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Full-Text Articles in Physical Sciences and Mathematics
In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento
In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento
Journal of Humanistic Mathematics
This article is a gentle introduction to K-means, a mathematical technique of processing data for further classification. We begin with a brief historical introduction, where we find connections with Plato’s Timæus, von Linné’s binomial classification, and the star clustering concept of Mary Sommerville and collaborators. Artificial intelligence algorithms use K-means as a classification methodology to learn about data in a very accurate way, because it is a quantitative procedure based on similarities.
Rainbow Turán Problems For Paths And Forests Of Stars, Daniel Johnston, Cory Palmer, Amites Sarkar
Rainbow Turán Problems For Paths And Forests Of Stars, Daniel Johnston, Cory Palmer, Amites Sarkar
Mathematics Faculty Publications
For a fixed graph F, we would like to determine the maximum number of edges in a properly edge-colored graph on n vertices which does not contain a rainbow copy of F, that is, a copy of F all of whose edges receive a different color. This maximum, denoted by ex∗ (n, F), is the rainbow Turán number of F, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstraëte [Combinatorics, Probability and Computing 16 (2007)]. We determine ex∗ (n, F) exactly when F is a forest of stars, and …