The bottom two plots show a collection of curves from two more datasets. The second shows knee and hip angles for one boy during his gait cycle.

The first shows a growth curve for one infant during the first 40 days from birth. The top two plots show only a single functional data observation from a sample. The following figure contains four examples of functional data analysis. However, the continuum may not always be time for example, we might have measurements of the coordinates in a plane of children's gaits. The continuum is usually time for example, the high frequency, tick by tick values of a stock market index. It makes more sense to think of each sample as being observed on a continuum. With advances in data collection methods, there are now several fields that generate samples at such a fine grid. For example, treating blood vessels in a human body as tree-structured data or 3D brain images as a special mathematical manifold. In some applications, it is useful to consider more general objects as the unit of measurement under study. Whereas in, multivariate statistics, we take multiple measurements for each subject/unit, e.g. In classical statistics, we work with measurements that consist of a single number, such as a person's weight. In today's post I'll explain why and when to use functional data analysis and show you some examples. Functional data analysis refers to a collection of methods for analyzing data over a curve, surface or continuum.

Functional analysis