کاهش ابعاد خطی در مقابل غیر خطی برای پیش بینی رتبه بندی اعتباری بانک ها

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-Isomap), 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-Isomap outperformed PCA by consistently providing more accurate predictions.

Dimensionality reduction techniques aim at finding meaningful with low-dimensional representations of high-dimensional data. They may prove quite useful both for unsupervised tasks, such as clustering or data visualization, and supervised learning, to reduce the training time and increase the classification accuracy. Several approaches have been developed for dimensionality reduction. Traditional methods dealing with linear data projections include principal component analysis (PCA) [20] and factor analysis. These techniques are easy to implement and have shown their effectiveness for data visualization and classification in a wide range of application domains. More recently, a large number of nonlinear dimensionality reduction methods have been proposed in order to properly handle data with complex nonlinear structures. Within the family of nonlinear algorithms manifold learning methods have attracted great attention. They include, among others, isometric feature mapping (Isomap) [35], locally linear embedding [31] and Laplacian eigenmaps [2]. Manifold learning methods attempt to uncover the low-dimensional manifold along which data are supposed to lie. Given a set of m data points View the MathML sourceSm={xi,i∈M={1,2,…,m}}⊂Rn arranged along a nonlinear manifold M of intrinsic dimension d , with d ≪ n , they aim at finding a function f:M→Rdf:M→Rd mapping View the MathML sourceSmintoDm={zi,i∈M={1,2,…,m}}⊂Rd such that some geometrical properties of the data in the input space are preserved in the projection space. Manifold learning techniques exhibited noteworthy performance in the analysis of artificial and real world data sets in several contexts. An empirical comparison of these methods for microarray data classification is presented in [24]. Credit ratings are opinions expressed in terms of ordinal measures which reflect the current financial creditworthiness of issuers, like governments, firms or financial institutions. These ratings are conferred by rating agencies, such as Fitch Ratings, Moody’s and Standard and Poor’s (S&P’s), and may be regarded as comprehensive evaluations of issuers’ ability to fully meet their financial obligations on time. Hence, they play a crucial role by providing participants in financial markets with useful information for financial decision planning. For banks’ rating assessment, agencies resort to a broad set of financial and non-financial information, including domain experts expectations. General guidelines on the rating decision process are usually delivered, but the detailed description of the rating criteria and of the determinants of banks’ rating is not explicitly provided. Thus, several research efforts have been recently devoted to the development of reliable quantitative methods for automatic banks’ classification according to their financial strength. The motivation for the present study is to evaluate whether dimensionality reduction, accomplished by linear or nonlinear data projections, may enhance the performance of classical and well-established supervised learning techniques for banks’ credit rating prediction, so that the resulting methods can be used as forecasting tools for generating credit ratings on the base of a set of measurable financial variables. In particular, the paper has three main objectives. First, we intend to determine whether linear and nonlinear dimensionality reduction methods, namely principal component analysis and double-bounded tree-connected Isomap (dbt-Isomap), may be effectively used for credit rating prediction when they are combined with support vector machines, naı¨ve Bayes classifier and k-nearest neighbor. Then, we are interested in investigating whether nonlinear dimensionality reduction dominates its linear counterpart. Finally, we aim at analyzing the key explanatory factors exploited by both methods in order to highlight the different role of the financial variables on the prediction task. Hybrid approaches based on PCA and manifold learning were proposed in [21], [29] and [30] for predicting business failure. We are not aware of any previous study resorting to manifold learning for dimensionality reduction to model and predict banks’ credit ratings. The remainder of the paper is organized as follows. Section 2 offers a brief review of the literature on prediction models for banks’ credit rating. Section 3 provides a general description of the dimensionality reduction techniques considered in this study. Sections 4 and 5 illustrate the credit rating data sets and the experimental settings, respectively. Section 6 presents the most relevant empirical findings. Conclusions and future extensions are discussed in Section 7.

Several research efforts have been recently devoted to the development of reliable quantitative methods for automatic banks’ classification according to their financial soundness. This paper presents an empirical evaluation of the effectiveness of two linear and nonlinear dimensionality reduction techniques represented by PCA and dbt-Isomap, a variant of isometric feature mapping, for banks’ credit rating prediction. To this aim, extensive computational experiments were performed on six credit rating data sets entirely drawn from the BankScope database. The results indicate that resorting to dimensionality reduction accomplished by nonlinear projections often leads to an improvement in the classification accuracy compared with the direct application of supervised learning algorithms in the original input space. Furthermore, classifiers based on dbt-Isomap outperformed those relying on PCA by consistently providing more accurate predictions, with an increase in accuracy ranging in the interval [1.1%, 13%]. A further analysis was also applied to identify the most relevant financial variables exploited for data projection. Despite some predictors were jointly considered by both methods, dimensionality reduction performed by PCA and dbt-Isomap was based on different sets of representative features. In particular, net interest margin, return on average equity, cost to income ratio and loans on total assets emerged as the most influential explanatory factors in the optimal dbt-Isomap models. The empirical results obtained in the present study have the following managerial implications. From one side, well-established classifiers combined with nonlinear dimensionality reduction may be used as objective and reliable automatic systems for generating banks’ rating on the base of measurable financial variables. Credit ratings represent a fundamental reference for investment decisions. Therefore, most participants in financial markets, such as issuers, investors and intermediaries may benefit from the use of these tools in order to systematically diagnose the soundness of individual banks, forecast changes in credit ratings, capture the weakness of institutions in advance and build early warning systems. From the other side, the study of the financial predictors used by the proposed models may help analysts to gain knowledge on the most relevant factors considered in the rating decision process and capture those variables which, among others, mainly explain connections and dissimilarities, in terms of credit ratings, across different markets. The present study could be extended in various directions by investigating the effectiveness, on the same prediction task, of other manifold learning algorithms such as locally linear embedding or Laplacian eigenmaps. It would also be worthwhile to combine isometric feature mapping with distance metrics for categorical attributes, in order to include additional country-specific variables modeling, for example, country risk or the regulatory environment of the market where the bank operates.