clusters. This work addressed this problem considering agglomerative methods, namely single, average, median, complete, centroid and Ward's approaches applied to unimodal and bimodal datasets obeying uniform, gaussian, exponential and power-law distributions. A model of clusters was also adopted, involving a higher density nucleus surrounded by a transition, followed by outliers. This paved the way to defining an objective means for identifying the clusters from dendrograms. The adopted model also al…

Reliable Agglomerative Clustering

Standard agglomerative clustering suggests establishing a new reliable linkage at every step. However, in order to provide adaptive, density-consistent and flexible solutions, we study extracting all the reliable linkages at each step, instead of the smallest one. Such a strategy can be applied with all common criteria for agglomerative hierarchical clustering. We also study that this strategy with the single linkage criterion yields a minimum spanning tree algorithm. We perform experiments on several real-world datasets to demonstrate the performance of this strategy compared to the standard …

ClustGeo: an R package for hierarchical clustering with spatial constraints

In this paper, we propose a Ward-like hierarchical clustering algorithm including spatial/geographical constraints. Two dissimilarity matrices $D_0$ and $D_1$ are inputted, along with a mixing parameter $α\in [0,1]$. The dissimilarities can be non-Euclidean and the weights of the observations can be non-uniform. The first matrix gives the dissimilarities in the "feature space" and the second matrix gives the dissimilarities in the "constraint space". The criterion minimized at each stage is a convex combination of the homogeneity criterion calculated with $D_0$ and the homogeneity criterion ca…

Unsupervised Embedding of Hierarchical Structure in Euclidean Space

Deep embedding methods have influenced many areas of unsupervised learning. However, the best methods for learning hierarchical structure use non-Euclidean representations, whereas Euclidean geometry underlies the theory behind many hierarchical clustering algorithms. To bridge the gap between these two areas, we consider learning a non-linear embedding of data into Euclidean space as a way to improve the hierarchical clustering produced by agglomerative algorithms. To learn the embedding, we revisit using a variational autoencoder with a Gaussian mixture prior, and we show that rescaling the …

基于点积的层次聚类恢复隐藏树结构

Hierarchical clustering with dot products recovers hidden tree structure

提出一种按最大平均点积合并簇的凝聚式聚类变体，并在通用概率图模型下证明其可恢复隐藏生成树结构，真实数据表现优于 UPGMA、Ward 与 HDBSCAN。