Applied functional data analysis methods and case studies
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To transform discrete observations into a continuous curve, we fit a function.
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The method brings a new perspective to data treatment: 30 years of daily temperature now becomes 30 data samples, and so do your handwriting or 2D images of an object. But surprisingly, since more than two decades ago, Ramsay & Silverman have already written about a new research branch that defined time as a feature dimension, glued all the observations to a single entity and called it Functional Data Analysis (FDA).Īs in the name, functional data view data in the form of a function (or curve) y=f(t) that smoothly spreads across a continuum t, be it time, probability density, or even cyclical shape (draw it with a single stroke) of an object. There are indeed sophisticated algorithms, say, RNN, that can embed time recursively. However, despite being a solid factor indicating the shape pattern, to my knowledge, the time continuum primarily plays a non-essential role as a fixed frame capturing observation interdependency. But surprisingly, since more than two decades ago, Ramsay & Silverman have already Speaking of time-series data, people commonly relate to a sequence of observations taken at equal intervals across the time dimension. Speaking of time-series data, people commonly relate to a sequence of observations taken at equal intervals across the time dimension.