{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1676"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1676","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"The Diver's Distance","abstract":"The visual assessment of clustering tendency (VAT) method, which was developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance and its properties. From the theoretical results, we develop an algorithm (ddVAT) to efficiently compute an ODM of diver's distances; its corresponding ODI proves to be more informative than the ODI obtained from VAT. Moreover, ddVAT turns out to be very efficient with linear clusters and very useful in cases where there is difficulty to satisfactorily represent cluster point representatives.","abstract_html":"The visual assessment of clustering tendency (VAT) method, which was developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance and its properties. From the theoretical results, we develop an algorithm (ddVAT) to efficiently compute an ODM of diver's distances; its corresponding ODI proves to be more informative than the ODI obtained from VAT. Moreover, ddVAT turns out to be very efficient with linear clusters and very useful in cases where there is difficulty to satisfactorily represent cluster point representatives.","abstract_has_math":false,"creators":["Sanou, Aristide Zezouma"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["James Bergin","James J. Burnham","Abebayehu Tekleselassie"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-01T07:00:00Z","date_published":"2012-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Clustering","Similiraty Measure","Data visualization","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/676","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["James Bergin","James J. 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C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance and its properties. From the theoretical results, we develop an algorithm (ddVAT) to efficiently compute an ODM of diver's distances; its corresponding ODI proves to be more informative than the ODI obtained from VAT. Moreover, ddVAT turns out to be very efficient with linear clusters and very useful in cases where there is difficulty to satisfactorily represent cluster point representatives."]},{"key":"dc:title","label":"Title","values":["The Diver's Distance"]}]}],"canonical_facts":{"dc:contributor":["James Bergin","James J. Burnham","Abebayehu Tekleselassie"],"dc:creator":["Sanou, Aristide Zezouma"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["The visual assessment of clustering tendency (VAT) method, which was developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance and its properties. From the theoretical results, we develop an algorithm (ddVAT) to efficiently compute an ODM of diver's distances; its corresponding ODI proves to be more informative than the ODI obtained from VAT. Moreover, ddVAT turns out to be very efficient with linear clusters and very useful in cases where there is difficulty to satisfactorily represent cluster point representatives."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/676"],"dc:subject":["ETD","Clustering","Similiraty Measure","Data visualization","Mathematics"],"dc:title":["The Diver's Distance"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}