🕸️On Graph Theory: On Clusters (-1999)

"To the untrained eye, randomness appears as regularity or tendency to cluster." (William Feller, "An Introduction to Probability Theory and its Applications", 1950) 

"An average is sometimes called a 'measure of central tendency' because individual values of the variable usually cluster around it. Averages are useful, however, for certain  types of data in which there is little or no central tendency." (William A Spirr & Charles P Bonini, "Statistical Analysis for Business Decisions" 3rd Ed., 1967)

"In comparison with Predicate Calculus encoding s of factual knowledge, semantic nets seem more natural and understandable. This is due to the one-to-one correspondence between nodes and the concepts they denote, to the clustering about a particular node of propositions about a particular thing, and to the visual immediacy of 'interrelationships' between concepts, i.e., their connections via sequences of propositional links." (Lenhart K Schubert, "Extending the Expressive Power of Semantic Networks", Artificial Intelligence 7, 1976)

"Unlike the theory, models are restricted by technical considerations to a few components at a time, even in systems which are complex. Thus a satisfactory theory is usually a cluster of models. These models are related to each other in several ways : as coordinate alternative models for the same set of phenomena, they jointly produce robust theorems; as complementary models they can cope with different aspects of the same problem and give complementary as well as overlapping results; as hierarchically arranged 'nested' models, each provides an interpretation of the sufficient parameters of the next higher level where they are taken as given." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"Randomness is a difficult notion for people to accept. When events come in clusters and streaks, people look for explanations and patterns. They refuse to believe that such patterns - which frequently occur in random data - could equally well be derived from tossing a coin. So it is in the stock market as well." (Burton G Malkiel, "A Random Walk Down Wall Street", 1989)

"In physics, there are numerous phenomena that are said to be 'true on all scales', such as the Heisenberg uncertainty relation, to which no exception has been found over vast ranges of the variables involved (such as energy versus time, or momentum versus position). But even when the size ranges are limited, as in galaxy clusters (by the size of the universe) or the magnetic domains in a piece of iron near the transition point to ferromagnetism (by the size of the magnet), the concept true on all scales is an important postulate in analyzing otherwise often obscure observations." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"[…] semantic nets fail to be distinctive in the way they (1) represent propositions, (2) cluster information for access, (3) handle property inheritance, and (4) handle general inference; in other words, they lack distinctive representational properties (i.e., 1) and distinctive computational properties (i.e., 2-4). Certain propagation mechanisms, notably 'spreading activation', 'intersection search', or 'inference propagation' have sometimes been regarded as earmarks of semantic nets, but since most extant semantic nets lack such mechanisms, they cannot be considered criterial in current usage." (Lenhart K Schubert, "Semantic Nets are in the Eye of the Beholder", 1990)

"Black-noise phenomena govern natural and unnatural catastrophes like floods, droughts, bear markets, and various outrageous outages, such as those of electrical power. Because of their black spectra, such disasters often come in clusters." (Manfred R Schroeder, "Fractals, Chaos, Power Laws", 1991)

"Many of the basic functions performed by neural networks are mirrored by human abilities. These include making distinctions between items (classification), dividing similar things into groups (clustering), associating two or more things (associative memory), learning to predict outcomes based on examples (modeling), being able to predict into the future (time-series forecasting), and finally juggling multiple goals and coming up with a good- enough solution (constraint satisfaction)." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Regression to the mean occurs when the process produces results that are statistically independent or negatively correlated. With strong negative serial correlation, extremes are likely to be reversed each time (which would reinforce the instructors' error). In contrast, with strong positive dependence, extreme results are quite likely to be clustered together." (Dan Trietsch, "Statistical Quality Control : A loss minimization approach", 1998)