What is Functional Data Analysis

High dimensional data are becoming more and more common in data analysis. This is especially true in fields that are related to spectrometric data, such as chemometrics. Due to development of more accurate spectrometers one can obtain spectra of thousands of data points. Such a high dimensional data are problematic in machine learning due to increased computational time and the curse of dimensionality (Haykin, 1999; Verleysen & François, 2005; Bengio, Delalleau, & Le Roux, 2006). It is therefore advisable to reduce the dimensionality of the data. In the case of chemometrics, the spectra are usually rather smooth and low on noise, so function fitting is a convenient tool for dimensionality reduction. The fitting is obtained by fixing a set of basis functions and computing the fitting weights according to the least squares error criterion. This article describes a unsupervised method for finding a good function basis that is specifically built to suit the data set at hand. The basis consists of a set of Gaussian functions that are optimized for an accurate fitting. The obtained weights are further scaled using a Delta Test (DT) to improve the prediction performance. Least Squares Support Vector Machine (LS-SVM) model is used for estimation.