Shape complexity in cluster analysis.
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the workhorse in this preprocessing phase has been to divide the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2023-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0286312 |
| _version_ | 1797799806283808768 |
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| author | Eduardo J Aguilar Valmir C Barbosa |
| author_facet | Eduardo J Aguilar Valmir C Barbosa |
| author_sort | Eduardo J Aguilar |
| collection | DOAJ |
| description | In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the workhorse in this preprocessing phase has been to divide the data by the standard deviation along each dimension. Like division by the standard deviation, the great majority of scaling techniques can be said to have roots in some sort of statistical take on the data. Here we explore the use of multidimensional shapes of data, aiming to obtain scaling factors for use prior to clustering by some method, like k-means, that makes explicit use of distances between samples. We borrow from the field of cosmology and related areas the recently introduced notion of shape complexity, which in the variant we use is a relatively simple, data-dependent nonlinear function that we show can be used to help with the determination of appropriate scaling factors. Focusing on what might be called "midrange" distances, we formulate a constrained nonlinear programming problem and use it to produce candidate scaling-factor sets that can be sifted on the basis of further considerations of the data, say via expert knowledge. We give results on some iconic data sets, highlighting the strengths and potential weaknesses of the new approach. These results are generally positive across all the data sets used. |
| first_indexed | 2024-03-13T04:25:31Z |
| format | Article |
| id | doaj.art-140d489a278d46e19ae3894a0953ce11 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-03-13T04:25:31Z |
| publishDate | 2023-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-140d489a278d46e19ae3894a0953ce112023-06-20T05:31:19ZengPublic Library of Science (PLoS)PLoS ONE1932-62032023-01-01185e028631210.1371/journal.pone.0286312Shape complexity in cluster analysis.Eduardo J AguilarValmir C BarbosaIn cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the workhorse in this preprocessing phase has been to divide the data by the standard deviation along each dimension. Like division by the standard deviation, the great majority of scaling techniques can be said to have roots in some sort of statistical take on the data. Here we explore the use of multidimensional shapes of data, aiming to obtain scaling factors for use prior to clustering by some method, like k-means, that makes explicit use of distances between samples. We borrow from the field of cosmology and related areas the recently introduced notion of shape complexity, which in the variant we use is a relatively simple, data-dependent nonlinear function that we show can be used to help with the determination of appropriate scaling factors. Focusing on what might be called "midrange" distances, we formulate a constrained nonlinear programming problem and use it to produce candidate scaling-factor sets that can be sifted on the basis of further considerations of the data, say via expert knowledge. We give results on some iconic data sets, highlighting the strengths and potential weaknesses of the new approach. These results are generally positive across all the data sets used.https://doi.org/10.1371/journal.pone.0286312 |
| spellingShingle | Eduardo J Aguilar Valmir C Barbosa Shape complexity in cluster analysis. PLoS ONE |
| title | Shape complexity in cluster analysis. |
| title_full | Shape complexity in cluster analysis. |
| title_fullStr | Shape complexity in cluster analysis. |
| title_full_unstemmed | Shape complexity in cluster analysis. |
| title_short | Shape complexity in cluster analysis. |
| title_sort | shape complexity in cluster analysis |
| url | https://doi.org/10.1371/journal.pone.0286312 |
| work_keys_str_mv | AT eduardojaguilar shapecomplexityinclusteranalysis AT valmircbarbosa shapecomplexityinclusteranalysis |