Spectral Graph Embedding for Dimension Reduction in Financial Risk Assessment

The economic downturn in recent years has had a significant negative impact on corporates performance. In the last two years, as in the last years of 2010s, many companies have been influenced by the economic conditions and some have gone bankrupt. This has led to an increase in companies' financial risk. One of the significant branches of financial risk is the emph{company's credit risk}. Lenders and investors attach great importance to determining a company's credit risk when granting a credit facility. Credit risk means the possibility of default on repayment of facilities received by a company. There are various models for assessing credit risk using statistical models or machine learning. In this paper, we will investigate the machine learning task of the binary classification of firms into bankrupt and healthy based on the emph{spectral graph theory}. We first construct an emph{adjacency graph} from a list of firms with their corresponding emph{feature vectors}. Next, we first embed this graph into a one-dimensional Euclidean space and then into a two dimensional Euclidean space to obtain two lower-dimensional representations of the original data points. Finally, we apply the emph{support vector machine} and the emph{multi-layer perceptron} neural network techniques to proceed binary emph{node classification}. The results of the proposed method on the given dataset (selected firms of Tehran stock exchange market) show a comparative advantage over PCA method of emph{dimension reduction}. Finally, we conclude the paper with some discussions on further research directions.