Functional Analysis: Fundamental Approaches and Implementation
[Academic Review] An introduction to two core approaches for processing low-dimensional signal data using functional analysis.
This presentation covers four main topics in functional analysis. The first two sections focus on signal smoothing and compression using Natural Cubic Spline estimators and Inverse Matrix Methods, as well as Penalized Least Squares optimization. The third topic presents a practical sample case applying spline and kernel smoothing techniques to functional mean data. Finally, the presentation discusses the classification of functional data by combining spline smoothing with Functional Principal Component Analysis (Functional-PCA).
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