{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T11:59:44Z","timestamp":1777031984581,"version":"3.51.4"},"reference-count":144,"publisher":"Elsevier","isbn-type":[{"value":"9780444862174","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1982]]},"DOI":"10.1016\/s0169-7161(82)02016-1","type":"book-chapter","created":{"date-parts":[[2005,4,18]],"date-time":"2005-04-18T19:58:53Z","timestamp":1113854333000},"page":"285-316","source":"Crossref","is-referenced-by-count":57,"title":["13 Theory of multidimensional scaling"],"prefix":"10.1016","author":[{"given":"Jan","family":"de Leeuw","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Willem","family":"Heiser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0169-7161(82)02016-1_bib1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4064\/fm-55-1-23-55","article-title":"Metric characterizations of Banach and Euclidean spaces","volume":"55","author":"Andalafte","year":"1964","journal-title":"Fund. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib2","doi-asserted-by":"crossref","first-page":"516","DOI":"10.2307\/1418869","article-title":"Dimensions of similarity","volume":"63","author":"Attneave","year":"1950","journal-title":"Amer. J. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib3","article-title":"An asymmetric Euclidean model: an alternating least squares method with optimal scaling features","author":"Baker","year":"1979","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib4","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF01115107","article-title":"Metrics and geodesics induced by order relations","volume":"101","author":"Beals","year":"1967","journal-title":"Math. Z."},{"key":"10.1016\/S0169-7161(82)02016-1_bib5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1037\/h0025470","article-title":"Foundations of multidimensional scaling","volume":"75","author":"Beals","year":"1968","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/BF02288932","article-title":"Multidimensional unfolding, determining the dimensionality of ranked preference data","volume":"25","author":"Bennett","year":"1960","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib7","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/0022-2496(78)90027-5","article-title":"Restricted multidimensional scaling","volume":"17","author":"Bentler","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib8","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/BF02293648","article-title":"Constrained multidimensional scaling in N-spaces","volume":"43","author":"Bloxom","year":"1978","journal-title":"Psychometrika"},{"issue":"2","key":"10.1016\/S0169-7161(82)02016-1_bib9","article-title":"Distance geometries","volume":"13","author":"Blumenthal","year":"1938","journal-title":"Univ. Missouri Studies"},{"key":"10.1016\/S0169-7161(82)02016-1_bib10","series-title":"Theory and Applications of Distance Geometry","author":"Blumenthal","year":"1953"},{"key":"10.1016\/S0169-7161(82)02016-1_bib11","series-title":"The Geometry of Metric and Linear Spaces","article-title":"Four point properties and norm postulates","volume":"490","author":"Blumenthal","year":"1975"},{"key":"10.1016\/S0169-7161(82)02016-1_bib12","series-title":"Mathematics in the Archeological and Historical Sciences","article-title":"The recovery of trees from measures of dissimilarity","author":"Bunemann","year":"1971"},{"key":"10.1016\/S0169-7161(82)02016-1_bib13","series-title":"The Geometry of Geodesics","author":"Busemann","year":"1955"},{"key":"10.1016\/S0169-7161(82)02016-1_bib14","series-title":"Recent Synthetic Differential Geometry","author":"Busemann","year":"1970"},{"key":"10.1016\/S0169-7161(82)02016-1_bib15","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1007\/BF02296969","article-title":"Spatial, non-spatial and hybrid models for scaling","volume":"41","author":"Carroll","year":"1976","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib16","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1146\/annurev.ps.31.020180.003135","article-title":"Multidimensional scaling","volume":"31","author":"Carroll","year":"1980","journal-title":"Ann. Rev. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib17","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF02310791","article-title":"Analysis of individual differences in multidimensional scaling via an N-way generalization of \u2018Eckart-Young\u2019 decomposition","volume":"35","author":"Carroll","year":"1970","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib18","series-title":"International Congress of Psychology","article-title":"CANDELINC: a new method for multidimensional analysis with constrained solutions","author":"Carroll","year":"1976"},{"key":"10.1016\/S0169-7161(82)02016-1_bib19","series-title":"American Psychological Association Meeting","article-title":"MULTILINC: multiway CANDELINC","author":"Carroll","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib20","series-title":"Contemporary Developments in Mathematical Psychology","article-title":"Models and methods for three-way multidimensional scaling","author":"Carroll","year":"1974"},{"key":"10.1016\/S0169-7161(82)02016-1_bib21","first-page":"267","article-title":"On a theorem in the geometry of position","volume":"2","author":"Cayley","year":"1841","journal-title":"Cambridge Math. J."},{"key":"10.1016\/S0169-7161(82)02016-1_bib22","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1146\/annurev.ps.24.020173.002353","article-title":"Scaling","volume":"24","author":"Cliff","year":"1973","journal-title":"Ann. Rev. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib23","doi-asserted-by":"crossref","first-page":"297","DOI":"10.2307\/2347165","article-title":"Graphical representation of asymmetric matrices","volume":"27","author":"Constantine","year":"1978","journal-title":"Appl. Statist."},{"key":"10.1016\/S0169-7161(82)02016-1_bib24","series-title":"A Theory of Data","author":"Coombs","year":"1964"},{"key":"10.1016\/S0169-7161(82)02016-1_bib25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.2307\/2344237","article-title":"A review of classification","volume":"134","author":"Cormack","year":"1971","journal-title":"J. Roy. Statist. Soc. Ser A."},{"key":"10.1016\/S0169-7161(82)02016-1_bib26","article-title":"Multidimensional scaling: a critique and an alternative","author":"Critchley","year":"1978"},{"key":"10.1016\/S0169-7161(82)02016-1_bib27","series-title":"Stimulus Generalization","article-title":"Metric properties of multidimensional stimulus generalization","author":"Cross","year":"1965"},{"key":"10.1016\/S0169-7161(82)02016-1_bib28","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0022-2496(78)90029-9","article-title":"Free trees and bidirectional trees as representations of psychological distance","volume":"17","author":"Cunningham","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib29","article-title":"The Euclidean distance model","author":"De Leeuw","year":"1970"},{"key":"10.1016\/S0169-7161(82)02016-1_bib30","series-title":"Progress in Statistics","article-title":"Applications of convex analysis to multidimensional scaling","author":"De Leeuw","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib31","series-title":"Geometric Representations of Relational Data","article-title":"Convergence of correction matrix algorithms for multidimensional scaling","author":"De Leeuw","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib32","series-title":"Maximum likelihood multidimensional scaling of interaction data","author":"De Leeuw","year":"1979"},{"key":"10.1016\/S0169-7161(82)02016-1_bib33","article-title":"Multidimensional scaling with restrictions on the configuration","volume":"Vol. V","author":"De Leeuw","year":"1980"},{"key":"10.1016\/S0169-7161(82)02016-1_bib34","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF02293809","article-title":"A new computational method to fit the weighted Euclidean model","volume":"43","author":"De Leeuw","year":"1978","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib35","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1111\/j.2044-8317.1973.tb00518.x","article-title":"The algebraic and statistical tractability of the city block metric","volume":"26","author":"Eisler","year":"1973","journal-title":"Brit. J. Math. Statist. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib36","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1086\/279880","article-title":"The systematic location of genes by means of cross-over ratios","volume":"56","author":"Fisher","year":"1922","journal-title":"American Naturalist"},{"key":"10.1016\/S0169-7161(82)02016-1_bib37","doi-asserted-by":"crossref","first-page":"705","DOI":"10.2307\/1968652","article-title":"Sur la d\u00e9finition axiomatique d'une classe d'espaces distanci\u00e9s vectoriellement applicable sur l'espace de Hilbert","volume":"36","author":"Fr\u00e9chet","year":"1935","journal-title":"Ann. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib38","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/BF02291494","article-title":"Metric unfolding: data requirements for unique solution and clarification of Sch\u00f6nemann's algorithm","volume":"38","author":"Gold","year":"1973","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib39","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/BF02441206","article-title":"\u00dcber \u00c4hnlichkeit bei gesehenen Figuren","volume":"21","author":"Goldmeier","year":"1937","journal-title":"Psychol. Forschung"},{"key":"10.1016\/S0169-7161(82)02016-1_bib40","series-title":"Progress in Statistics","article-title":"The analysis of asymmetry and orthogonality","author":"Gower","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib41","series-title":"The Prediction of Personal Adjustment","article-title":"The quantification of a class of attributes: a theory and method of scale construction","author":"Guttman","year":"1941"},{"key":"10.1016\/S0169-7161(82)02016-1_bib42","doi-asserted-by":"crossref","first-page":"139","DOI":"10.2307\/2086306","article-title":"A basis for scaling qualitative data","volume":"9","author":"Guttman","year":"1944","journal-title":"Amer. Sociol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib43","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1214\/aoms\/1177730977","article-title":"An approach for quantifying paired comparisons and rank order","volume":"17","author":"Guttman","year":"1946","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02016-1_bib44","series-title":"Measurement and Prediction","article-title":"The principal components of scale analysis","author":"Guttman","year":"1950"},{"key":"10.1016\/S0169-7161(82)02016-1_bib45","series-title":"Fifteenth Int. Congress Psychol.","article-title":"Introduction to facet design and analysis","author":"Guttman","year":"1957"},{"key":"10.1016\/S0169-7161(82)02016-1_bib46","first-page":"257","article-title":"Metricizing rank-ordered or unordered data for a linear factor analysis","volume":"21","author":"Guttman","year":"1959","journal-title":"Sankhya"},{"key":"10.1016\/S0169-7161(82)02016-1_bib47","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF02290164","article-title":"A general nonmetric technique for finding the smallest coordinate space for a configuration of points","volume":"33","author":"Guttman","year":"1968","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib48","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF02291362","article-title":"Measurement as structural theory","volume":"36","author":"Guttman","year":"1971","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib49","series-title":"The Analysis of Frequency Data","author":"Haberman","year":"1974"},{"key":"10.1016\/S0169-7161(82)02016-1_bib50","series-title":"Foundations of the PARAFAC procedure: models and conditions for an explanatory multi-modal factor analysis","author":"Harshman","year":"1970"},{"key":"10.1016\/S0169-7161(82)02016-1_bib51","article-title":"PARAFAC2: mathematical and technical notes","author":"Harshman","year":"1972"},{"key":"10.1016\/S0169-7161(82)02016-1_bib52","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1080\/01621459.1967.10500922","article-title":"Representation of similarity matrices by trees","volume":"62","author":"Hartigan","year":"1967","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02016-1_bib53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2333\/bhmk.1.1","article-title":"Minimum dimension analysis MDA: one of the methods of multidimensional quantification","volume":"1","author":"Hayashi","year":"1974","journal-title":"Behaviormetrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib54","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF02289716","article-title":"Multidimensional unfolding: determining configuration from complete rank order preference data","volume":"26","author":"Hays","year":"1961","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib55","series-title":"How to use SMACOF-I","author":"Heiser","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib56","first-page":"26","article-title":"Metric multidimensional unfolding","volume":"4","author":"Heiser","year":"1979","journal-title":"MDN, Bulletin VVS"},{"key":"10.1016\/S0169-7161(82)02016-1_bib57","series-title":"How to use SMACOF-III","author":"Heiser","year":"1979"},{"key":"10.1016\/S0169-7161(82)02016-1_bib58","series-title":"A multidimensional ratio scaling analysis of color relations","author":"Helm","year":"1959"},{"key":"10.1016\/S0169-7161(82)02016-1_bib59","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF02291218","article-title":"The relation between hierarchical and Euclidean models for psychological distances","volume":"37","author":"Holman","year":"1972","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib60","series-title":"US-Japan seminar on MDS","article-title":"An application of MDS to study binocular visual space","author":"Indow","year":"1975"},{"key":"10.1016\/S0169-7161(82)02016-1_bib61","first-page":"1323","article-title":"Symmetry and marginal homogeneity in an r \u00d7 r contingency table","volume":"64","author":"Ireland","year":"1969","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02016-1_bib62","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF02289588","article-title":"Hierarchical clustering schemes","volume":"32","author":"Johnson","year":"1967","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib63","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/BF02293808","article-title":"Structural analysis of covariance and correlation matrices","volume":"43","author":"J\u00f6reskog","year":"1978","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib64","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1093\/biomet\/49.1-2.239","article-title":"Factorization of matrices by least squares","volume":"49","author":"Keller","year":"1962","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib65","doi-asserted-by":"crossref","first-page":"298","DOI":"10.4153\/CJM-1968-029-7","article-title":"Products of zero-one matrices","volume":"20","author":"Kelly","year":"1968","journal-title":"Can. J. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib66","series-title":"The Geometry of Metric and Linear Spaces","article-title":"Hypermetric spaces","volume":"490","author":"Kelly","year":"1975"},{"key":"10.1016\/S0169-7161(82)02016-1_bib67","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF02288590","article-title":"Studies in measurement of the relations between sovereign states","volume":"6","author":"Klingberg","year":"1941","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib68","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/0022-2496(67)90051-X","article-title":"Rational distance functions for multidimensional scaling","volume":"4","author":"Krantz","year":"1967","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib69","series-title":"Mathematics of the Decision Sciences","article-title":"A survey of measurement theory","author":"Krantz","year":"1968"},{"key":"10.1016\/S0169-7161(82)02016-1_bib70","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/0022-2496(75)90047-4","article-title":"Similarity of rectangles: an analysis of subjective dimensions","volume":"12","author":"Krantz","year":"1975","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib71","article-title":"TUCKALS2: a principal component analysis of three mode data","author":"Kroonenberg","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib72","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1037\/0033-295X.85.5.445","article-title":"Concerning the applicability of geometric models to similarity data: the interrelationship between similarity and spatial density","volume":"85","author":"Krumhansl","year":"1978","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib73","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02289565","article-title":"Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis","volume":"29","author":"Kruskal","year":"1964","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib74","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1007\/BF02289694","article-title":"Nonmetric multidimensional scaling: a numerical method","volume":"29","author":"Kruskal","year":"1964","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib75","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF02293554","article-title":"More factors than subjects, tests, and treatments: an indeterminacy theorem for canonical decomposition and individual differences scaling","volume":"41","author":"Kruskal","year":"1976","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib76","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0024-3795(77)90069-6","article-title":"Trilinear decomposition of three-way arrays: rank and uniqueness in arithmetic complexity and in statistical models","volume":"18","author":"Kruskal","year":"1977","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0169-7161(82)02016-1_bib77","series-title":"Statistical Methods for Digital Computers","article-title":"Multidimensional scaling and other methods for discovering structure","author":"Kruskal","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib78","article-title":"Geometric models and badness of fit functions","volume":"Vol. II","author":"Kruskal","year":"1969"},{"key":"10.1016\/S0169-7161(82)02016-1_bib79","series-title":"Multidimensional Scaling","author":"Kruskal","year":"1978"},{"key":"10.1016\/S0169-7161(82)02016-1_bib80","series-title":"How to use KYST-2, a very flexible program to do multidimensional scaling and unfolding","author":"Kruskal","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib81","series-title":"Numerik und Anwendungen von Eigenwertaufgaben und Verzweigungsproblemen","article-title":"A review of numerical methods for eigenvalue problems nonlinear in the parameter","volume":"38","author":"Lancaster","year":"1977"},{"key":"10.1016\/S0169-7161(82)02016-1_bib82","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF02478456","article-title":"Neural mechanisms for the concepts of difference and similarity","volume":"7","author":"Landahl","year":"1945","journal-title":"Bull. Math. Biophysics"},{"key":"10.1016\/S0169-7161(82)02016-1_bib83","doi-asserted-by":"crossref","first-page":"344","DOI":"10.2307\/2373716","article-title":"Preorder relations and pseudoconvex metrics","volume":"97","author":"Lew","year":"1975","journal-title":"Amer. J. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib84","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0022-2496(78)90019-6","article-title":"Some counterexamples in multidimensional scaling","volume":"17","author":"Lew","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib85","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0022-2496(78)90025-1","article-title":"Constant curvature Riemannian scaling","volume":"17","author":"Lindman","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib86","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/BF02291398","article-title":"Some boundary conditions for a monotone analysis of symmetric matrices","volume":"36","author":"Lingoes","year":"1971","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib87","article-title":"A mathematical and empirical analysis of two multidimensional scaling algorithms","volume":"38","author":"Lingoes","year":"1973","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib88","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF02289711","article-title":"A choice theory analysis of similarity judgements","volume":"26","author":"Luce","year":"1961","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib89","article-title":"Detection and recognition","volume":"Vol. I","author":"Luce","year":"1963"},{"key":"10.1016\/S0169-7161(82)02016-1_bib90","series-title":"Mathematical Analysis of Binocular Vision","author":"Luneborg","year":"1947"},{"key":"10.1016\/S0169-7161(82)02016-1_bib91","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF02294055","article-title":"Effects of conditionality on INDSCAL and ALSCAL weights","volume":"42","author":"MacCallum","year":"1977","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib92","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF02293658","article-title":"A Monte Carlo investigation of recovery of structure by ALSCAL","volume":"42","author":"MacCallum","year":"1977","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib93","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF01448840","article-title":"Untersuchungen \u00fcber allgemeine Metrik","volume":"100","author":"Menger","year":"1928","journal-title":"Math. Ann."},{"key":"10.1016\/S0169-7161(82)02016-1_bib94","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1177\/001316445601600107","article-title":"Some recent theoretical developments in multidimensional scaling","volume":"16","author":"Messick","year":"1956","journal-title":"Ed. Psychol. Meas."},{"key":"10.1016\/S0169-7161(82)02016-1_bib95","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02289083","article-title":"The additive constant problem in multidimensional scaling","volume":"21","author":"Messick","year":"1956","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib96","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/0022-2496(72)90008-9","article-title":"Confusion-choice model for multidimensional psychophysics","volume":"9","author":"Nakatani","year":"1972","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib97","series-title":"Squared distance scaling as an alternative to principal components analysis","author":"Obenchain","year":"1971"},{"key":"10.1016\/S0169-7161(82)02016-1_bib98","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/0022-2496(75)90004-8","article-title":"Multidimensional scaling in Riemannian space","volume":"12","author":"Pieszko","year":"1975","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib99","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF02291762","article-title":"Solving implicit equations in psychometric data analysis","volume":"40","author":"Ramsay","year":"1975","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib100","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF02294052","article-title":"Maximum likelihood estimation in multidimensional scaling","volume":"42","author":"Ramsay","year":"1977","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib101","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF02293859","article-title":"Confidence regions for multidimensional scaling analysis","volume":"43","author":"Ramsay","year":"1978","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib102","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02289843","article-title":"A metric and an ordering on sets","volume":"24","author":"Restle","year":"1959","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib103","first-page":"659","article-title":"Multidimensional psychophysics","volume":"35","author":"Richardson","year":"1938","journal-title":"Psychol. Bull."},{"key":"10.1016\/S0169-7161(82)02016-1_bib104","series-title":"Metric analysis of ordinal data in psychology","author":"Roskam","year":"1968"},{"key":"10.1016\/S0169-7161(82)02016-1_bib105","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/BF02219773","article-title":"Simultaneous iteration method for symmetric matrices","volume":"16","author":"Rutishauser","year":"1970","journal-title":"Numer. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib106","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF02293862","article-title":"An alternative procedure to the additive constant problem in metric multidimensional scaling","volume":"43","author":"Saito","year":"1978","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib107","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF02293654","article-title":"Additive similarity trees","volume":"42","author":"Sattath","year":"1977","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib108","doi-asserted-by":"crossref","first-page":"724","DOI":"10.2307\/1968654","article-title":"Remarks to Maurice Fr\u00e9chet's article \u201cSur la d\u00e9finition axiomatique d'une classe d'espaces distanci\u00e9s vectoriellement applicable sur l'espace de Hilbert","volume":"38","author":"Schoenberg","year":"1935","journal-title":"Ann. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib109","doi-asserted-by":"crossref","first-page":"787","DOI":"10.2307\/1968835","article-title":"On certain metric spaces arising from Euclidean space by a change of metric and their imbedding in Hilbert space","volume":"40","author":"Schoenberg","year":"1937","journal-title":"Ann. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib110","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1090\/S0002-9947-1938-1501980-0","article-title":"Metric spaces and positive definite functions","volume":"44","author":"Schoenberg","year":"1938","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0169-7161(82)02016-1_bib111","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF02310794","article-title":"On metric multidimensional unfolding","volume":"35","author":"Sch\u00f6nemann","year":"1970","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib112","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/BF02291220","article-title":"An algebraic solution for a class of subjective metrics models","volume":"37","author":"Sch\u00f6nemann","year":"1972","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib113","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0022-2496(77)90065-7","article-title":"Similarity of rectangles","volume":"16","author":"Sch\u00f6nemann","year":"1977","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib114_1","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S1385-7258(55)50047-3","article-title":"Angles and distances in n-dimensional Euclidean and non-Euclidean geometry. Parts I, II, III","volume":"17","author":"Seidel","year":"1955","journal-title":"Indag. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib114_2","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/S1385-7258(55)50048-5","article-title":"Angles and distances in n-dimensional Euclidean and non-Euclidean geometry. Parts I, II, III","volume":"17","author":"Seidel","year":"1955","journal-title":"Indag. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib114_3","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/S1385-7258(55)50073-4","article-title":"Angles and distances in n-dimensional Euclidean and non-Euclidean geometry. Parts I, II, III","volume":"17","author":"Seidel","year":"1955","journal-title":"Indag. Math."},{"key":"10.1016\/S0169-7161(82)02016-1_bib115","series-title":"The Geometry of Metric and Linear Spaces","article-title":"Metric problems in elliptic geometry","volume":"490","author":"Seidel","year":"1975"},{"key":"10.1016\/S0169-7161(82)02016-1_bib116","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02288967","article-title":"Stimulus and response generalization: a stochastic model relating generalization to distance in psychological space","volume":"22","author":"Shepard","year":"1957","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib117","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1037\/h0042354","article-title":"Stimulus and response generalization: tests of a model relating generalization to distance in psychological space","volume":"55","author":"Shepard","year":"1958","journal-title":"J. Exp. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib118","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1037\/h0043083","article-title":"Stimulus and response generalization: deduction of the generalization gradient from a trace model","volume":"65","author":"Shepard","year":"1958","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib119_1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/BF02289630","article-title":"The analysis of proximities: multidimensional scaling with an unknown distance function, Parts I, II","volume":"27","author":"Shepard","year":"1962","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib119_2","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF02289621","article-title":"The analysis of proximities: multidimensional scaling with an unknown distance function, Parts I, II","volume":"27","author":"Shepard","year":"1962","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib120","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0022-2496(66)90017-4","article-title":"Metric structures in ordinal data","volume":"3","author":"Shepard","year":"1966","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib121","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02291665","article-title":"Representation of structure in similarity data: problems and prospects","volume":"39","author":"Shepard","year":"1974","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib122","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1037\/0033-295X.86.2.87","article-title":"Additive clustering: representation of similarities as combinations of discrete overlapping properties","volume":"86","author":"Shepard","year":"1979","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib123","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1111\/j.2517-6161.1972.tb00910.x","article-title":"Order-invariant methods for data analysis","volume":"34","author":"Sibson","year":"1972","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"key":"10.1016\/S0169-7161(82)02016-1_bib124","volume":"Vol. I and II","author":"Stumpf","year":"1880"},{"key":"10.1016\/S0169-7161(82)02016-1_bib125","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/BF02293745","article-title":"Nonmetric individual differences in multidimensional scaling: an alternating least squares method with optimal scaling features","volume":"42","author":"Takane","year":"1977","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib126","doi-asserted-by":"crossref","first-page":"672","DOI":"10.2307\/2305561","article-title":"A recurring theorem on determinants","volume":"56","author":"Taussky","year":"1949","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/S0169-7161(82)02016-1_bib127","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/BF02288916","article-title":"Multidimensional scaling I\u2014theory and methods","volume":"17","author":"Torgerson","year":"1952","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib128","series-title":"Theory and Methods of Scaling","author":"Torgerson","year":"1958"},{"key":"10.1016\/S0169-7161(82)02016-1_bib129","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF02289530","article-title":"Multidimensional scaling of similarity","volume":"30","author":"Torgerson","year":"1965","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib130","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0022-2496(78)90046-9","article-title":"A clarification of some current multiplicative confusion models","volume":"18","author":"Townsend","year":"1978","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib131","series-title":"The dimensional representation and the metric structure of similarity data","author":"Tversky","year":"1966"},{"key":"10.1016\/S0169-7161(82)02016-1_bib132","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1037\/0033-295X.84.4.327","article-title":"Features of similarity","volume":"84","author":"Tversky","year":"1977","journal-title":"Psychol. Rev."},{"key":"10.1016\/S0169-7161(82)02016-1_bib133","doi-asserted-by":"crossref","first-page":"124","DOI":"10.3758\/BF03210535","article-title":"Similarity of schematic faces: a test of interdimensional additivity","volume":"5","author":"Tversky","year":"1969","journal-title":"Perception and Psychophysics"},{"key":"10.1016\/S0169-7161(82)02016-1_bib134","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1016\/0022-2496(70)90041-6","article-title":"The dimensional representation and the metric structure of similarity data","volume":"7","author":"Tversky","year":"1970","journal-title":"J. Math. Psychol."},{"key":"10.1016\/S0169-7161(82)02016-1_bib135","first-page":"607","article-title":"Hyperbolic spaces and quadratic forms","volume":"37","author":"Valentine","year":"1969"},{"key":"10.1016\/S0169-7161(82)02016-1_bib136","doi-asserted-by":"crossref","first-page":"30","DOI":"10.3758\/BF03205762","article-title":"A test of independence of dimensions in multidimensional scaling","volume":"10","author":"Wender","year":"1971","journal-title":"Perception and Psychophysics"},{"key":"10.1016\/S0169-7161(82)02016-1_bib137","article-title":"A model for polynomial conjoint analysis algorithms","volume":"Vol. 1","author":"Young","year":"1972"},{"key":"10.1016\/S0169-7161(82)02016-1_bib138","series-title":"Similarity and Choice","article-title":"Quantifying qualitative data","author":"Young","year":"1980"},{"key":"10.1016\/S0169-7161(82)02016-1_bib139","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF02293652","article-title":"Three notes on ALSCAL","volume":"43","author":"Young","year":"1978","journal-title":"Psychometrika"},{"key":"10.1016\/S0169-7161(82)02016-1_bib140","series-title":"ALSCAL-4 User's guide","author":"Young","year":"1979"},{"key":"10.1016\/S0169-7161(82)02016-1_bib141","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF02287916","article-title":"discussion of a set of points in terms of their mutual distances","volume":"3","author":"Young","year":"1938","journal-title":"Psychometrika"}],"container-title":["Handbook of Statistics","Classification Pattern Recognition and Reduction of Dimensionality"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T19:31:41Z","timestamp":1735673501000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0169716182020161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982]]},"ISBN":["9780444862174"],"references-count":144,"URL":"https:\/\/doi.org\/10.1016\/s0169-7161(82)02016-1","relation":{},"ISSN":["0169-7161"],"issn-type":[{"value":"0169-7161","type":"print"}],"subject":[],"published":{"date-parts":[[1982]]}}}