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Massive Data Clustering in Moderate Dimensions from the Dual Spaces of Observation and Attribute Data Clouds
Fionn Murtagh
Cluster analysis of very high dimensional data can benefit from the properties of such high dimensionality. Informally expressed, in this work, our focus is on the analogous situat…
Big Data Scaling through Metric Mapping: Exploiting the Remarkable Simplicity of Very High Dimensional Spaces using Correspondence Analysis
Fionn Murtagh
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysi…
Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm
Fionn Murtagh, Pierre Legendre
The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in va…
Fast, Linear Time, m-Adic Hierarchical Clustering for Search and Retrieval using the Baire Metric, with linkages to Generalized Ultrametrics, Hashing, Formal Concept Analysis, and Precision of Data Measurement
Fionn Murtagh, Pedro Contreras
We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operat…
Fast, Linear Time Hierarchical Clustering using the Baire Metric
Pedro Contreras, Fionn Murtagh
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering al…
Hierarchical Clustering for Finding Symmetries and Other Patterns in Massive, High Dimensional Datasets
Fionn Murtagh, Pedro Contreras
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of sym…