# Hening Rydström: A study and further development of nonlinear unsupervised methods with applications to financial data

**Tid: **
Må 2019-02-11 kl 15.00 - 16.30

**Föreläsare: **
Hening Rydström

**Plats: ** PlatsRoom 3418, math department KTH, floor 4 (bottom floor)

Abstract: The main focus for this thesis is nonlinear dimensionality reduction. When analysing data of high dimension it is often vital to find a lower dimension representation of the data, while preserving as much information as possible. Dimension reduction is therefore used in many fields of science and in many industries.

This thesis will deal with applications in finance, and hence financial data. The thesis was made in collaboration with the third national Swedish pension fund, AP3. They wanted a dimension reduction method that is efficient, noise robust and which preserves both linear and nonlinear patterns in the data. Consequently, the main purpose of this thesis is to develop such a method. The method proposed by this thesis is a combination of published and self-developed extensions of the Isomap method.

For investigating different methods they are applied on both academic data sets in three dimensions, such as the Swiss-roll and the S-plane, and on specific financial data sets such as the S\&P 500 and commodity prices. The results from the academic examples indicate that the proposed method manages to find nonlinear structures in noisy data in an efficient way. The results from the financial data sets are interesting but much harder to interpret. AP3s idea is to use our proposed method as a pre-processing step in their big data algorithms for trading and economic analysis, but that application is out of scope for this thesis.

The last part of the thesis will make a brief introduction to Topological data analysis (TDA). It will cover the basic theory and will be used for some simple applications on financial data.