Empirical Validation of Functional Multidimensional Scaling via Numerical Simulation and Real-World Application

This article presents an empirical validation of the functional multidimensional scaling model, a novel approach that improves the smoothness of time-varying dissimilarities in a low-dimensional space, embedding a modified Adam stochastic gradient descent method. We conduct a numerical simulation study to evaluate the feasibility of the functional multidimensional scaling model under various controlled scenarios and to assess the goodness of the approximation of the estimators with a curvilinear search method, demonstrating its robustness and scalability in dynamic structures. To further explore its effectiveness in practice, we implement the functional multidimensional scaling model in a real-world case with stock market data, revealing strong clustering capabilities in visualization. The experiments in this article indicate that the functional multidimensional scaling model performs robustly on synthetic benchmarks and provides meaningful insights of high-dimensional and time-varying data in the real world, reinforcing its value in practical applications.