Abstract
We give a first comparison between the Principal Component Analysis PCA (“one of the oldest and best known techniques of multivariate analysis” cf. JOLLIFFE [6]) respectively of the analysis using biplots (GABRIEL [1], [2]) and an algebraic technique for the visualization of data, namely the Formal Concept Analysis FCA (WILLE [11]) by applying both methods to matrices, called Repertory Grids, which are the usual data form in many psychological investigations (SLATER [8]).
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Bibliography
Gabriel, K.R. (1971): The biplot graphic display of matrices with application to principal component analysis. Biometrica 58, 453–467.
Gabriel, K.R. (1981): Biplot display of multivariate matrices for inspection of data and diagnosis. In: V. Barnett (ed.): Interpreting multivariate data. Wiley, Chichester, 147–173.
Ganter, B., Stahl, J., Wille, R. (1986): Conceptual measurement and manyvalued contexts. In: Gaul, W., Schader, M. (eds.): Classification as a tool of research. North-Holland, Amsterdam, 169–176.
Ganter, B., Wille, R. (1988): Conceptual Scaling. FB4-Preprint Nr. 1174, TH Darmstadt.
Golub, G.H., Reinsch, C. (1971): Singular Value Decomposition and Least Squares Solutions. In: Wilkinson, J.H., Reinsch, C: Linear Algebra, Springer Verlag, Berlin, Heidelberg, New York, 134–151.
Jolliffe, I.T. (1986): Principal Component Analysis. Springer-Verlag, New York.
Roberts, F.S. (1979): Measurement theory. Addison-Wesley, Reading.
Slater, P. (1977): The measurement of interpersonal space by Grid Technique. Vol. I and II, Wiley, New York.
Spangenberg, N., Wolff, K.E. (1988): Conceptual grid evaluation. In: Bock, H.H. (ed.): Classification and related methods of data analysis. Proceedings of the First Conference of the International Federation of Classification Societies, Technical University of Aachen/FRG, 1987, North Holland, Amsterdam 577–580.
pangenberg, N., Wolff, K.E.: Formal Concept Analysis of Repertory Grids: A case study of a patient with Anorexia nervosa. To appear in the J. of Personality Assessment, Florida, USA.
Wille, R. (1982): Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.): Ordered Sets. Reidel, Dordrecht-Boston, 445–470.
Wille, R. (1987): Bedeutungen von Begriffsverbänden. In: Ganter, B., Wille, R., Wolff, K.E. (eds.): Beiträge zur Begriffsanalyse. B.I.-Wissenschaftsverlag, Mannheim/Wien/Zürich, 161–211.
Wille. R. (1989): Lattices in data analysis: How to draw them with a computer. In: Rival, I. (ed.): Algorithms and order. Kluver Academic Publishers, 33–58.
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© 1991 Springer-Verlag Berlin · Heidelberg
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Spangenberg, N., Wolff, K.E. (1991). Comparison of Biplot Analysis and Formal Concept Analysis in the case of a Repertory Grid. In: Bock, HH., Ihm, P. (eds) Classification, Data Analysis, and Knowledge Organization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76307-6_15
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DOI: https://doi.org/10.1007/978-3-642-76307-6_15
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