Linear versus nonlinear dimensionality reduction for banks' credit rating prediction

摘要

Dimensionality reduction methods have shown their usefulness for both supervised and unsupervised tasks in a wide range of application domains. Several linear and nonlinear approaches have been proposed in order to derive meaningful low-dimensional representations of high-dimensional data. Among nonlinear algorithms manifold learning methods, such as isometric feature mapping (Isomap), have recently attracted great attention by providing noteworthy results on artificial and real world data sets. The paper presents an empirical evaluation of two linear and nonlinear techniques, namely principal component analysis (PCA) and double-bounded tree-connected Isomap (dbt-lsomap), in order to assess their effectiveness for dimensionality reduction in banks' credit rating prediction, and to determine the key financial variables endowed with the most explanatory power. Extensive computational tests concerning the classification of six banks' rating data sets showed that the use of dimensionality reduction accomplished by nonlinear projections often induced an improvement in the classification accuracy, and that dbt-lsomap outperformed PCA by consistently providing more accurate predictions.