Abstract
Bankruptcy involves considerable costs, so it can have significant effects on a country's economy. Thus, bankruptcy prediction is an important issue. Over the past several decades, many researchers have addressed topics associated with bankruptcy prediction. Early research on bankruptcy prediction employed conventional statistical methods such as univariate analysis, discriminant analysis, multiple regression, and logistic regression. Later on, many studies began utilizing artificial intelligence techniques such as inductive learning, neural networks, and case-based reasoning. Currently, ensemble models are being utilized to enhance the accuracy of bankruptcy prediction. Ensemble classification involves combining multiple classifiers to obtain more accurate predictions than those obtained using individual models. Ensemble learning techniques are known to be very useful for improving the generalization ability of the classifier. Base classifiers in the ensemble must be as accurate and diverse as possible in order to enhance the generalization ability of an ensemble model. Commonly used methods for constructing ensemble classifiers include bagging, boosting, and random subspace. The random subspace method selects a random feature subset for each classifier from the original feature space to diversify the base classifiers of an ensemble. Each ensemble member is trained by a randomly chosen feature subspace from the original feature set, and predictions from each ensemble member are combined by an aggregation method. The k-nearest neighbors (KNN) classifier is robust with respect to variations in the dataset but is very sensitive to changes in the feature space. For this reason, KNN is a good classifier for the random subspace method. The KNN random subspace ensemble model has been shown to be very effective for improving an individual KNN model. The k parameter of KNN base classifiers and selected feature subsets for base classifiers play an important role in determining the performance of the KNN ensemble model. However, few studies have focused on optimizing the k parameter and feature subsets of base classifiers in the ensemble. This study proposed a new ensemble method that improves upon the performance KNN ensemble model by optimizing both k parameters and feature subsets of base classifiers. A genetic algorithm was used to optimize the KNN ensemble model and improve the prediction accuracy of the ensemble model. The proposed model was applied to a bankruptcy prediction problem by using a real dataset from Korean companies. The research data included 1800 externally non-audited firms that filed for bankruptcy (900 cases) or non-bankruptcy (900 cases). Initially, the dataset consisted of 134 financial ratios. Prior to the experiments, 75 financial ratios were selected based on an independent sample t-test of each financial ratio as an input variable and bankruptcy or non-bankruptcy as an output variable. Of these, 24 financial ratios were selected by using a logistic regression backward feature selection method. The complete dataset was separated into two parts: training and validation. The training dataset was further divided into two portions: one for the training model and the other to avoid overfitting. The prediction accuracy against this dataset was used to determine the fitness value in order to avoid overfitting. The validation dataset was used to evaluate the effectiveness of the final model. A 10-fold cross-validation was implemented to compare the performances of the proposed model and other models. To evaluate the effectiveness of the proposed model, the classification accuracy of the proposed model was compared with that of other models. The Q-statistic values and average classification accuracies of base classifiers were investigated. The experimental results showed that the proposed model outperformed other models, such as the single model and random subspace ensemble model.
앙상블 분류기란 개별 분류기보다 더 좋은 성과를 내기 위해 다수의 분류기를 결합하는 것을 의미한다. 이와 같은 앙상블 분류기는 단일 분류기의 일반화 성능을 향상시키는데 매우 유용한 것으로 알려져 있다. 랜덤 서브스페이스 앙상블 기법은 각각의 기저 분류기들을 위해 원 입력 변수 집합으로부터 랜덤하게 입력 변수 집합을 선택하며 이를 통해 기저 분류기들을 다양화 시키는 기법이다. k-최근접 이웃(KNN: k nearest neighbor)을 기저 분류기로 하는 랜덤 서브스페이스 앙상블 모형의 성과는 단일 모형의 성과를 개선시키는 데 효과적인 것으로 알려져 있으며, 이와 같은 랜덤 서브스페이스 앙상블의 성과는 각 기저 분류기를 위해 랜덤하게 선택된 입력 변수 집합과 KNN의 파라미터 k의 값이 중요한 영향을 미친다. 하지만, 단일 모형을 위한 k의 최적 선택이나 단일 모형을 위한 입력 변수 집합의 최적 선택에 관한 연구는 있었지만 KNN을 기저 분류기로 하는 앙상블 모형에서 이들의 최적화와 관련된 연구는 없는 것이 현실이다. 이에 본 연구에서는 KNN을 기저 분류기로 하는 앙상블 모형의 성과 개선을 위해 각 기저 분류기들의 k 파라미터 값과 입력 변수 집합을 동시에 최적화하는 새로운 형태의 앙상블 모형을 제안하였다. 본 논문에서 제안한 방법은 앙상블을 구성하게 될 각각의 KNN 기저 분류기들에 대해 최적의 앙상블 성과가 나올 수 있도록 각각의 기저 분류기가 사용할 파라미터 k의 값과 입력 변수를 유전자 알고리즘을 이용해 탐색하였다. 제안한 모형의 검증을 위해 국내 기업의 부도 예측 관련 데이터를 가지고 다양한 실험을 하였으며, 실험 결과 제안한 모형이 기존의 앙상블 모형보다 기저 분류기의 다양화와 예측 성과 개선에 효과적임을 알 수 있었다.