16 August 2026

🕸️On Graph Theory: On Clusters (2020-2029)

"[...] scatterplots had advantages over earlier graphic forms: the ability to see clusters, patterns, trends, and relations in a cloud of points. Perhaps most importantly, it allowed the addition of visual annotations (point symbols, lines, curves, enclosing contours, etc.) to make those relationships more coherent and tell more nuanced stories." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"A small-world network is characterized by a high clustering coefficient and a short average path length, meaning that most nodes can be reached from any other node through a small number of intermediate connections. This structure often mirrors real-world social networks, where individuals are typically connected through a few mutual acquaintances, allowing for rapid information dissemination." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"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)

"ML is a useful - and under-utilized - framework for studying LLMs. For one thing, LLMs are literally composed of simple ML algorithms (linear weighted averages and nonlinear transformations). Furthermore, using ML techniques like regression, classification, and clustering, can help reveal how concepts like grammar rules are represented inside LLMs. And finally, many people find LLMs to be intimidatingly complicated while finding ML to be much more approachable. Thus, using ML to study LLMs involves using simple tools to understand complicated tools." (Mike X Cohen,"50 ML Projects To Understand LLMs", 2026)

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