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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of classification 11 (1994), S. 195-207 
    ISSN: 1432-1343
    Keywords: Canonical variate analysis ; Categorical and mixed data ; Distances ; Diversity coefficients ; Metric scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A low-dimensional representation of multivariate data is often sought when the individuals belong to a set ofa-priori groups and the objective is to highlight between-group variation relative to that within groups. If all the data are continuous then this objective can be achieved by means of canonical variate analysis, but no corresponding technique exists when the data are categorical or mixed continuous and categorical. On the other hand, if there is noa-priori grouping of the individuals, then ordination of any form of data can be achieved by use of metric scaling (principal coordinate analysis). In this paper we consider a simple extension of the latter approach to incorporate grouped data, and discuss to what extent this method can be viewed as a generalization of canonical variate analysis. Some illustrative examples are also provided.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of classification 7 (1990), S. 81-98 
    ISSN: 1432-1343
    Keywords: Between-group analysis ; Canonical variate analysis ; Common principal component model ; Eigenvalues and eigenvectors ; Matusita distance between populations ; Metric scaling ; Principal component analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Analysis of between-group differences using canonical variates assumes equality of population covariance matrices. Sometimes these matrices are sufficiently different for the null hypothesis of equality to be rejected, but there exist some common features which should be exploited in any analysis. The common principal component model is often suitable in such circumstances, and this model is shown to be appropriate in a practical example. Two methods for between-group analysis are proposed when this model replaces the equal dispersion matrix assumption. One method is by extension of the two-stage approach to canonical variate analysis using sequential principal component analyses as described by Campbell and Atchley (1981). The second method is by definition of a distance function between populations satisfying the common principal component model, followed by metric scaling of the resulting between-populations distance matrix. The two methods are compared with each other and with ordinary canonical variate analysis on the previously introduced data set.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Statistics and computing 10 (2000), S. 209-229 
    ISSN: 1573-1375
    Keywords: cross-validation ; ridge regression ; partial least squares ; prediction ; assessment of predictive models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a Monte Carlo investigation of a number of variants of cross-validation for the assessment of performance of predictive models, including different values of k in leave-k-out cross-validation, and implementation either in a one-deep or a two-deep fashion. We assume an underlying linear model that is being fitted using either ridge regression or partial least squares, and vary a number of design factors such as sample size n relative to number of variables p, and error variance. The investigation encompasses both the non-singular (i.e. n 〉 p) and the singular (i.e. n ≤ p) cases. The latter is now common in areas such as chemometrics but has as yet received little rigorous investigation. Results of the experiments enable us to reach some definite conclusions and to make some practical recommendations.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 9 (1995), S. 509-520 
    ISSN: 0886-9383
    Keywords: canonical variates ; discriminant analysis ; partial least squares ; principal components ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new set of derived variables is proposed for exhibiting group separation in multivariate data on for preprocessing such data prior to discriminant analysis. The technique combines optimal features of canonical variate analysis and principal component analysis: the derived variables are linear combinations of the original variables that optimize the canonical variate criterion (ratio of between-group to within-group variance) but subject to the orthogonality constraints of principal components. In this formulation the canonical variates can be derived even when the within-group matrix is singular (i.e. when there are more variables than objects in the data matrix). A simple computational algorithm for extraction of these variables is proposed. The methods are illustrated on several data sets and compared with alternative techniques such as principal component analysis and partial least squares.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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