📉Graphical Representation: Dendrogram (Just the Quotes

"Hierarchical clustering creates a hierarchy of clusters which can be represented in a treelike diagram, called a dendrogram. In the dendrogram, units in the same cluster are joined by a horizontal line, with the scale on the y-axis of the dendrogram reflecting a measure of the distances of the units within the cluster. The leaves at the bottom of the dendrogram represent the individual units; leaves are combined to form small branches, small branches are combined into larger branches, until one reaches the trunk or root of the tree that represents a single cluster containing all units. Dendrograms are quite useful as they give us a visual representation of the clusters." (Johannes Ledolter, "Data mining and business analytics with R", 2013)

"Different joining/linkage rules change how the final hierarchical clustering is presented. [...] Since the barrier for merging observations and clusters is lowest with the single linkage approach, the clustering dendrogram may contain chains of clusters as well as clusters that are spread out. The barrier to joining clusters is highest with complete linkage; however, it is possible that an observation is closer to observations in other clusters than the cluster to which it has been assigned. The average linkage approach moderates the tendencies of the single or complete linkage approaches." (Glenn J Myatt & Wayne P Johnson. 

"Making sense of data I: a practical guide to exploratory data analysis and data mining" 2nd. Ed., 2014)

"Horizontal trees have proved highly efficient for archetypal models such as classification trees, flow charts, mind maps, dendrograms, and, notably, in the display of files on several software applications and operating systems. If you are a computer user, there is a strong chance you have interacted with some version of a horizontal tree - perhaps on a daily basis." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 2014)

"Determining the optimal number of clusters in a data set is a fundamental issue in partitioning clustering, such as k-means clustering, which requires the user to specify the number of clusters k to be generated. Unfortunately, there is no definitive answer to this question. The optimal number of clusters is somehow subjective and depends on the method used for measuring similarities and the parameters used for partitioning. A simple and popular solution consists of inspecting the dendrogram produced using hierarchical clustering to see if it suggests a particular number of clusters. Unfortunately, this approach is also subjective." (Alboukadel Kassambara, "Practical Guide To  Cluster Analysis in R: Unsupervised Machine Learning", 2016)

"The dendrogram is a multilevel hierarchy where clusters at one level are joined together to form the clusters at the next levels. This makes it possible to decide the level at which to cut the tree for generating suitable groups of a data objects." (Alboukadel Kassambara, "Practical Guide To  Cluster Analysis in R: Unsupervised Machine Learning", 2016)

"Hierarchical clustering is comprised of a general family of clustering algorithms that construct nested clusters by successive merging or splitting of data. The hierarchy of clusters is represented as a tree. The tree is usually called a dendrogram. The root of the dendrogram is the single cluster that contains all the samples; the leaves are the clusters containing only one sample each. This is a nice tool, since it can be straightforwardly interpreted: it 'explains' how clusters are formed and visualizes clusters at different scales. The tree that results from the technique shows the similarity between the samples. Partitioning is computed by selecting a cut on the tree at a certain level." (Laura Igual & Santi Seguí, "Introduction to Data Science: A Python Approach to Concepts, Techniques and Applications", 2017) 

"A tree-like structure or a tree diagram, one showing taxonomic (classification-related) relationships, is created. It is known as a dendrogram. It has branches pointing toward categories or classes. It is a pattern formed by a series of splits or segments of a given quantity of data over a set of compartments and the flow components. From this pattern, a description can be made of the profile of data allocation over the set of functional or structural compartments. The merger of clusters is terminated after every data point lies in one single cluster at the top of the tree." (Vinod K Khanna, "Introduction to Machine Learning Algorithms:  Basic Principles and Mathematics", 2026)

"Hierarchical clustering is summarised by a dendrogram, which sequentially shows points being joined to form a cluster, with the corresponding distances. Breaking the data into clusters is done by cutting the dendrogram at the long edges. [...] Plotting the dendrogram in the data space can help you understand how the hierarchical clustering has collected the points together into clusters. You can learn if the algorithm has been confused by nuisance patterns in the data, and how different choices of linkage method affect the result." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Viewing the dendrograms in high dimensions provides insight into how the algorithm has joined points to clusters. For example, single linkage often has edges leading to a single focal point, which might not yield a useful clustering but might help to identify outliers. If the edges point to multiple focal points, with long edges bridging gaps in the data, the result is more likely yielding a useful clustering." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)