### Abstract

Reading the clusters from a data set such that the overall computational complexity is linear in both data dimensionality and in the number of data elements has been carried out through filtering the data in wavelet transform space. This objective is also carried out after an initial transforming of the data to a canonical order. Including high dimensional, high cardinality data, such a canonical order is provided by row and column permutations of the data matrix. In our recent work, we induce a hierarchical clustering from seriation through unidimensional representation of our observations. This linear time hierarchical classification is directly derived from the use of the Baire metric, which is simultaneously an ultrametric. In our previous work, the linear time construction of a hierarchical clustering is studied from the following viewpoint: representing the hierarchy initially in an m-adic, m = 10, tree representation, followed by decreasing m to smaller valued representations that include p-adic representations, where p is prime and m is a non-prime positive integer. This has the advantage of facilitating a more direct visualization and hence interpretation of the hierarchy. In this work we present further case studies and examples of how this approach is very advantageous for such an ultrametric topological data mapping.

Original language | English |
---|---|

Pages (from-to) | 37-42 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 56 |

DOIs | |

Publication status | Published - 1 Dec 2016 |

Externally published | Yes |

Event | 1st Institute of Mathematics Conference on Theoretical and Computational Discrete Mathematics - University of Derby, Derby, United Kingdom Duration: 22 Mar 2016 → 23 Mar 2016 https://ima.org.uk/1350/1st-ima-conference-theoretical-computational-discrete-mathematics/ (Link to Conference Website) |

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### Cite this

*Electronic Notes in Discrete Mathematics*,

*56*, 37-42. https://doi.org/10.1016/j.endm.2016.11.006

}

*Electronic Notes in Discrete Mathematics*, vol. 56, pp. 37-42. https://doi.org/10.1016/j.endm.2016.11.006

**Direct Reading Algorithm for Hierarchical Clustering.** / Murtagh, Fionn; Contreras, Pedro.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Direct Reading Algorithm for Hierarchical Clustering

AU - Murtagh, Fionn

AU - Contreras, Pedro

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Reading the clusters from a data set such that the overall computational complexity is linear in both data dimensionality and in the number of data elements has been carried out through filtering the data in wavelet transform space. This objective is also carried out after an initial transforming of the data to a canonical order. Including high dimensional, high cardinality data, such a canonical order is provided by row and column permutations of the data matrix. In our recent work, we induce a hierarchical clustering from seriation through unidimensional representation of our observations. This linear time hierarchical classification is directly derived from the use of the Baire metric, which is simultaneously an ultrametric. In our previous work, the linear time construction of a hierarchical clustering is studied from the following viewpoint: representing the hierarchy initially in an m-adic, m = 10, tree representation, followed by decreasing m to smaller valued representations that include p-adic representations, where p is prime and m is a non-prime positive integer. This has the advantage of facilitating a more direct visualization and hence interpretation of the hierarchy. In this work we present further case studies and examples of how this approach is very advantageous for such an ultrametric topological data mapping.

AB - Reading the clusters from a data set such that the overall computational complexity is linear in both data dimensionality and in the number of data elements has been carried out through filtering the data in wavelet transform space. This objective is also carried out after an initial transforming of the data to a canonical order. Including high dimensional, high cardinality data, such a canonical order is provided by row and column permutations of the data matrix. In our recent work, we induce a hierarchical clustering from seriation through unidimensional representation of our observations. This linear time hierarchical classification is directly derived from the use of the Baire metric, which is simultaneously an ultrametric. In our previous work, the linear time construction of a hierarchical clustering is studied from the following viewpoint: representing the hierarchy initially in an m-adic, m = 10, tree representation, followed by decreasing m to smaller valued representations that include p-adic representations, where p is prime and m is a non-prime positive integer. This has the advantage of facilitating a more direct visualization and hence interpretation of the hierarchy. In this work we present further case studies and examples of how this approach is very advantageous for such an ultrametric topological data mapping.

KW - analytics

KW - hierarchical clustering

KW - linear time computational complexity

KW - p-adic and m-adic number representation

KW - ultrametric topology

UR - http://www.scopus.com/inward/record.url?scp=85000350905&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2016.11.006

DO - 10.1016/j.endm.2016.11.006

M3 - Article

VL - 56

SP - 37

EP - 42

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -