Palomino Lescano, Velcy

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    Normalized and weighted multivariate functional principal components analysis for clustering
    (2024-05-09) Palomino Lescano, Velcy; Acuña Fernández, Edgar; College of Engineering; Santana Morant, Dámaris; Aparicio Carrasco, Roxana; Almodóvar Rivera, Israel; Department of Computer Science and Engineering; Serrano Rivera, Guillermo
    Most processes in real life are continuous, and thanks to the technological progress in many fields of application, these processes can be recorded at high frequency. Thus, Functional Data Analysis (FDA) has been an active field of research. In this research we focus on Multivariate Functional Principal Components Analysis (MFPCA) when functional variables differ in scale, variability, or domain. We develop different alternatives of normalized and weighted MFPCA. Particularly, when a weighted MFPCA is employed, we provide a strategy to estimate the weights based on the variability of Functional Principal Components (FPC) scores. The performance of normalized and weighted MFPCA are evaluated in the context of clustering using different simulated and real datasets. The simulations include cases of Multivariate Functional Data (MFD) on the same one-dimensional interval and MFD defined on different domains i.e. MFD including multivariate curves and MFD including curves and images. Similarly, real datasets include cases of MFD containing multivariate curves and a MFD consisting of curves and vectors. Normalized and weighted MFPCA can improve the clustering performance. Furthermore, our strategy proposed to estimate the weights in weighted MFPCA is a good alternative, since this provides comparable results to other methods and it is more efficient in running time.