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 consideredd 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 smootihing 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 l 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 São Paulo, Brazil.
Each data set was arranged in the three-way array of dimension (24 hours ´ 5 days ´ 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.

Keywords.
PARAFAC; Smoothing Splines; Carbon Monoxide.

Keywords Plus.
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