A Meta Path Based Evaluation Method for Enterprise Credit Risk

A heterogeneous information network 2016A is a classical data structure used to model objects and relations in a directed graph. This graph structure has shown its superiority in representing and storing knowledge about the natural world for many applications 2013Modeling 2013Recommendation 2019Cash . Given different objects in information networks, logical connections can be effectively constructed, and semantic relationships can be easily captured. Hence, we also build our model in a information network which is defined as follows:

In this paper, our model is built as a heterogeneous information network of SMEs. The SME schema is shown in Figure 2.

In our model, enterprise ($\mathcal{A}_{e}$) , commodity ($\mathcal{A}_{c}$), person ($\mathcal{A}_{p}$) and news ($\mathcal{A}_{n}$) are four fundamental object types in studying SME credit risk. The studied relation types are summarized from public enterprise information and objective facts, such as the shareholder relation between enterprise and person, the produce relation between enterprise and commodity, and the report relation between enterprise and news. The types mentioned in this paper are listed in Table 1.

With the SME schema defined, an example of SME heterogeneous information network is shown in Figure 3.

We can see that $v_{1}$, $v_{2}$, $v_{7}$ are enterprise, that we have $\tau(v_{1})=\mathcal{A}_{e}$, the same as $\tau(v_{2})$ and $\tau(v_{7})$ are. The $v_{6}$, $v_{9}$ are commodities, that we have $\tau(v_{6})=\mathcal{A}_{c}$, the same as $\tau(v_{9})$. The $v_{5}$, $v_{10}$, $v_{11}$, $v_{12}$, $v_{13}$ are news, that we have $\tau(v_{5})=\mathcal{A}_{n}$, the same as $\tau(v_{10})$, $\tau(v_{11})$, $\tau(v_{12})$, and $\tau(v_{13})$ are. The $v_{3}$, $v_{4}$, $v_{8}$ are persons, that we have $\tau(v_{3})=\mathcal{A}_{p}$, the same as $\tau(v_{4})$ and $\tau(v_{8})$ are. The $e_{5}$, $e_{8}$ are the relation of produces, that we have $\phi(e_{5})=\mathcal{R}_{produce}$, the same as $\phi(e_{8})$. The $e_{4}$, $e_{9}$,$e_{10}$, $e_{11}$, $e_{12}$ are the relation of reports, that we have $\phi(e_{4})=\mathcal{R}_{report}$, the same as $\phi(e_{9})$, $\phi(e_{10})$, $\phi(e_{11})$, and $\phi(e_{12})$ are. The $e_{6}$ is the relation of supply, $e_{1}$ is the relation of parent, that we have $\phi(e_{6})=\mathcal{R}_{supply}$, and $\phi(e_{1})=\mathcal{R}_{parent}$. The $e_{7}$, $e_{2}$ are the relation of controller, $e_{3}$ is the relation of employee, that we have $\phi(e_{7})=\mathcal{R}_{control}$, the same as $\phi(e_{2})$, and $\phi(e_{3})=\mathcal{R}_{employee}$. The $e_{13}$ is the relation of relate, that we have $\phi(e_{13})=\mathcal{R}_{relate}$.

In the SME network graph we build in Section 3.1, a graph edge is used to present the relationship between two objects. Limited by the definition of edge, the represented relationships can only be some simple ones, which are insufficient to describe the relationships used in the problem of SME credit risk. In order to model complicated relationships, in this section, we introduce another data structure, meta path (MP), to represent complicated and implicit relations in SME network.

For simplicity, we use the names of object types and relation types denoting the MP: $P=\mathcal{A}_{1}{\cdot}\mathcal{R}_{1}{\cdot}\mathcal{A}_{2}\ldots\mathcal{R}_{n}{\cdot}\mathcal{A}_{n+1}$. With the definition of meta path, a path $p=v_{1}{\cdot}e_{1}{\cdot}v_{2}\ldots e_{n}{\cdot}v_{n+1}$ in graph $G$ follows a meta path $P$, if for any vertex $v_{i}\in\mathcal{V}$ and any edge $e_{i}\in\mathcal{E}$, there have edge $e_{i}$ is between $v_{i}$ and $v_{i+1}$, $\tau(v_{i})={\mathcal{A}_{i}}$ and $\phi(e_{i})={\mathcal{R}_{i}}$. We also call $p$ as a path instance of $P$ with the denotation $p\in P$.

According to the definition, some examples of meta paths can be seen in Figure 2. $P=\mathcal{A}_{e}{\cdot}\mathcal{R}_{parent}{\cdot}\mathcal{A}_{e}{\cdot}\mathcal{R}_{report}{\cdot}\mathcal{A}_{n}$ is a MP, which represent the information that the SME’s parent enterprise has report a news. According to Figure 3, there is a path instance $p=v_{1}{\cdot}e_{1}{\cdot}v_{2}{\cdot}e_{9}{\cdot}v_{10}$ of MP $P$. Because $\tau(v_{1})=\mathcal{A}_{e}$, $\tau(v_{2})=\mathcal{A}_{e}$, $\tau(v_{10})=\mathcal{A}_{n}$, $\phi(e_{1})=\mathcal{R}_{parent}$, $\phi(e_{9})=\mathcal{R}_{report}$.

The given MP definition structures logical connections between objects, making our model more expressive and interpretable. It not only can show explicit reasons of factors affecting SMEs on credit risk, but also can explain implicit logics of correlation between objects having no direct links in SME information network.

Compared to the information carried by objects, the information carried by meta paths is more critical in evaluating the credit risk of SMEs. The reason is that the expression ability of meta paths is more stronger. Through different meta paths, the same financial object may affect another financial object significantly differently. For instance, in Figure 3 we can see that there exist two paths from person $v_{4}$ to enterprise $v_{1}$. The first one is $p=v_{1}{\cdot}e_{3}{\cdot}v_{4}$ following meta path $P=\mathcal{A}_{e}{\cdot}\mathcal{R}_{employee}{\cdot}\mathcal{A}_{p}$ and the second one is $p=v_{1}{\cdot}e_{2}{\cdot}v_{3}{\cdot}e_{13}{\cdot}v_{4}$ following meta path $P=\mathcal{A}_{e}{\cdot}\mathcal{R}_{control}{\cdot}\mathcal{A}_{p}{\cdot}\mathcal{R}_{relate}{\cdot}\mathcal{A}_{p}$. From the first path, the bribery scandal of an outsourcing employee $v_{4}$ may do limited harm to the enterprise $v_{1}$ since $v_{1}$ may have many other outsourcing employees to replace the role of $v_{4}$. However, from the second path, the bribery scandal of the outsourcing employee $v_{4}$ may do significant harm to enterprise $v_{1}$ since $v_{4}$ has a domestic relation with $v_{3}$ who directs enterprise $v_{1}$. Therefore, instead of inspecting each object’s direct impact, our model regards a whole logical path consisting of objects and relations as a factor, in evaluating the credit risk of SMEs.

Before introducing meta path features, we first give a method to identify if there exists potential risk in financial objects themselves. According to the object types studied in Section 3.1, except thenews object which is used to provide negative or positive information, a commodity object is regarded with potential risks if its quality is not reliable; a person object is regarded with potential risks if his capability is not qualified; an enterprise object is regarded with potential risks if it is lack of credibility. In this paper, in order to inference if potential risks exist, considering applicability and generality, we use Naive Bayes model to inference if the mentioned objects is risky or not. Our probabilistic model is learnt from public historical data, such as financial statements, annual reports, and online public news. The definition of our Naive Bayes inference model is given as the following:

With the inference function, we are able to identify the risk of a financial object by its own information. For instance, a commodity object with low sales volume, high repair rate, and high refund will be inferred as risky one; a person object with irrelevant education background, irrelevant working experience, and short working years will be inferred as risky one; an enterprise object with low ROE ratio, low quick ratio, and high asset-liability ratio will be inferred as risky one. In the next, we will study how to inference the potential risk from MP level.

In an SME information network, an enterprise may have many paths linking to other financial objects, as shown in Figure 4. We can see enterprise $J$ has $5$ path instances for meta path $P$ = $\mathcal{A}_{e}{\cdot}\mathcal{R}_{control}{\cdot}\mathcal{A}_{p}{\cdot}\mathcal{R}_{shareholder}{\cdot}\mathcal{A}_{e}$ and enterprise $K$ has $4$ path instances for MP $P$.

With the inference function defined above, we are able to identify if objects in the above information network are risky or not. Thus, for a specific MP, with the objects linked by its path instances, it is natural to infer that an enterprise is most likely to be risky if potential risks exist in most of its linked objects. Based on this straight intuition, we next present several features to elaborate such risk from meta paths.

In our experiments, three datasets recording enterprises’ statistics are used for comparison. GEM(The Growth Enterprise Market from Shenzhen Stock Exchange) and STAR (The Science and Technology Innovation Board from Shanghai Stock Exchange) datasets are about the SMEs of high technology, and SB (The Small and Medium-sized Enterprise Board from Shenzhen Stock Exchange) dataset are about traditional enterprises. All the datasets can be downloaded from CSMAR (https://www.gtarsc.com). As this paper only considers four types of financial entities (person, commodity, enterprise and news), our experiments are only performed on the enterprises those at least relate to one person, one commodity, one other enterprise and one piece of news.

The risk information about whether an enterprise is lack of credibilities, a person is lack of qualifications and a commodity is lack of reliabilities is obtained from CSMAR and cninf (http://www.cninfo.com.cn), which provide an authoritative and professional assessment on the entities. The news information is collected from China Judgements Online (https://wenshu.court.gov.cn). The final details of datasets is shown in Table 2.

As the gathered risk information may not be complete, for some important but unknown entities, we use the model in Section 4.1 to infer their risk. If an entity’s inferred probability is larger than $0.75$, it is deemed as risky.

Since the brought impact from a meta path decreases with its length increasing, we only consider the meta paths with length less than 6. And, the meta paths which do not start with SME type are not selected for our experiments. With the proposed MP features, we test their performance using a default prediction model which is used to learn the weights associated with those features. The logistic regression model is taken as the prediction model, which is optimized by MLE (Maximum Likelihood Estimation).

In this section, all experiments were performed using Python 2.7.17 in Win $8.1+$ with CPU $i5-9300+$ processor and $8G+$ RAM.

Even limited by the length constraint, there may still exist numerous meta paths. Among all possible meta path features, which ones are the most valuable ones? In this section, we will run experiments to show the importance of meta path features.

We first generate 40 meta path features according to Definition 4 for simplicity. Then each feature is tested under Wald test and the $p$-value of the feature associated with its meta path is used to evaluate the feature’s importance. The test is performed on all three datasets. From the results, we list the top 20 significant meta path features for each dataset in Tables 3 - 5 and the bottom 20 meta path features in Table 6 - 8 . We can see that for all three datasets, the controller’s ability, parent enterprise financial status, and news reported for enterprise, plays very significant roles in determining SME status. However, the longer the relation chains, the worse the performance of MP features. This may be due to the fact that longer links contain less valuable information. Or the longer the chain, the more distracting and inaccurate information it contains. Look into details, we find that for GEM and STAR datasets, the MP features containing personnel relations are most significant, while those containing enterprise relations are the least. For SB dataset, the opposite is true. It is reasonable, that the conventional SME, due to their own resource constraints, will pay more attention to the relationship with stakeholders in order to ensure stable development. The high-technology SME mainly focus on technology research and development, so the ability of personnel has a significant impact on the enterprise.