Non Symmetrical Data Analysis: New Methods and Applications


  • Prof. Carlo Lauro
    Dipartimento di Matematica e Statistica – Universita’ degli Studi di Napoli “Federico II
  • FCUL – DEIO – Bloco C/2 – Piso 2 – Sala 2.2.47 – 15h
  • Segunda-feira, 16 de Dezembro de 2002
 Most of the well known and widely used techniques of multidimensional data analysis originated from Canonical Correlation Analysis (CCA), e.g. Discriminant Analysis and Correspondence Analysis. However, the application context of CCA is restricted to symmetrical relationships between two sets of quantitative variables or properly coded qualitative ones. In order to encompass this limit, some techniques, constituting the framework of Non Symmetrical Data Analysis, have been developed which take into account a priori information on the different roles of the variables. In this direction, Principal Component Analysis onto a Reference Subspace for quantitative variables and Non Symmetrical Correspondence Analysis for qualitative variables were developed by Lauro and D‚Ambra („Analisi in componenti principali in rapporto a un sottospazio di riferimento‰, Rivista di Statistica Applicata, 15, 1982; „L‚analyse non symetrique des correspondances‰ in: Data Analysis and Informatics, III  E. Diday et al. Eds.  North Holland, Amsterdam, 1984). Since then, particular attention has been paid to inferential problems in terms of suitable models (Lauro C. and Siciliano R. „Exploratory methods and modelling for contingency tables analysis: an integrated approach‰, Italian Journal of Applied Statistics, 1, 1989; Siciliano R., et al. „A probabilistic model for non-symmetric correspondence analysis and prediction in contingency tables‰, Journal of Italian Statistical Society, 1, 1993), stability and validation of results (Balbi S. „On stability in non symmetrical correspondence analysis using bootstrap‰, Statistica Applicata, 4, 1992). The most recent developments of Non Symmetrical Data Analysis extend the treatment to mixed variables (quantitative, ordinal and categorical data) and multiway data. This allows to improve the practice in various fields such as Marketing Research, Repeated Surveys and Quality Control. In fact, some theoretical relationships enable to enrich the interpretation of classical Conjoint Analysis (Lauro et al. „A Multidimensional Approach to Conjoint Analysis‰, Proceedings of Applied Stochastic Models and Data Analysis, Rocco Curto Editore – Napoli, 1997) and regression trees (Siciliano R. and Mola F. „Ternary Classification Trees: a Factorial Analysis‰ in: Visualisation of Categorical Data  M. Greenacre and J. Blasius eds.  Academic Press, 1997), to graphically compare panel data by means of trajectories (Lauro et al. „A multiway data analysis technique for comparing surveys‰, Methodologica, 3, 1994) and Procrustean rotations (Balbi S. and Esposito V. „Rotated Canonical Analysis onto a Reference Subspace‰, Invited lecture, Second IASC World Conference, Pasadena, 1997), to build non parametric multidimensional confidence regions useful for Total Quality Control (Lauro et al. „Differenti approcci nella costruzione di carte di controllo multivariato‰, Studi in onore di Giampiero Landenna, Giuffrè Editore, 1996). The present lecture intends to give an overview on the methodological framework and algorithms of Non Symmetrical Data Analysis highlighting the application aspects of the mentioned extensions as well as to show some promising developments for the treatment of highly structured data such as symbolic data and evolutionary data.