IDENTIFICATION OF DATA STRUCTURES AND RELATIONSHIPS BY MATRIX REORDERING TECHNIQUES

THIS RESEARCH PAPER PRESENTS THE RESULTS OF A STUDY CONDUCTED TO DEVELOP ALOGIRTHMS FOR ORDERING AND ORGANIZING DATA THAT CAN BE PRESENTED IN A TWO-DIMENSIONAL MATRIX FORM. THE ONLY RESTRICTION IMPOSED ON THE ANALYSIS WAS THAT THE ROWS AND COLUMNS OF THE RAW INPUT DATA MATRICES COULD ONLY BE REORDERED, THUS PREVENTING THE CREATION OF ARTIFICIAL COEFFICIENTS OR LOSS OF ESSENTIAL INPUT INFORMATION. THIS STUDY DEVELOPS METHODS TO EXTRACT LATENT DATA PATTERNS, GROUPINGS, AND STRUCTURAL RELATIONSHIP WHICH ARE NOT APPARENT FROM THE RAW MATRIX DATA. THREE DISTINCT ALGORITHMS WERE DEVELOPED AND PRESENTED IN DETAIL. THE FIRST, THE BOND ENERGY ALGORITHM, IS CAPABLE OF IDENTIFYING AND DISPLAYING NATURAL GROUPS AND CLUSTERS THAT OCCUR IN COMPLEX DATA MATRICES. THE SECOND METHOD IS THE MOMENT ORDERING ALGORITHM, WHOSE PURPOSE IS TO IDENTIFY THE SINGLE DOMINANT RELATIONSHIP IN AN ARRAY OF DATA, AND TO REORDER THE ROWS AND COLUMNS OF THE ARRAY TO PRODUCE A RANKING UNDER THIS DOMINANT RELATIONSHIP. THE MOMENT COMPRESSION ALGORITHM IS DESIGNED TO IDENTIFY NATURAL GROUPS AND CLUSTERS OF ENTITIES BY FACTORING THE DATA RELATIONSHIP MATRIX INTO A NUMBER OF PIECES. THE AUTHORS CONCLUDED THAT THE BOND ENERGY ALGORITHM PROVED TO BE THE MOST GENERALLY USEFUL AND VERSATILE OF THE THREE ALGORITHMS FOR TREATING CERTAIN PROBLEMS OF MULTI-VARIATE ANALYSIS, WHILE THE MOMENT ORDERING ALGORITHM IS AN EFFICIENT TECHNIQUE FOR UNCOVERING AND DISPLAYING A UNIVARIATE RELATIONSHIP INHERENT IN THE DATA. IT IS A FAST AND DIRECT METHOD FOR UNCOVERING THE PRINCIPAL AXIS OF A DATA STRUCTURE. THE EFFICIENCY OF THE ALGORITHM WAS FOUND TO BE IN DIRECT PROPORTION TO ITS ULTIMATE SUCCESS IN IDENTIFYING A PRINCIPAL AXIS. /UMTA/

  • Supplemental Notes:
    • PROJ NO TRD-51
  • Corporate Authors:

    National Urban Coalition

    ,    
  • Authors:
    • Mccormic, W T
    • Deutsch, S B
    • MARTIN, J J
    • Schweitzer, P J
  • Publication Date: 1969-12

Subject/Index Terms

Filing Info

  • Accession Number: 00228285
  • Record Type: Publication
  • Source Agency: Urban Mass Transportation Administration
  • Files: TRIS, USDOT
  • Created Date: Jan 3 1973 12:00AM