Reproducing, extending and updating dimensionalty reductions

Abstract

Dimensionality reduction techniques play a key role in data visualization and analysis, as these techniques project high-dimensional data in low-dimensional space by preserving critical information about the data in low-dimensional space. Dimensionality reduction techniques may suffer from various drawbacks, e.g., many dimensionality reduction techniques are missing a natural out-of-sample extension, i.e., the ability to insert additional data points into an existing projection. Therefore when a data set grows and new data points are introduced, the projection has to be recalculated, which often cannot be well related to the previous projection. This thesis proposes a technique based on kernel PCA to reproduce and update the result of dimensionality reduction techniques to overcome the stated problems with better run-time performance. The proposed technique uses an initial projection provided by an arbitrary dimensionality reduction technique as a template of the embedding space. A corresponding kernel matrix is then approximated to project out-of-sample instances. The approach is evaluated on several datasets for reproduction of projections of different dimensionality reduction techniques. It is shown that the proposed technique provides a coherent projection for out-of-sample data, and has a better run-time performance than several other dimensionality reduction techniques.