  This paper introduces a novel methodology for Feature Selection for
Functional Classification, FSFC, that addresses the challenge of jointly
performing feature selection and classification of functional data in scenarios
with categorical responses and multivariate longitudinal features. FSFC tackles
a newly defined optimization problem that integrates logistic loss and
functional features to identify the most crucial variables for classification.
To address the minimization procedure, we employ functional principal
components and develop a new adaptive version of the Dual Augmented Lagrangian
algorithm. The computational efficiency of FSFC enables handling
high-dimensional scenarios where the number of features may considerably exceed
the number of statistical units. Simulation experiments demonstrate that FSFC
outperforms other machine learning and deep learning methods in computational
time and classification accuracy. Furthermore, the FSFC feature selection
capability can be leveraged to significantly reduce the problem's
dimensionality and enhance the performances of other classification algorithms.
The efficacy of FSFC is also demonstrated through a real data application,
analyzing relationships between four chronic diseases and other health and
demographic factors.
