Computer Engineering Commons^™

K-Means Clustering Using Gravity Distance, Ajinkya Vishwas Indulkar

Masters Theses & Specialist Projects

Clustering is an important topic in data modeling. K-means Clustering is a well-known partitional clustering algorithm, where a dataset is separated into groups sharing similar properties. Clustering an unbalanced dataset is a challenging problem in data modeling, where some group has a much larger number of data points than others. When a K-means clustering algorithm with Euclidean distance is applied to such data, the algorithm fails to form good clusters. The standard K-means tends to split data into smaller clusters during a clustering process evenly.

We propose a new K-means clustering algorithm to overcome the disadvantage by introducing a different …

Topological Hierarchies And Decomposition: From Clustering To Persistence, Kyle A. Brown

Browse all Theses and Dissertations

Hierarchical clustering is a class of algorithms commonly used in exploratory data analysis (EDA) and supervised learning. However, they suffer from some drawbacks, including the difficulty of interpreting the resulting dendrogram, arbitrariness in the choice of cut to obtain a flat clustering, and the lack of an obvious way of comparing individual clusters. In this dissertation, we develop the notion of a topological hierarchy on recursively-defined subsets of a metric space. We look to the field of topological data analysis (TDA) for the mathematical background to associate topological structures such as simplicial complexes and maps of covers to clusters in …