In functional classification problems the data available for learning are characterized by functions, rather than vectors of attributes. In consequence, multivariate classifiers need to be adapted, and new types of classifiers designed to take into account the special characteristics of these types of data. In this work, an empirical evaluation of different classification methods is carried out using a variety of functional classification problems from different areas of application. The classifiers considered include nearest centroids with functional means as class prototypes and functional distances, standard multivariate classifiers used in combination with a variable selection method, classifiers based on the notion of functional depth, a functional version of k-nearest neighbors (k-NN), and random forest. From the results of this comparative study one concludes that random forest is among the best off-the-shelf classifiers not only for multivariate but also for functional classification problems. The variable selection method used in combination with a quadratic discriminant has fairly good overall accuracy using only a small set of impact points. This dimensionality reduction leads to improvements both in efficiency and interpretability. Finally, a functional version of k-NN that uses the α-Mahalanobis distance exhibits consistently good predictive performance in all the problems considered. This robustness makes k-NN a good benchmark for functional classification.

Machine learning from functional data poses particular challenges that require specific computational tools that take into account their structure. In this work, we present scikit-fda, a Python library for functional data analysis, visualization, preprocessing, and machine learning. The library is designed for smooth integration in the Python scientific ecosystem. In particular, it complements and can be used in combination with scikit-learn, the reference Python library for machine learning. The functionality of scikit-fda is illustrated in clustering, regression, and classification problems from different areas of application.

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than standard simensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.