Alternative common bases and signal compression for wavelets application in chemometrics |
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Authors: | Michele Forina Paolo Oliveri Monica Casale |
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Institution: | 1.Dipartimento di Chimica e Tecnologie Farmaceutiche ed Alimentari,Università di Genova,Genova,Italy |
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Abstract: | Representation or compression of data sets in the wavelet space is usually performed to retain the maximum variance of the
original or pretreated data, like in the compression by means of principal components. In order to represent together a number
of objects in the wavelet space, a common basis is required, and this common basis is usually obtained by means of the variance
spectrum or of the variance wavelet tree. In this study, the use of alternative common bases is suggested, both for classification
and regression problems. In the case of classification or class-modeling, the suggested common bases are based on the spectrum
of the Fisher weights (a measure of the between-class to within-class variance ratio) or on the spectrum of the SIMCA discriminant
weights. In the case of regression, the suggested common bases are obtained by the correlation spectrum (the correlation coefficients
of the predictor variables with a response variable) or by the PLS (Partial Least Squares regression) importance of the predictors
(the product between the absolute value of the regression coefficient of the predictor in the PLS model and its standard deviation).
Other alternative strategies apply the Gram–Schmidt supervised orthogonalization to the wavelet coefficients. The results
indicate that, both in classification and regression, the information retained after compression in the wavelets space can
be more efficient than that retained with a common basis obtained by variance. |
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