Enhancing Functional Data Analysis with Sequential Neural Networks:
  Advantages and Comparative Study
J. Zhao J. Li M. Chen S. Jadhav
Functional Data Analysis (FDA) is a statistical domain developed to handle
functional data characterized by high dimensionality and complex data
structures. Sequential Neural Networks (SNNs) are specialized neural networks
capable of processing sequence data, a fundamental aspect of functional data.
Despite their great flexibility in modeling functional data, SNNs have been
inadequately employed in the FDA community. One notable advantage of SNNs is
the ease of implementation, making them accessible to a broad audience beyond
academia. Conversely, FDA-based methodologies present challenges, particularly
for practitioners outside the field, due to their intricate complexity. In
light of this, we propose utilizing SNNs in FDA applications and demonstrate
their effectiveness through comparative analyses against popular FDA regression
models based on numerical experiments and real-world data analysis. SNN
architectures allow us to surpass the limitations of traditional FDA methods,
offering scalability, flexibility, and improved analytical performance. Our
findings highlight the potential of SNN-based methodologies as powerful tools
for data applications involving functional data.