Dimensional Reduction of Functional Data by means of Principal Differential Analysis
Keywords
Statistical learning
Code:
01/2011
Title:
Dimensional Reduction of Functional Data by means of Principal Differential Analysis
Date:
Wednesday 5th January 2011
Author(s):
Dalla Rosa, M.; Sangalli, L. M.; Vantini, S.
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Abstract:
We explore the use of principal differential analysis (PDA) as a tool for performing dimensional reduction of functional data sets. In particular, we compare the results provided by PDA and by functional principal component
analysis (FPCA) in the dimensional reduction of three synthetic data sets, and of a real data set concerning 65 vascular geometries (i.e., the AneuRisk data set).
The analyses of the synthetic data sets show that PDA can provide an alternative and effective representation of functional data that is always
easily interpretable in terms of constant, exponential, sinusoidal, or dampedsinusoidal
functions and not affected by the presence of clusters or strong correlations among the original components. Moreover, in the analysis of
the AneuRisk data set, PDA is able to detect important features of the data that FPCA is not able to detect.
This report, or a modified version of it, has been also submitted to, or published on
Matilde Dalla Rosa, Laura M. Sangalli and Simone Vantini (2014), Principal Differential Analysis of the Aneurisk65 Data Set. Advances in Data Analysis and Classification, Vol. 8, Issue 3, pp. 287-302.
Matilde Dalla Rosa, Laura M. Sangalli and Simone Vantini (2014), Principal Differential Analysis of the Aneurisk65 Data Set. Advances in Data Analysis and Classification, Vol. 8, Issue 3, pp. 287-302.