SocioLink: Leveraging Relational Information in Knowledge Graphs for Startup Recommendations

Figures & data

Figure 1. SocioLink: Relation-based recommendation framework.

Figure 2. Venture capital knowledge graph schema.

Figure 3. Instantiation of the venture capital knowledge graph.

Table 1. Meta-path design.

Relation	Meta-Path and Semantic Meaning	Key References
Employment Affiliation	Path 1: The target startup and the VC employs/employed the same person.$V{C}_1\stackrel{employ}{\to }Perso{n}_1\stackrel{emplo{y}^{-1}}{\to }Startu{p}_1$	Shi et al 2016 [51]
	Path 2: The target startup employs/employed a person who has worked for an existing portfolio company of the VC. $V{C}_1\stackrel{investedin}{\to }Startu{p}_2\stackrel{employ}{\to }Perso{n}_1\stackrel{emplo{y}^{-1}}{\to }Startu{p}_1$	Hallen 2008 [25]
Educational Connection	Path 3: The target startup and the VC employs/employed persons who attended the same educational institution. $V{C}_1\stackrel{employ}{\to }Perso{n}_1\stackrel{attended}{\to }Edu.Ins.\stackrel{attende{d}^{-1}}{\to }Perso{n}_2\stackrel{emplo{y}^{-1}}{\to }Startu{p}_1$	Cohen et al. 2008 [9]; Rider 2012 [48]
Ethnic Connection	Path 4: The target startup and the VC employs/employed persons who belong to the same origin. $V{C}_1\stackrel{employ}{\to }Perso{n}_1\stackrel{belongto}{\to }Origin\stackrel{belongt{o}^{-1}}{\to }Perso{n}_2\stackrel{emplo{y}^{-1}}{\to }Startu{p}_1$	Hegde and Tumlinson 2014 [27]
Geographic Proximity	Path 5: The target startup locates in the same city as the VC.$V{C}_1\stackrel{locatein}{\to }City\stackrel{locatei{n}^{-1}}{\to }Startu{p}_1$	Cumming and Dai 2010 [10]
Industry Relatedness	Path 6: The target startup operates in the same industry as the VC. $V{C}_1\stackrel{operatein}{\to }Industry\stackrel{operatei{n}^{-1}}{\to }Startu{p}_1$	Lerner 2013 [36]; Shi et al. 2016 [51]
	Path 7: The target startup operates in the same industry as an existing portfolio company of the VC. $V{C}_1\stackrel{investedin}{\to }Startu{p}_2\stackrel{operatein}{\to }Industry\stackrel{operatei{n}^{-1}}{\to }Startu{p}_1$	Sorenson and Stuart 2001 [54]

Table 2. Summary of training, validation, and test sets.

	Train	Validation	Test
Years	2014-2016	2017	2018
# of VCs	652	387	364
# of Startups	8,511	3,391	3,174
# of Initial Investment Deals	13,282	4,101	3,736
Average # of Deals per VC	20.4	10.6	10.3
Density (Percent)	0.2	0.3	0.3

Note. VC, venture capitalist. We remove VCs that have less than five annual investment deals to ensure sufficient actual investment deals for each VC in the dataset.

Table 3. Summary statistics of the venture capital knowledge graph before 2018.

Panel A: Summary of Entities
Entity Type	#Instances	Geographical Area
Venture Capitalist	4,537	U.S.
Startup	24,223	U.S.
Person	73,479	U.S.
Educational Institution	3,524	Worldwide
Ethnic Origin	19	Worldwide
City	1,703	U.S.
Industry	22	U.S.
Total # of Entities	107,507
Panel B: Summary of Relations
Relation Type	#Instances	Geographical Area	Time Period
Venture Capital Investment	60,433	U.S.	2000-2017
Founder/Co-founder	35,641	U.S.	N.A.
Investment Partner	4,994	U.S.	2000-2017
Employment (executive)	65,235	U.S.	1970-2017
Employment (board member)	11,703	U.S.	1970-2017
Employment (advisor)	5,318	U.S.	1970-2017
Employment (board observer)	1,331	U.S.	1970-2017
Educational attainment	60,461	Worldwide	N.A.
Ethnicity assignment	73,479	Worldwide	N.A.
Location	28,760	U.S.	N.A.
Industry	28,760	U.S.	N.A.
Total # of Relations	376,115

Note. 19 ethnic origins include Anglo-Celtic, West European, South European, East European, North European, Jewish, Chinese, Indian, Korean, Japanese, other East Asian, Singaporean, Malaysian, Indonesian, other Southeast Asian, Oceanian, Muslim, not found, and others.

Table 4. Performance in recommending startups to VCs on the test set.

Model	MAP	MRR	Recall @50 (Percent)	Recall @100 (Percent)	Recall @200 (Percent)	Recall @300 (Percent)
Benchmark Methods
Non-relational Features	0.007	0.020	2.17	4.61	9.62	13.68
WR-MF	0.010	0.035	2.97	5.57	9.21	11.76
ItemKNN: CF+Attribute	0.013	0.050	4.67	7.62	12.58	17.14
Non-relational Features+Geo+Industry	0.026	0.080	8.16	12.28	18.97	24.63
Our Methods Using Solely Relational Information
Graph Embedding Approach (DissimilarityScore)	0.024	0.080	8.07	11.68	18.51	23.29
Meta-path-based Approach (Meta-paths)	0.038	0.173	9.14	13.16	17.84	22.40
DissimilarityScore+Meta-paths	0.042	0.194	11.02	15.42	22.07	29.13
Our Methods Using Both Non-relational and Relational Information
DissimilarityScore+Non-relational Features	0.039	0.147	12.52	18.15	26.18	32.34
Meta-paths+Non-relational Features	0.047	0.195	11.82	17.31	25.41	30.96
SocioLink: DissimilarityScore+Meta-paths+Non-relational Features	0.051	0.197	14.08	19.73	28.23	34.88
Differences between SocioLink and Benchmark Methods
SocioLink vs. Non-relational Features	0.044***	0.177***	11.91***	15.12***	18.61***	21.20***
SocioLink vs. WR-MF	0.041***	0.162***	11.11***	14.16***	19.02***	23.12***
SocioLink vs. ItemKNN	0.038***	0.147***	9.41***	12.11***	15.65***	17.74***
SocioLink vs. Non-relational Features+Geo+Industry	0.025***	0.117***	5.92***	7.45***	9.26***	10.25***

Notes. VC, venture capitalist; MAP, mean average precision; MRR, mean reciprocal rank; WR-MF, weighted regularized matrix factorization. For each model, we use whether a VC has invested in the startup for the first time in a specific year as evaluation basis. We conduct a t-test to examine the significance level of performance difference between SocioLink and each benchmark; * p < 0.1. ** p < 0.05. *** p < 0.01.

Table 5. Performance of different relational modelling approaches on the test set.

Model	MAP	MRR	Recall @50 (Percent)	Recall @100 (Percent)	Recall @200 (Percent)	Recall @300 (Percent)
Matrix Factorization Methods with Various Relations
WR-MF (+co-work)	0.013	0.054	3.87	5.65	8.83	10.92
WR-MF (+education connection)	0.005	0.018	1.19	2.06	5.05	7.63
WR-MF (+ethnic connection)	0.006	0.018	1.46	2.42	5.11	7.46
WR-MF (+3 social relations)	0.005	0.015	1.41	2.71	4.85	6.92
WR-MF (+geographic proximity)	0.006	0.026	2.22	4.04	6.96	9.26
WR-MF (+industry relatedness)	0.007	0.026	2.36	4.11	6.90	9.30
WR-MF (+5 relations)	0.005	0.019	1.01	2.19	4.42	6.26
Feature-based Model with Simple Relational Dummies
Non-relational Features+Co-work+Education+Ethnic+Geo+Industry	0.039	0.172	9.69	14.1	21.1	26.67
Our Method based on Knowledge Graph
SocioLink: DissimilarityScore+Meta-paths+Non-relational Features	0.051	0.197	14.08	19.73	28.23	34.88
Differences between SocioLink and Modified Benchmarks
SocioLink vs. WR-MF (+co-work)	0.038***	0.143***	10.21***	14.08***	19.4***	23.96***
SocioLink vs. Non-relational Features+Co-work+Education+Ethnic+Geo+Industry	0.012**	0.025	4.39***	5.63***	7.13***	8.21***

Notes. VC, venture capitalist; MAP, mean average precision; MRR, mean reciprocal rank; WR-MF, weighted regularized matrix factorization. For each model, we use whether a VC has invested in the startup for the first time in a specific year as evaluation basis. We conduct a t-test to examine the significance level of performance difference between SocioLink and each modified benchmark; * p < 0.1. ** p < 0.05. *** p < 0.01.

Figure 4. Feature importance analysis.

Table 6. Performance in recommending successful startups to VCs on the test set.

Model	MAP	MRR	Recall @50 (Percent)	Recall @100 (Percent)	Recall @200 (Percent)	Recall @300 (Percent)
Benchmark Methods
Non-relational Features	0.008	0.022	4.71	7.39	14.44	19.69
WR-MF	0.017	0.032	9.81	10.20	10.20	10.20
ItemKNN: CF+Attribute	0.025	0.038	7.07	9.41	15.27	18.26
Non-relational Features+Geo+Industry	0.014	0.021	6.76	12.25	20.91	25.83
Our Methods Using Solely Relational Information
Graph Embedding Approach (DissimilarityScore)	0.015	0.026	7.32	11.28	18.68	25.18
Meta-path-based Approach (Meta-paths)	0.028	0.045	8.88	11.21	16.03	20.40
DissimilarityScore+Meta-paths	0.029	0.045	8.75	13.82	21.33	27.95
Our Method Using Both Non-relational and Relational Information
SocioLink: DissimilarityScore+Meta-paths+Non-relational Features	0.034	0.057	13.09	19.38	27.52	35.30
Differences between SocioLink and Benchmark Methods
SocioLink vs. Non-relational Features	0.026***	0.035***	8.38***	11.99***	13.08***	15.61***
SocioLink vs. WR-MF	0.017*	0.025*	3.28	9.18***	17.32***	25.10***
SocioLink vs. ItemKNN	0.009	0.019	6.02***	9.97***	12.25***	17.04***
SocioLink vs. Non-relational Features+Geo+Industry	0.020**	0.036***	6.33***	7.13**	6.61**	9.47***

Notes. VC, venture capitalist; MAP, mean average precision; MRR, mean reciprocal rank; WR-MF, weighted regularized matrix factorization. For each model, we use whether a startup has been invested by a VC for the first time in a specific year and has exited through IPO or acquisition by 2021 as evaluation basis. We conduct a t-test to examine the significance level of performance difference between SocioLink and each benchmark; * p < 0.1. ** p < 0.05. *** p < 0.01.

Figure 5. Illustrations of meta-paths between Cisco investments and startups ranked differently by the graph embedding approach.

Shi, Z.; Lee, G.M.; and Whinston, A.B. Toward a better measure of business proximity: Topic modeling for industry intelligence. MIS Quarterly, 40, 4 (2016), 1035–1056.

 Web of Science ®Google Scholar

Hallen, B.L. The causes and consequences of the initial network positions of new organizations: From whom do entrepreneurs receive investments? Administrative Science Quarterly, 53, 4 (2008), 685–718.

 Web of Science ®Google Scholar

Cohen, L.; Frazzini, A.; and Malloy, C. The small world of investing: Board connections and mutual fund returns. Journal of Political Economy, 116, 5 (2008), 951–979.

 Web of Science ®Google Scholar

Rider, C.I. How Employees’ prior affiliations constrain organizational network change: A study of US venture capital and private equity. Administrative Science Quarterly, 57, 3 (2012), 453–483.

 Web of Science ®Google Scholar

Hegde, D.; and Tumlinson, J. Does social proximity enhance business partnerships? Theory and evidence from ethnicity’s role in U.S. venture capital. Management Science, 60, 9 (2014), 2355–2380.

 Web of Science ®Google Scholar

Cumming, D.; and Dai, N. Local bias in venture capital investments. Journal of Empirical Finance, 17, 3 (2010), 362–380.

 Web of Science ®Google Scholar

Lerner J. Corporate venturing. Harvard Business Review, 91, 10, (2013), 86–94.

 Web of Science ®Google Scholar

Sorenson, O.; and Stuart, T.E. Syndication networks and the spatial distribution of venture capital investments. American Journal of Sociology, 106, 6 (2001), 1546–1588.

 Web of Science ®Google Scholar