Elsevier

Neurocomputing

Volume 177, 12 February 2016, Pages 636-642
Neurocomputing

A nonlinear subspace multiple kernel learning for financial distress prediction of Chinese listed companies

https://doi.org/10.1016/j.neucom.2015.11.078Get rights and content

Abstract

Financial distress prediction (FDP) is of great importance for managers, creditors and investors to take correct measures so as to reduce loss. Many quantitative methods have been proposed to develop empirical models for FDP recently. In this paper, a nonlinear subspace multiple kernel learning (MKL) method is proposed for the task of FDP. A key point is how basis kernels could be well explored for measuring similarity between samples while a MKL strategy is used for FDP. In the proposed MKL method, a divide-and-conquer strategy is adopted to learn the weights of the basis kernels and the optimal predictor for FDP, respectively. The optimal weights of the basis kernels in linear combination is derived through solving a nonlinear form of maximum eigenvalue problem instead of solving complicated multiple-kernel optimization. Support vector machine (SVM) is then used to generate an optimal predictor with the optimally linearly-combined kernel. In experiments, the proposed method is compared with other FDP methods on Normal and ST Chinese listed companies during the period of 2006–2013, in order to demonstrate the prediction performance. The performance of the proposed method is superior to the state-of-the-art predictor compared in the experiments.

Introduction

As the world׳s second largest economy, Chinese economic development has brought a great power to the global economic recovery, but the enterprise management mechanism remains backward state, including listed companies’ financial distress study. Accurate judgment before arising the company financial distress will benefit to reduce property loss form of country and companies׳ themselves. The companies can take some effective measure to stop this situation spend and bring it back on track. Financial distress prediction (FDP) is using some useful methods to catch this situation, analyzing the report data from enterprises before distress arising [1], [2], [3].

In the early stages, some methods were developed for FDP, such as univariate analysis [1], multiple discriminant analysis (MDA) [2], logistic regression algorithm (Logit) [1]. With the development of some artificial intelligence methods, these methods are also used in FDP, like neural networks (NNs) [4], [5], support vector machine (SVM) [5], [6], [7]. In recent years, some combinations of multiple classifiers are also present to solve the limited explanatory ability problem in single classifiers, such as Bagging method and Adaboost method [9]. Most of researches focus on the model learning for FDP but ignore the importance of financial ratios selection. Although there have already exist some state-of-the-art feature selection method which can be used for ratio selection, like Principal Component Analysis (PCA) [10], Linear Discriminate Analysis (LDA) [11], Kernel-PCA [12] and Kernel-LDA [13], those feature selection are not suitable for FDP and not have a sufficient interpretability. Recently, SVM method has present excellent nonlinear generalization ability to high dimension and small sample evaluation problem and can get upper prediction accuracy using kernel method. SVM has been recently applied for FDP task and demonstrated good performance [7], [8]. The conventional SVM only use single kernel like Gaussian kernel with fixed parameters to measure similarity of samples from same class or different classes.

In recent years, the limitation of SVM with single kernel has been recognized gradually. The limitation of single kernel learning motivates researchers to develop new kind of kernel learning methods, called multiple kernel learning (MKL). The Multiple Kernel Learning (MKL) methods based on SVM framework can get a better perform, using a composite kernel effectively to increase the adaptive capacity [14], [15], [16], [17], [18]. Essentially, multiple basis kernels with different forms or same forms but different parameters provide more enhanced ability to measure sample similarity. Integrating the basis kernels will results in better generalization capability and better classification performance. In our previous work, a two-step multiple kernel regression (MKR) was proposed for macroeconomic data forecasting of China [19]. Those existing MKL algorithms demonstrate better performance than the conventional SVM for forecasting and FDP. However, better utilizing the potential of basis kernels for measuring sample similarity is still an open topic.

In this paper, a nonlinear subspace multiple kernel learning (MKL) method is proposed for the task of FDP. In the proposed MKL method, a divide-and-conquer strategy is adopted to separately learn the weights of the basis kernels and the optimal predictor for FDP. The optimal weights of basis kernels in linear combination is derived through solving a nonlinear form of maximum eigenvalue problem instead of solving complicated multiple-kernel optimization. Support vector machine (SVM) is then used to form an optimal predictor with the optimally linearly-combined kernel. The main contribution of this paper can be summarized as follow. In the existing MKL algorithms, two main ways to learn a linear combination of the basis kernels. One is to directly solve a complicated optimization problem which simultaneously optimizes the weights and the final classification results. The other one adopts linear subspace methods to learn the optimally linear combination of the basis kernels. Compared to the existing state-of-the-art, the main contribution of this work is to adopt more effectively nonlinear subspace methods to get a combined kernel which has excellent ability to learn samples.

The rest of the paper is divided into five sections. Section 2 briefly describes the kernel learning and MKL. Section 3 represents the proposed MKL method and its׳ flowchart for task of FDP. Section 4 gives a detailed description of the test data, i.e. the Chinese listed companies׳ ratios data and analysis of the experimental result. The last section provides conclusion.

Section snippets

The proposed MKL method

In the proposed MKL method, the basis kernels are firstly generated by means of Gaussian kernels with different bandwidth parameters. The optimal weights of the basis kernels in linear combination form are learned via subspace learning manner. In other words, searching the optimal weights is converted into a subspace learning problem. In order to solve the subspace learning problem, an eigenvalue decomposition method is performed on basis kernels in Reproduced Kernel Hilbert Space (RKHS). The

Dataset description

In order to validate the performance of financial distress prediction for Chinese listed companies based on the proposed nonlinear subspace multiple kernel learning, a real dataset collected from Chinese listed companies is adopted for experiments. The principles of data selecting contain the diversity type of companies, the time continuity, the proportionate number of each type samples and financial ratios diversity. 203 normal companies and 203 ST companies are selected for the period from

Conclusions

In this paper, a nonlinear subspace multiple kernel learning method is proposed for FDP. In the proposed method, the predefined basis kernels are firstly converted from matrix form into vector form. A kernel-based nonlinear subspace method is adopted to learn an ‘optimal’ combined kernel from the vector-form basis kernels. The optimally combined kernel can represent the predefined basis kernels in sense of maximizing variance in feature space. The experiments were conducted to prove the

Acknowledgement

This work is supported by the Humanities and Social Sciences Project of Heilongjiang Province Education Department under the Grant 12532303.

Xiangrong Zhang She was born in Heilongjiang, China, in 1979. She received bachelor degree from Heilongjiang University, 1999, master degree from Harbin Engineering University, 2006. Now she is working toward the Ph.D. degree in School of Management, Harbin Institute of Technology, China. Her interests of researches include technical innovation, data analysis, forecasting.

References (19)

There are more references available in the full text version of this article.

Cited by (14)

  • Multi-class financial distress prediction based on support vector machines integrated with the decomposition and fusion methods

    2021, Information Sciences
    Citation Excerpt :

    Fallahpour et al. [12] used the sequential floating forward selection algorithm to select the best eigenvalues and then combined it with the SVM classifier to construct the FDP model and experimentally verified its effectiveness. Zhang and Hu [61] used the nonlinear subspace multicore learning method to solve the optimal weight of the base kernel in the linear combination and then optimized the SVM to construct an optimized FDP model. Huang and Yen [18] found that the hybrid model, by integrating the deep belief network (DBN) and SVM, was able to generate more accurate FDP than the use of either the DBN or the SVM in isolation.

  • Minimum class variance multiple kernel learning

    2020, Knowledge-Based Systems
    Citation Excerpt :

    Previous studies [4–16] have shown that MKL can provide needed flexibility. MKL has shown promising performance in many practical applications [17–26] and its basic idea has been extended to many kernel-based methods [27–29], a typical representative of which is support vector machines (SVM) [30]. SVM is a powerful classifier.

  • Imbalanced credit risk evaluation based on multiple sampling, multiple kernel fuzzy self-organizing map and local accuracy ensemble

    2020, Applied Soft Computing Journal
    Citation Excerpt :

    However, these methods still employ the original Euclidean distance to measure the similar between two points, which is unsuitable for the complicated financial data. Because of the feature of the non-linear transformation without a specific mapping rule, the kernel function technique has had a good effect in practice [35–37]. This technique can be a good solution to such problem.

  • A three-level Multiple-Kernel Learning approach for soil spectral analysis

    2020, Neurocomputing
    Citation Excerpt :

    Models may also be developed in either one-stage or two-stages: in the former, the optimal kernel combination parameters and the structural parameters of the classifier / regressor are learned simultaneously, whilst the latter decouples these processes. MKL has been applied in a plethora of domains, such as image classification [36], remote sensing [37], financial distress prediction [38], face recognition [39], with multimedia [40], and to identify drug side effects [41]. Recent advances in MKL have proposed a hybrid kernel alignment method, by introducing a combination of the traditional global and a local kernel [42].

  • Heterogeneous visual features integration for image recognition optimization in internet of things

    2018, Journal of Computational Science
    Citation Excerpt :

    Most of them focused on addressing multimodal retrieval and classification [21–23]. The models in these literatures involve deep autoencoders [18], [24], deep Boltzmann machines [17], CNN [25], and MKL [26,27]. Although an army of multi-modal deep learning approaches have been presented to integrate the multimodal data, there is no deep learning structure to integrate heterogeneous image visual features to the best of our knowledge.

  • A multi-kernel framework with nonparallel support vector machine

    2017, Neurocomputing
    Citation Excerpt :

    Much effort has been devoted to yield an optimal kernel for specific applications. Existing MKL algorithms can be divided into three categories: linear combination methods [19,20], nonlinear combination methods [21] and data-dependent combination methods [5,22]. A great deal of research is focused on learning a linear combination with unweighted sum or weighted sum of the basis kernels [29].

View all citing articles on Scopus

Xiangrong Zhang She was born in Heilongjiang, China, in 1979. She received bachelor degree from Heilongjiang University, 1999, master degree from Harbin Engineering University, 2006. Now she is working toward the Ph.D. degree in School of Management, Harbin Institute of Technology, China. Her interests of researches include technical innovation, data analysis, forecasting.

Longying Hu He was born in Harbin, China, in 1960. He received the Ph.D. degree in technical economics and management, in 2000. Currently, he is a professor in School of Management, Harbin Institute of Technology, China. His interests of researches include technical innovation, technical economics, and strategyalliance.

View full text