T-61.6030 Special Course in Computer and Information Science III L:

Introductory Elements of Functional Data Analysis

Functional data analysis (FDA) is a framework for analyzing data in function spaces. Instead of discrete vectors, the data consists of functions and is thus infinite dimensional. FDA offers statistical tools for handling the high dimensionality of the data using smoothness properties of the functions. Functional data analysis combines statistical methods with well-known mathematical techniques for analyzing curves. The usefulness of these methods depends largely on the smoothness of the functions.

Many classical statistical and machine learning methods have their functional counterparts. Often this type of generalization of well-known methods leads to surprisingly elegant interpretations, which show totally new ways to use the methods.

Functional data analysis is not only of theoretical interest, but arises from practical needs. Functional data is common for example in chemometry, econometrics and machine learning. Further information on FDA can be found here.

Each student gives a presentation in the seminar. In addition, requirements include a project work and active participation in the lectures (one absence is allowed).

We will use the following two books:

[1] J. O. Ramsay and B. W. Silverman. Functional Data Analysis, second edition. Springer, New York. 2005.
[2] F. Ferraty and P. Vieu. Non-parametric Functional Data Analysis. Springer. 2006.

The books can be ordered for example at http://booky.fi.

Information about the project work is available here.