Classification and dissimilarity analysis
著者
書誌事項
Classification and dissimilarity analysis
(Lecture notes in statistics, v. 93)
Springer-Verlag, c1994
大学図書館所蔵 全49件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 225-238
内容説明・目次
内容説明
Classifying objects according to their likeness seems to have been a step in the human process of acquiring knowledge, and it is certainly a basic part of many of the sciences. Historically, the scientific process has involved classification and organization particularly in sciences such as botany, geology, astronomy, and linguistics. In a modern context, we may view classification as deriving a hierarchical clustering of objects. Thus, classification is close to factorial analysis methods and to multi-dimensional scaling methods. It provides a mathematical underpinning to the analysis of dissimilarities between objects.
目次
1 Introduction.- 1.1 Classification in the history of Science.- 1.2 Dissimilarity analysis.- 1.3 Organisation of this publication.- 1.4 References.- 2 The partial order by inclusion of the principal classes of dissimilarity on a finite set, and some of their basic properties.- 2.1 Introduction.- 2.1.1 What is dissimilarity analysis?.- 2.1.2 What's in this chapter?.- 2.2 Preliminaries.- 2.2.1 The vector space D generated by the dissimilarities.- 2.2.2 Some elementary dissimilarities.- 2.2.3 Some general types of dissimilarities.- 2.2.4 Stability under increasing transformations.- 2.2.5 The quotient space of an even dissimilarity.- 2.2.6 Embeddability in a metric space.- 2.2.7 The set of all semi-distances.- 2.2.8 Stability under replication.- 2.3 The general structures of dissimilarity data analysis and their geometrical and topological nature.- 2.3.1 Euclidean semi-distances.- 2.3.2 Semi-distances of L1-type.- 2.3.3 Hypermetric semi-distances.- 2.3.4 Quasi-hypermetric dissimilarities.- 2.3.5 Ultrametric semi-distances.- 2.3.6 Tree semi-distances.- 2.3.7 Star semi-distances.- 2.3.8 Robinsonian dissimilarities.- 2.3.9 Strongly-Robinsonian dissimilarities.- 2.4 Inclusions.- 2.4.1 Some immediate inclusions.- 2.4.2 Other inclusions.- 2.5 The convex hulls.- 2.6 When are the inclusions strict?.- 2.7 The inclusions shown are exhaustive.- 2.8 Discussion.- 2.8.1 Further mathematical study.- 2.8.2 Extensions to other types of data.- 2.8.3 Connections with neighbouring disciplines.- 2.8.4 The future of dissimilarity analysis.- Acknowledgements.- References.- 3 Similarity functions.- 3.1 Introduction.- 3.2 Definitions. Examples.- 3.2.1 Definitions.- 3.2.2 Examples.- 3.2.2.1 Linear function.- 3.2.2.2 Homographic function.- 3.2.2.3 Quadratic function.- 3.2.2.4 Exponential function.- 3.2.2.5 Circular function.- 3.2.2.6 Graphical representations.- 3.3 The WM (DP) forms.- 3.3.1 Definitions and properties.- 3.3.2 The WM(D2) form.- Torgerson form.- 3.3.3 Transformations of D.- D? and the Euclidean distances.- 3.4 The WM(D) form.- 3.4.1 Geometrical interpretations and properties.- 3.4.2 About metric projection.- 3.4.3 WM(D) and "M1-type" distance.- Appendix: Some indices of dissimilarity for categorical variables.- References.- 4 An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. I.- 4.1 Introduction and overview.- 4.2 A few notes on ordered sets.- 4.2.1 Introduction.- 4.2.2 Duality and order-isomorphisms.- 4.2.3 Semi-lattices and lattices.- 4.2.4 Residual and residuated mappings.- 4.3 Predissimilarities.- 4.4 Bijections.- 4.4.0 Overview.- 4.4.1 Indexed hierarchies (S finite, L = ?+).- 4.4.2 Dendrograms (S finite, L = ?+).- 4.4.3 Numerically stratified clusterings (S finite, L = ?+).- 4.4.4 Indexed regular generalised hierarchies (S arbitrary, L = ?+).- 4.4.5 Generalised dendrograms (S arbitrary, L = ?+).- 4.4.6 Prefilters (S arbitrary, L = ?+).- 4.4.6 Residual maps (S finite, L obeys LMIN and JSL).- 4.5 The unifying and generalising result.- 4.6 Further properties of an ordered set.- 4.7 Stratifications and generalised stratifications.- 4.8 Residual maps.- 4.9 On the associated residuated maps.- 4.10 Some applications to mathematical classification.- Acknowledgements.- Appendix A: Proofs.- References.- 5 An order-theoretic unification and generalisation of certain fundamental bijections in mathematical classification. II.- 5.1 Introduction and overview.- 5.2 The case E = A x B of theorem 4.5.1.- 5.3 Other aspects of the case E = A x B.- 5.3.1 Duality.- 5.3.2 Multiway data.- 5.3.3 Residual maps.- 5.4 Prefilters.- 5.5 Ultrametrics and reflexive level foliations.- 5.5.1 The main result.- 5.5.2 Remarks on Theorem 5.5.1.- 5.5.3 Variants of Theorem 5.5.1.- 5.6 On generalisations of indexed hierarchies.- 5.6.1 Introduction.- 5.6.2 Benzecri structures.- 5.6.3 Special cases of Benzecri structures.- 5.6.4 The condition LSU.- 5.7 Benzecri structures.- 5.8 Subdominants.- Acknowledgements.- Appendix B: Proofs.- References.- 6 The residuation model for the ordinal construction of dissimilarities and other valued objects.- 6.1 Introduction.- 6.2 Residuated mappings and closure operators.- 6.2.1 Residuated and residual mappings.- 6.2.2 Closure and anticlosure operators.- 6.3 Lattices of objects and lattices of values.- 6.3.1 Lattices.- 6.3.2 Distributivity.- 6.3.3 Lattices of objects: ten examples.- 6.3.4 Lattices of values.- 6.4 Valued objects.- 6.4.1 Consequences of the lattice structures hypothesis.- 6.4.2 Valued objects: definitions and examples.- 6.5 Lattices of valued objects.- 6.6 Notes and conclusions.- Acknowledgements.- References.- 7 On exchangeability-based equivalence relations induced by strongly Robinson and, in particular, by quadripolar Robinson dissimilarity matrices.- 7.1 Overview.- 7.1.1 Preamble.- 7.1.2 Quadripolar, Robinson and strongly Robinson matrices.- 7.1.3 Plan and principal results.- 7.2 Preliminaries.- 7.3 Quadripolar Robinson matrices of order four.- Equivalence relations induced by strongly Robinson matrices.- 7.4.1 Exchangeability and connectedness.- 7.4.2 Internal evenness.- 7.4.3 Logical relationships.- 7.5 Reduced forms.- 7.5.1 External evenness.- 7.5.2 Properties of reduced forms.- 7.6 Limiting r-forms of strongly Robinson matrices.- 7.4 Limiting r-forms of quadripolar Robinson matrices.- References.- 8 Dimensionality problems in L1-norm representations.- 8.1 Introduction.- 8.2 Preliminaries and notations.- 8.2.1 Dissimilarities.- 8.2.2 Some notations.- 8.2.3 Some characterizations.- 8.3 Dimensionality for semi-distances of Lp-type.- 8.4 Dimensionality for semi-distances of L1-type.- 8.5 Numerical characterizations of semi-distances of L1-type.- 8.5.1 Solving the general problem.- 8.5.2 Reducing the problem.- 8.5.3 Approximations.- 8.5.3.1 Least absolute deviations approximations.- 8.5.3.2 Least squares approximation.- 8.5.3.3 The additive constants.- 8.6 Appendices.- 8.6.1 Appendix 1.- 8.6.2 Appendix 2.- 8.6.3 Appendix 3.- 8.6.4 Appendix 4.- References.- Unified reference list.
「Nielsen BookData」 より