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|Type:||Artigo de evento|
|Title:||Parafac With Splines: A Case Study|
|Abstract:||The PARAFAC model has been used in several applications in chemistry, e.g. for overlapped spectra resolution and second-order calibration. In general, the PARAFAC method uses a vector space approach by considering the matrices resulting from the decomposition as a collection of vectors. This paper presents a PARAFAC application where the factors resulting from the decomposition are considered as functions. The functional objects used for this are spline functions. The methodology used performs the Spline-PARAFAC decomposition based on the Bro-Sidiropoulos approach for the unimodality constraint. One of the advantages of using splines is the possibility of achieving a controlled degree of smoothing on the decomposed components. The amount of smoothing applied on the components in the presented methodology is controlled by a penalty parameter or by the number of basis functions. Thus Spline-PARAFAC requires the calculation of the parameter γ and the number of basis functions, which were determined in this work by using ordinary cross-validation (OCV). Spline-PARAFAC was applied to a carbon monoxide data set comprising concentrations measured every hour during the years 1997 and 1999 in the city of Sao Paulo, Brazil. Each data set was arranged in a three-way array of dimension (24 hours x 5 days x 52 weeks). Spline-PARAFAC showed a good performance, producing smoothed profiles describing the daily variations in emitted gas and the seasonal effects during the year. Copyright ©2002 John Wiley & Sons, Ltd.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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