Non-Gaussian component analysis: New ideas, new proofs, new applications
- Panov, Vladimir A.
2010 Mathematics Subject Classification
- 62G05 62H99 62G10 62H30 60G35 93E10 62H10 00A73 62P20
- dimension reduction, non-Gaussian components, NGCA, EDR subspace, classification problem, Value at Risk
In this article, we present new ideas concerning Non-Gaussian Component Analysis (NGCA). We use the structural assumption that a high-dimensional random vector $vX$ can be represented as a sum of two components - a low-dimensional signal $vS$ and a noise component $vN$. We show that this assumption enables us for a special representation for the density function of $vX$. Similar facts are proven in original papers about NGCA, but our representation differs from the previous versions. The new form helps us to provide a strong theoretical support for the algorithm; moreover, it gives some ideas about new approaches in multidimensional statistical analysis. In this paper, we establish important results for the NGCA procedure using the new representation, and show benefits of our method.