Isbn: 9781330286982 - asymptotic properties of univariate sample k-means clusters (classic reprint) (3 risultati)

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condizione: New. Print on Demand. This book delves into the fascinating world of k-means clustering, a widely used method for grouping data points into distinct clusters. The author meticulously examines the properties of k-means clusters when the number of clusters, k, grows indefinitely alongside the sample size. The book's unique approach lies in its exploration of asymptotic properties, allowing readers to grasp the behavior of k-means clustering as both k and the sample size approach infinity. Through rigorous mathematical analysis, the author unveils the intriguing relationship between the lengths of neighboring clusters, demonstrating that they are inversely proportional to the cube root of the underlying density at their midpoints. Moreover, the book delves into the within-cluster sums of squares, a measure of cluster compactness. The author proves that in the asymptotic limit, these sums become asymptotically equal, providing valuable insights into the optimality of k-means clustering. This book is an invaluable resource for statisticians, data scientists, and researchers seeking a deeper understanding of the theoretical foundations of k-means clustering. Its insights shed light on the strengths and limitations of this widely applied clustering technique, ultimately contributing to more effective data analysis and decision-making. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.…