Understanding the Impact of Startups’ Features on Investor Recommendation Task via Weighted Heterogeneous Information Network

Investor recommendation is a critical and challenging task for startups, which can assist startups in locating suitable investors and enhancing the possibility of obtaining investment. While some efforts have been made for investor recommendation, few of them explore the impact of startups’ features, including partners, rounds, and fields, to investor recommendation performance. Along this line, in this paper, with the help of the heterogeneous information network, we propose a FEatures’ COntribution Measurement approach of startups on investor recommendation, named FECOM. Specifically, we construct the venture capital heterogeneous information network at first.-en, we define six venture capital metapaths to represent the features of startups that we focus on. In this way, we can measure the contribution of startups’ features on the investor recommendation task by validating the recommendation performance based on different metapaths. Finally, we extract four practical rules to assist in further investment tasks by using our proposed FECOM approach.


Introduction
Venture capital (VC) is an important source of funding for startups [1]. It plays a key role in startups' sustainable growth and performance [2] and the innovation in the economy [3]. Investment companies provide financial support for startups. Besides that, they provide startups with necessary experience and knowledge for their development. However, there is information asymmetry between startups and investment companies, and it is challenging for startups to find suitable investors, especially for the startups that have no previous investors before [4]. Finance is an integral part of the startups' process, yet obtaining it is challenging [5]. For this reason, an investor-filtering system for startups can be extremely beneficial [4]. erefore, achieving information filtering and then recommending suitable investors for startups who can meet their personalized financial needs by using recommendation techniques have become a key problem to be solved in the domain of VC.
In the domain of VC, the extensive recommendation studies mainly focus on helping VC companies to find suitable startups [1,[6][7][8], while effective methods that support startups in finding investors are relatively rare. Xu et al. [4] achieved the investor recommendation by constructing a tripartite network representation containing virtual links. Antonio et al. [9] pointed out that finding a suitable investor who is interested in the startups' fields usually requires long-term research, which is especially difficult for new startups. Furthermore, recommending suitable investors who are interested in the startups' features is also challenging due to their inexperience. However, as for the new startups which have not been invested before, the resources they can utilize is limited. ey have no previous investors to be mined, and the features of startups are the limited resources available for finding suitable investors for them. Along this line, we try to employ the startups' features to study the investor recommendation problem, by measuring the contribution of startups' features on the investor recommendation performance. e features we care about in this paper include partners, rounds, and field. An example of startups is shown in Table 1, the startup Ziroom and Bitmain have the same round, the startup Vxiaoke is in Angel Investment, and the former two startups have the same investor, while the investor of the third startup is different from them. erefore, we consider that the feature of round may affect the decision of investors. And, there may be various impacts on investors by different startups' features. To this end, how to measure the contribution of startups' features on the investor recommendation performance is a vital task for startups. In this paper, we aim to address startups' features contribution measurement problem.
For exploring the impact of startups' features on the investor recommendation task, there are two challenges that need to be solved. (1) How to represent the features related to the investor recommendation task? (2) How to recommend a investor to a startup based on the focused features? Notably, the VC network is a typical heterogeneous information network (HIN), which contains multiple types of nodes and multiple edges between nodes. ere is rich structural information and semantic information in the VC network, which provides us the opportunity to address the two challenges based on HIN.
HIN has been successfully applied in recommender systems [10]. erefore, in this paper, we propose a features' contribution measurement approach of startups on investor recommendation named FECOM, based on HIN. e purpose of this paper is to explore the impact of startups' features on the investor recommendation task and extract the rules to assist in further investment tasks. Specifically, we integrate various types of VC data into the form of HIN at first, by which the venture capital heterogeneous information network (VC-HIN) can be constructed. en, the venture capital metapaths (VC-metapaths) are defined to represent the features of startups that we focus on. Based on this, we propose the FECOM approach, which can conduct the investor recommendation task by utilizing different VCmetapaths. In this way, we can measure the contribution of startups' features on the investor recommendation task according to different VC-metapaths, and extract beneficial rules to assist in further investment tasks, by analysing the recommendation performance. e main contributions of this paper can be summarized as follows: (1) We define the venture capital heterogeneous information network (VC-HIN), by which the structural information contained in the VC network can be expressed. (2) We formulate the venture capital metapaths (VCmetapaths) to represent the features related to the investor recommendation task, and the semantic information contained in the VC network can be indicated.
(3) We propose a features' contribution measurement approach of startups on investor recommendation named FECOM. On the basis of it, we can analyse the impact of startups' features on investor recommendation by validating the recommendation performance based on different metapaths. (4) We extract four practical rules by exploiting the proposed FECOM approach, which are beneficial for further investment tasks. e paper is structured as follows. In Section 2, we introduce the related works. In Section 3, we propose two definitions about the proposed FECOM, which are the basis of FECOM. In Section 4, we provide the framework and the details of the proposed FECOM. In Section 5, we explore the impact of startups' features on investor recommendation and extract four practical rules to assist in further investment tasks through experiments. In Section 6, we conclude the paper.

Related Work
In this section, we briefly review related works on the VC, VC recommendations, and HIN.
In recent years, related research studies in the domain of VC have continued to grow. Chircop et al. [11] studied the influence of religious belief on VC decision-making. Andrieu and Groh [12] established a startups' investor selection model and found that startups would select investors based on the factors such as the quality of the investor support. Tian et al. [13] confirmed the nonlinear relationship between the geographic distance between the investors and the startups and the startups' performance through the research. Cheng and Tang [14] conducted the research on the impact of investment partner selection strategy, the industry of the startup, and geographic uncertainty on VC. Wu et al. [15] studied the influence of the network structure on VC alliance's successful exit from emerging markets. Zhang et al. [16] used multilayer network analysis to simulate the spread of risks in the VC market when external shocks affect investment companies or startups. Luo [17] put forward the countermeasures for the company's financial risk investment by predicting the stock premium. Salamzadeh and Kesim [5] tried to conceptualize the phenomenon "startup" and recognize the challenges they might face. Antonio et al. [9] examined the association between the presence of venture capital and the growth of startups.
However, as for the VC recommendation, there are few research studies focusing on that. Stone et al. [1] demonstrated the effectiveness of the collaborative filtering recommendation technique in the new application domain of finance and improved the recommendation quality of However, due to the information asymmetry between investors and startups, the financing process is usually challenging, especially for the startups that have not yet been invested before [4]. As the features of startups without investment are the limited resources available for them to find suitable investors, we try to exploit the features and measure the contribution of startups' features on the investor recommendation performance and then extract beneficial rules to assist in the further investment recommendation problem by analysing the recommendation performance.
As an emerging direction, HIN has attracted the attention of many scholars. HIN contains rich structural and semantic information [18]. e recommendation based on HIN can naturally simulate the rich information contained in the network and then realize personalized recommendation. Node similarity measurement, as a key part of information extraction from HIN-based recommendation, has been widely studied. Haveliwala [19] proposed the personalized PageRank algorithm (PRANK recommendation), which measures the similarity between nodes by randomly walking between nodes; Jeh and Widom [20] proposed the SimRank algorithm, which calculates the similarity between nodes through the similarity of their neighbors. However, both PRANK and SimRank ignored the semantic information contained in the HIN. In addition to those algorithms, there are many HIN-based recommendation techniques considering the metapath-based similarity [21]. Sun et al. [18] proposed the PathSim algorithm based on symmetric metapaths to achieve similarity measurement between nodes of the same type in the network; Lao and Cohen [22] proposed the PCRW algorithm to measure the similarity between different types of nodes in the network through a random walk model with path constraints; Shi et al. [23] proposed the HeteSim algorithm based on the arbitrary metapath, which can measure the similarity between any type of node in the network. e above three algorithms all use metapath-based similarity to measure the node similarity of network semantic information, but they do not consider the network structure information. All the above similarity measurement techniques have some limitations because they fail to consider the structure or semantic information of HIN at the same time. Lee et al. [24] proposed the PathRank algorithm to calculate the similarity between nodes by using the one-way random walk model. It realizes the measurement of nodes' similarity on the basis of fully extracting the structure and semantic information of HIN. Compared with the above node similarity measurement methods, the PathRank algorithm can utilize the rich information contained in the VC network. Furthermore, we will calculate the scores of investors to be recommended on the basis of the PathRank algorithm in the following sections by considering the rich structural information and semantic information in the VC network.
Among the above existing literature studies, there is less attention from scholars that has been devoted to the evaluation of the impact of startups' features on the investor recommendation task. Motivated by these observations, we propose a features' contribution measurement approach of startups on investor recommendation named FECOM. According to the proposed FECOM, the practical rules could be obtained to support the investment task by evaluating the recommendation performance based on different metapaths.

Preliminaries
In this section, we propose two definitions about the proposed FECOM approach, namely, venture capital heterogeneous information network (VC-HIN) and venture capital metapaths (VC-metapaths) in the VC network, which are the basis of the model. Specifically, VC-metapaths can provide various semantic information for the investor recommendation task. Venture capital heterogeneous information network (VC-HIN) is defined as a weighted heterogeneous information network constructed based on venture capital data, including different types of nodes and weighted edges.
} is the node set containing five kinds of node, namely, C-company, P-company partner, R-investment round, F-field, and I-investor, and E refers to the edge set including 14 kinds of edge types between different nodes, which are directed and reveal the relations between corresponding nodes. As for the weights of edges in VC-HIN, we define different weight calculation methods for different kinds of edges. In terms of the edge between I and C, its weight is the total number of times of the investor who used to invest in the startup. For the edge between I and P, the weight is the number of times of the investor invested in the companies built by P. Similarly, as to the edge between I and R, its weight is the number of times of the investor invested in companies in round R. And, the weight of the edge between I and F is the number of times of the investor invested in companies in field F. Particularly, the weights of edges between C and P, R, and F are defined as 1.
An example of VC-HIN is shown in Figure 1. ere are two company nodes C1 and C2, two investor nodes I1 and I2, two company partner nodes P1 and P2, two round nodes R1 and R2, and one field node F1. e lines represent the edges between nodes, and thicker lines indicate the edges with larger weights. For example, the line between I2 and F1 is thicker than that between I1 and F1, which indicates that the Complexity 3 weight of the edge linking I2 and F1 is larger than the edge linking I1 and F1. It proves that the investor I2 invests more in companies in the field F than I1. Similarly, the weight of the edge linking I1 and C1 is larger than the edge linking I2 and C1, revealing that the company C1 is invested by the investor I1 more than I2. Furthermore, the edges between different nodes are directed and reveal the relations between corresponding nodes, and the edges have two kinds of directions "+" and "−." For example, the edge C1 ⟶ invest in − I1 indicates that the company C1 is invested by the investor I1. And, the edge I1 ⟶ invest in + C1 implies that the investor I1 invests in the company C1.
Definition 2. Venture capital metapaths (VC-metapaths). e venture capital metapaths (VC-metapaths) in VC-HIN are defined specifically to the investor recommendation task studied in this paper. We first formulate the venture capital heterogeneous information network schema TG � (A, R) shown in Figure 2 with the node type mapping function ϕ V : V ⟶ A and the edge type mapping function ϕ E : E ⟶ R, where A represents the node type set and R represents the edge type set. Based on TG, we define VCmetapaths, which can represent the compound relation between different nodes in VC-HIN. A VC-metapath can be represented as . . , v i 〉 represents a node in the network, and the element in set 〈e1, e2, . . . , ei〉 represents an edge in VC-HIN. We are supposed to recommend suitable investors for startups; therefore, the first node in the VCmetapath is fixed as a company node, and the last node must be an investor node. As shown in Figure 2, there are five kinds of node types in the set A and 14 kinds of edge types including directions in the set R.
As we focus on the contribution of the target startups' features on the investor recommendation task, the commonly used features include startups' partners, rounds, and fields. As shown in Table 2, we formulate six VC-metapaths based on these three kinds of startups' features. e longer the metapath, the fuzzier the corresponding semantic information and the lower the reliability of the similarity measure [18]. erefore, we define that there will be no more than four nodes in VC-metapaths. e six VC-metapaths cannot only exploit the semantic information behind the different types of nodes and edges in VC-HIN but also simulate several classical recommendation methods, such as collaborative filtering recommendation and content-based filtering. Table 2 lists the six VC-metapaths, their semantic analysis conclusions, and similar methods. For example, the VC-metapath CPI can mine the semantic information behind startups' partners and the edge linking P and I contained in the metapath.
is metapath recommends investors who have invested in the partners of target companies, which is similar to the paradigm of contentbased recommendation. Figure 3 shows the six VC-metapaths, where the edges contained in the metapath are represented by solid lines. CPI and CPCI are shown in Figure 3(a), where CPI consists of the edge linking C and P and the edge linking P and I, while CPCI is composed of the edge linking C and P and the edge linking C and I. For the metapath CRI and CRCI in Figure 3(b), the edge linking C and R and the edge linking R and I make up CRI, and CRCI is comprised of the edge linking C and R and the edge linking C and I. Similarly, CFI and CFCI are shown in Figure 3(c), where CFI consists of the edge linking C and F and the edge linking F and I, while CFCI is composed of the edge linking C and F and the edge linking C and I.
Based on the basic concepts mentioned above, the proposed FECOM can consider the structure information contained in VC-HIN and the semantic information contained in multiple VC-metapaths at the same time, which will fully mine the rich information contained in the VC network and is able to explore the impact of startups' features to the investor recommendation task. e details about FECOM will be introduced in the next section.

FECOM Approach
In this section, we first provide the overall framework of the proposed FECOM approach and then illustrate its details.

Overview of FECOM.
In this section, we introduce the framework of FECOM. e framework of the proposed FECOM is shown in Figure 4, consisting of two main components: (1) Constructing Layer. We construct the VC-HIN and specify the VC-metapaths of VC-HIN in this layer   Recommending layer Figure 4: Framework of the proposed FECOM where the left part shows the constructing layer and the right part presents the recommending layer.

Complexity 5
firstly. e VC-HIN is built according to the VC data collected in advance, which is similar to Figure 1; however, it is bigger and more complex than Figure 1. e VC-metapaths are designed according to the information to be mined; since the target startups in this paper have no investors before, the partners, rounds, and fields of them can be exploited to realize the investor recommendation. As shown in Table 2 and Figure 3, the VC-metapaths in this paper have been designed. Herein, we give two kinds of transition matrices, the VC-HIN transition matrix T and the VC-metapath transition matrix Since there are six metapaths in Table 2, k is an integer less than or equal to 6. e VC-HIN transition matrix T is extracted from VC-HIN, which can express the structural information of VC-HIN. Similarly, the VC-metapath transition matrix T gk is calculated based on the VC-metapath, indicating the semantic information contained in the metapath.
is layer requires the VC-HIN transition matrix T and the VC-metapath transition matrix T gk as input and conducts the investor recommendation. e recommending layer contains two personalized investor recommendation strategies, which are based on the single metapath and the mixed metapath. e investor recommendation of the mixed metapath is derived from recommendation results of different single metapaths. As shown in the recommending layer, the VC-HIN transition matrix T and the VC-metapaths' transition matrices T g1 , T g2 , and T g3 are obtained in the constructing layer. Next, we utilize the VC-HIN transition matrix T and the VC-metapaths' transition matrices containing T g1 , T g2 , and T g3 in Figure 4, respectively, to obtain the optimal investor recommendation sets S 1 , S 2 , and S 3 based on the single metapaths g 1 , g 2 , and g 3 . e VC-metapaths' transition matrices T g1 and T g2 with better recommendation effectiveness will be selected to generate the mixed metapath transition matrix T gm of the mixed metapath g m after comparing the recommendation performance on each single metapath. In the end, the optimal investor recommendation set S m can be obtained based on the VC-HIN transition matrix T and the mixed metapath transition matrix T gm . By evaluating the performance of the recommendation set, we can analyse the impact of the corresponding VC-metapath on the investor recommendation task.
Next, based on the framework of FECOM mentioned above, the technical details about the constructing layer and recommending layer are interpreted, respectively.

Constructing Layer.
In the constructing layer, we are supposed to construct the VC-HIN and design the VCmetapaths based on the VC data collected before firstly. Next, we compute the VC-HIN transition matrix T and the VC-metapath transition matrix T gk based on the adjacency matrix P and the edge adjacency matrix P Rn , n ∈ 1, 2, . . . , 14 { }, respectively. Since there are 14 edge types in TG � (A, R), n is an integer less than or equal to 14.
For the adjacency matrix P, it is represented as a |V| × |V| matrix, where |V| is the total numbers of all the nodes in VC-HIN. And, the element P(i, j) of P represents the weight of the edge between the node v i and v j .
Based on the adjacency matrix P, the VC-HIN transition matrix T can be computed according to equation (1), which is a |V| × |V| matrix: where T (i, j) is the element of the ith row and the jth column in T , representing the probability of the transition between the node v i and the node v j . As for the edge adjacency matrix P Rn , it is also a |V| × |V| matrix, where R n is one of the edge types in the edge type set R and |V| is the total numbers of all the nodes in VC-HIN. e element P Rn (i, j) of P Rn reveals the weight of the edge linking the node v i and v j whose edge type belongs to the edge type R n .
For the metapath g k � v 1 ⟶ e 1 v 2 . . . v i ⟶ e i v i + 1 mentioned in Section 3, its transition matrix T gk can be calculated after normalizing the edge adjacency matrix P Rn . e normalized P Rn will be represented as N Rn , which is defined as follows: , if the edge type of e i linking v i and v j ∈ R n ∧i ≤ |V|∧j ≤ |V|∧n ≤ |R|, where N Rn (i, j) is the element of the ith row and the jth column in N Rn , demonstrating the probability of the random walk between the node v i and the node v j .
e VC-metapath transition matrix T gk can also be denoted as a |V| × |V| matrix, which can be represented as follows: 6 Complexity e basic idea is that the transition matrix of the metapath g k can be obtained by multiplying the normalized edge adjacency matrices of all the edges contained in the metapath g k .
In this section, on the basis of the adjacency matrix P and the edge adjacency matrix P Rn mentioned above, we introduce the calculation process of the VC-HIN transition matrix T and the VC-metapath transition matrix T gk . Hereafter, we interpret the recommending layer in detail.

Recommending Layer.
For exploring the contribution of different startups' features on investor recommendation task T gk , we utilize different types of metapaths to carry out the investor recommendation, respectively, in this layer. We will explain how to obtain the investor recommendation set for target startups under the single metapath and the mixed metapath in this section.

Investor Recommendation Based on the Single
Metapath.
e single metapaths are the VC-metapaths defined based on the venture capital heterogeneous information network schema, which can represent the compound relation between different nodes in VC-HIN. In this paper, the single metapath refers to the six VC-metapaths shown in Table 2 and Figure 3. e investor recommendation based on the single metapath mainly relies on the VC-metapaths mentioned before. We can obtain the investor recommendation sets according to the partners, rounds, and fields of startups. e investor recommendation based on the single metapath such as CPCI, CRCI, and CFCI can simulate the procedure of collaborative filtering recommendation. It will address the investor recommendation task for startups by exploring the performance of its features including partners, rounds, and fields. In addition, the investor recommendation based on the single metapath such as CPI, CRI, and CFI simulates the content-based recommendation.
FECOM exploits the VC-HIN transition matrix T and the VC-metapath transition matrix T gk to calculate the scores of investors based on PathRank [24]. As shown in equation (4), we first input the VC-HIN transition matrix T and the VC-metapath transition matrix T gk of each single metapath, respectively, to obtain the score set of all the investors to be recommended. en, the investor recommendation set is generated after sorting the scores of all the investors in the descending order: As shown in equation (4), r ⇀ represents the score set of all the investors to be recommended, which is a 1 × |V| vector. We first initialize and then continuously optimize r ⇀ by equation (4). When r ⇀ no longer changes, it will be the optimal score set.w trans , w path , and w re are all the probability weight parameters, t ⇀ is represented as a 1 × |V| restart vector, and the element t ⇀ (i) of t ⇀ is 1 when its corresponding node v i is the target startup.
Next, as there are several probability weight parameters in equation (4), we will obtain different investor recommendation sets by setting different values for the parameters. After comparing the performance of each single metapath under different parameter configurations, we can acquire the optimal performance of each single metapath. Meanwhile, the optimal investor recommendation sets can be produced. Finally, several single metapaths with better recommendation effectiveness will be selected to generate the mixed metapath g m .
We realize the investor recommendation based on the single metapaths in this section. Along this line, the investor recommendation based on the mixed metapath will be provided.

Investor Recommendation Based on the Mixed Metapath.
e mixed metapath is generated by the single metapaths mentioned above. In this paper, the mixed metapath is built by combining several single metapaths with good recommendation performance, where the number of metapaths to generate the mixed metapath is not fixed. We choose single metapaths based on their performance. e investor recommendation based on the mixed metapath can simulate the hybrid recommendation. It can realize the investor recommendation by mixing startups' various features including the partner, round, and field information. For example, the mixed metapath based on CPCI and CRI can consider the partners and rounds of the startups at the same time.
e generation process of the mixed metapath is shown in Figure 5. Firstly, we can obtain the VC-HIN transition matrix T and the VC-metapaths' transition matrices T g1 , T g2 , and T g3 for the metapath g 1 , g 2 , and g 3 from the constructing layer. en, the investor recommendation sets based on different single metapaths under different parameter configurations can be acquired. After comparing their performance, we can know the optimal performance of each single metapath. As shown in Figure 5, the investor recommendation sets S 1 , S 2 , and S 3 are the optimal investor recommendation sets based on the metapath g 1 , g 2 , and g 3 . As the mixed metapath is built by combining several single metapaths with good recommendation performance, we compare the recommendation effectiveness of different investor recommendation sets S 1 , S 2 , and S 3 by using evaluation metrics. And, the VC-metapaths' transition matrices T g1 and T g2 will be input into equation (5) to generate the mixed metapath transition matrix T gm , which derived from PathRank [24], because S 1 and S 2 perform better than S 3 : T gm � w 1 T g1 + w 2 T g2 + · · · + w k T gk .
As shown in equation (5), T gm represents the mixed metapath transition matrix of the mixed metapath gm, which is a |V| × |V| matrix just like the VC-metapath transition matrix T gk . T gk represents the VC-metapath Complexity transition matrix of the metapath gk, and wk is the metapath weight of the metapath g k .
After getting the mixed metapath transition matrix T gm , we will introduce the investor recommendation based on the mixed metapath. Firstly, we can obtain the score set of the investors by inputting the VC-HIN transition matrix T and the mixed metapath transition matrix T gm into equation (4). en, the optimal investor recommendation set of the mixed metapath can be collected after comparing the performance of the mixed metapath under different parameters.
In brief, after comparing the optimal investor recommendation sets based on different single metapaths and the mixed metapath by using evaluation metrics, the optimal investor recommendation set can be obtained. Along this line, we can know the contribution of each VC-metapath on the investor recommendation task; based on this, the impact of startups' features will be explored.

Experiments
In this section, we first evaluate the recommendation performance of FECOM on different single metapaths and the mixed metapath through real VC data. Along this line, we can analyse the effectiveness of different metapaths to the investor recommendation task.

Dataset.
e experimental dataset is collected from http://www.itjuzi.com. We delete the investment events with missing fields, rounds, and partners and remove the investors who have invested less than three times and their corresponding investment events, so as to avoid the coldstart problem for investors, which leaves us with 13573 investment events. As shown in Table 3, there are 6816 companies, 1328 investors, 4862 partners, 15 rounds, and 19 fields in the experimental dataset.
We divide the dataset into the training set and the testing set in the chronological order. e training set takes the first 80% of the original data, and the testing set takes the rest part. Besides, we aim to recommend investors to new startups that have no previous investors before; to this end, there are only 1602 investment events in the testing set. Since some startups appear in multiple investment events, there are actually 995 startups involved in the testing set.

Evaluation Metrics.
We choose two evaluation metrics, the ranking score (RS) [25] and the AUC (area under receiver operator curve) [26], to evaluate the effectiveness of our proposed FECOM in the investor recommendation task.

Ranking Score (RS).
e ranking score (RS) is an important indicator to measure the relative ranking of the investors in the recommendation set. For the target startup, the relevant investor refers to the investor whose investment record exists in the testing set, and the irrelevant investor refers to the investor who has not invested in the target startup in the training set. RS can measure the relative  ranking of relevant investors and measure the degree of uniformity between the recommendation set and the actual investor set. e smaller the RS, the more accurate the relative ranking of the investors in the recommendation set. On the contrary, the higher the RS, the less accurate the ranking. Since there are few actual investors for the target startup, the RS is a better evaluation metric than Precision and Recall [4].
As shown in equation (6), L u represents the number of investors to be ranked for the target startup and l ua represents the ranking of the investors to be ranked in the recommended list. e mean ranking score can be obtained by averaging the ranking scores of all the startups:

AUC (Area under Receiver Operator Curve).
e AUC can be approximated as the probability that the utility of the relevant investor is higher than the utility of the irrelevant investor. It can measure the ability of the recommendation technique to distinguish relevant investors from irrelevant investors. For the target startup, the higher the AUC, the stronger the ability of the recommended technique to distinguish relevant investors from irrelevant investors, the better the recommendation effectiveness, and the easier for the startup to find suitable investors. On the contrary, the lower the AUC, the more difficult for the startup to find suitable investors.
As shown in equation (7), for the target startup, a relevant investor and an irrelevant investor are randomly selected, n ′ means the number of times that the score of the relevant investor is greater than the score of the irrelevant investor, n ″ represents the number of times the two scores are equal, and n represents the number of startups. e mean AUC can be obtained by averaging the AUC of all the startups:

Recommendation Performance on VC-Metapaths.
We evaluate the investor recommendation based on the single metapath and the mixed metapath according to the evaluation metrics mentioned above in this section.

Recommendation Performance on Single Metapaths.
For locating the optimal recommendation result on each metapath, we set multiple probability parameters w trans , w path , and w re , where w trans ranges from 0 to 0.4, w path ranges from 0.6 to 1, and w re ranges from 0 to 0.2, and the step size of them are all 0.05. Specifically, when w trans and w re are 0, the recommendation effectiveness is poor, which is not reported in this paper. e values of RS and AUC based on each single metapath are shown in Tables 4 and 5. e values that need to be paid attention are in bold.
As shown in Table 4, among all the metapaths, when w trans is 0.2, w path is 0.6, and w re is 0.2, the recommendation based on the metapaths CPCI and CPI performs better. e best RS of CPCI is 0.211807, while the best RS of CPI is 0.213887. Furthermore, the investor recommendation based on the metapath CPCI performs better than the metapath CPI. Besides, when w trans is 0.35, w path is 0.6, and w re is 0.05, and the recommendation based on the metapaths CRCI, CRI, CFCI, and CFI performs best. Except for this, the recommendation based on the metapaths CFCI and CFI performs better than the metapaths CRCI and CRI.
As for AUC results shown in Table 5, when w trans is 0.15, w path is 0.7, and wre is 0.15, the investor recommendation based on the metapath CPCI performs best. Furthermore, when w trans is 0.15, w path is 0.7, and w re is 0.15, the investor recommendation based on the metapath CPI performs best. Among all the metapaths, the investor recommendation based on the two metapaths performs better than the other metapaths. At the same time, when w trans is 0.2, w path is 0.6, and w re is 0.2, the performance of the investor recommendation based on the two metapaths is still better. Additionally, the investor recommendation based on the metapath CPI performs better than the metapath CPCI. And, the investor recommendation based on the metapaths CFCI and CFI performs better than the metapaths CRCI and CRI.
In summary, the obtained results demonstrate that when w trans is 0.2, w path is 0.6, and w re is 0.2, the investor recommendation based on the metapaths CPCI and CPI performs better than other metapaths.

Recommendation Performance on the Mixed Metapath.
After optimizing the investor recommendation based on different single metapaths mentioned above, we plot their performance in Figures 6 and 7. e investor recommendation based on the metapath CPCI and CPI performs better than those based on other four metapaths apparently. erefore, we choose the two better single metapaths CPCI and CPI. Next, we will select the optimal parameter configuration and VC-metapaths' CPCI and CPI to generate the mixed metapath and conduct the investor recommendation. e metapath weight parameter of the single metapath CPCI is set to w 1 , the metapath weight parameter of CPI is set to w 2 , and w 1 + w 2 � 1. Furthermore, in the experiment, the step size of the two parameters is 0.1. e experiment results of the investor recommendation on the mixed metapath are shown in Figures 8 and 9. It shows that the RS and AUC of the investor recommendation based on the mixed metapath vary with the metapath weight parameters.
e RS gradually decreases as w 1 increases. Meanwhile, the performance of the investor recommendation based on the mixed metapath is getting better and better. e AUC is relatively volatile; however, it is generally on the rise. Besides, the investor recommendation based on the mixed metapath performs better in general. When the metapath weight parameter w 1 is 1 and w 2 is 0, the RS and AUC both perform best. It indicates that the performance of investor recommendation based on the single metapath Complexity 9 CPCI is better, compared with the results based on the mixed metapath.

Analysis of VC-Metapaths.
After assessing the performance of the investor recommendation based on the single metapath and the mixed metapath, we can now analyse the impact of each defined single metapath on the investor recommendation task and summarize four rules to assist in further investment tasks.
(1) e partners of startups contain much more precise semantic information for investor recommendation than the fields and rounds of startups. As shown in Tables 4 and 5, among all the VCmetapaths, the investor recommendation based on  Correspondingly, the partners involved in the two metapaths contain more precise semantic information than the fields and rounds of startups. erefore, the partners of startups could be followed when recommending investors for startups. For example, as for the startup Ziroom shown in Table 1, if we recommend investors for it based on its partners, rounds, or fields, its partners Lin Xiong and Guowei Li could contain more useful semantic information than its field Real Estate and its round A, and we could obtain good recommendation performance by mining its partners. (2) e fields of startups include richer related information about investor recommendation than the rounds. Tables 4 and 5 show that the recommendation based on the metapaths CFCI and CFI performs better than the metapaths CRCI and CRI, which illustrates that the metapaths CFCI and CFI include more plentiful information than the metapaths CRCI and CRI. Along this line, the fields of startups contain richer information than the rounds. ereby, we could focus on their fields in the investor recommendation task. Also, for the startup Ziroom shown in Table 1, if we recommend investors on the basis of its rounds or fields, its field Real Estate could contribute more to the recommendation task than its round A, and we could get good recommendation effectiveness by utilizing its field.
(3) e companies with the same partners as the target startup could contribute much more information to the investor recommendation task, than its partners. As shown in Table 4, the investor recommendation based on the VC-metapath CPCI is more effective than the investor recommendation based on the metapath CPI. e results indicate that it will make the relative ranking of relevant investors in the corresponding investor recommendation set more accurate when we mine the companies with the same partners as the target startup and recommend investors for the target startup. However, when we focus on the partners of startups and recommend investors for the target startup who have invested in the partners of the target startup, the accuracy of the relative ranking of relevant investors will be reduced.  erefore, the companies with the same partners as the target startup could contribute much more information to the investor recommendation task, than its partners. For example, if we recommend investors for the startup Ziroom shown in Table 1 based on its partners, Lin Xiong and Guowei Li, we could first focus on the companies with partners Lin Xiong and Guowei Li and then recommend the investors who have invested in those companies for Ziroom. (4) It will lead to worse performance, when the investor recommendation task is conducted by simultaneously utilizing the companies with the same partners as the target startup and the partners of the target startup. e experimental results shown in Tables 4 and 5 illustrate that the partners of startups are more important than the other features, such as fields and rounds of startups. As shown in Figures 8 and 9, when the metapath weight parameter w 1 is 1 and w 2 is 0, the RS and AUC of the investor recommendation based on the mixed metapath both perform best. As the metapath weight parameter w 1 is 1 and w 2 is 0, it indicates that the performance of investor recommendation based on the single metapath CPCI is better, compared with the result based on the mixed metapath. It shows that the mixed metapath generated by the metapaths CPCI and CPI will make the semantic information contained in the metapath fuzzier, which will lead to worse recommendation performance. For example, if we recommend investors for the startup Ziroom shown in Table 1 based on its partners Lin Xiong and Guowei Li, we define the investors who have invested in the companies with the same partners as the first kind of investor and the investors who are interested in the partners as the second kind of investor, and we could only recommend investors for Ziroom based on the first kind of investor. Furthermore, it will make the recommendation performance worse if we recommend investors for Ziroom on the basis of the two kinds of investors.

Conclusions
In this paper, we investigate how to mine practical rules to assist in further investment tasks, by measuring the impact of startups' features on the investor recommendation task. Along this line, we propose a features' contribution measurement approach of startups on investor recommendation, named FECOM. Specifically, we first construct the VC-HIN and design six VC-metapaths based on three startups' features, including partners, rounds, and fields. en, the two recommendation strategies contained in FECOM could be accomplished by exploiting different types of VC-metapaths. To this end, we could analyse the impact of startups' features on investor recommendation by validating the recommendation performance and summarize the practical rules beneficial for further investment tasks. Finally, four practical rules about the startups' features for the investment task are extracted based on a real-world dataset, which can be employed to guide in further investor recommendation.
However, if there is a large amount of VC data to be processed, the proposed FECOM will be time consuming. In the future, we will put efforts into reducing the time cost of FECOM. Besides, we will study the optimal number of single metapaths to generate the mixed metapath.

Data Availability
e data used to support the findings of this study are available from the corresponding author via gaox-iaonan0001@163.com upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.