IP Library › Granted Patent US 12,327,196
Granted Patent B2
US 12,327,196 · App. 17/333,385 · Granted Jun 10, 2025

Systems and methods for performing random walks on knowledge graphs

Inventors: Mariano Beguerisse-Díaz (London, GB); Till A. Hoffmann (London, GB); Dimitrios Korkinof (London, GB)
Assignee: Spotify AB
G06N5/02
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Quick Facts
Patent No.
US 12,327,196
App. No.
17/333,385
Granted
Jun 10, 2025
Kind
B2
Abstract

Systems, methods and computer program products are provided for performing random walks on knowledge graphs. Knowledge graphs are received and for each knowledge graph there is constructed a multilayer network having unipartite layers and bipartite layers and interlayer couplings that (i) connect nodes of the unipartite layers and the bipartite layers representing the same entity (ii) are directed and (iii) weighted with a weight that depends on an activity of a target node in the unipartite layer or bipartite layer in which the target node resides. A walk on a random walk model of the multilayer network that takes into account saliencies of the different interlayer and intralayer connections of the nodes is then processed and one or more actions based on the random walk model are performed.

Claims (160)

1. A system for performing random walks on knowledge graphs, comprising:

a memory; and

one or more processors to:

receive a plurality of knowledge graphs; and

for each knowledge graph:

construct a multilayer network having:

unipartite layers, wherein the unipartite layers comprise connections that originate from and terminate at the same node;

bipartite layers, wherein the bipartite layers comprise connections that originate from and terminate at different nodes; and

interlayer connections that:

 (i) connect nodes of the unipartite layers and the bipartite layers that represent the same entity;

 (ii) are directed; and

 (iii) are weighted with a weight that depends on an activity of a target node in the unipartite layer or the bipartite layer in which the target node resides;

process a random walk model of the multilayer network that takes into account saliencies of the interlayer connections and intralayer connections of the nodes; and

provide one or more media content recommendations based on the random walk model.

2. A system for performing random walks on knowledge graphs, comprising:

a memory; and

one or more processors to:

receive a plurality of knowledge graphs, each knowledge graph having a plurality of entities and a collection of types of labeled connections representing the relationships of the plurality of entities, each labeled connection being weighted or unweighted and each entity having:

(i) an entity type; and

(ii) a set of connections with other entities in the knowledge graph;

generate, for each type of labeled connection, a monolayer network, wherein each entity of the entity types connected by the labeled connection is represented by a node, thereby generating a plurality of monolayer networks;

assemble the plurality of monolayer networks into a multilayer network, wherein each layer of the multilayer network corresponds to one of the plurality of monolayer networks, wherein two or more nodes that represent the same entity are linked by an interlayer connection;

receive a first plurality of coupling strengths, each of the first coupling strengths corresponding to one of the labeled connections;

receive a second plurality of coupling strengths, each second coupling strength corresponding to the connections between nodes across layers of the multilayer network that represent the same entity;

construct a random walk model on the multilayer network, wherein a probability of visiting a first node of the plurality of nodes from a second node of the plurality of nodes is proportional to:

(i) the weight of the labeled connection between the first node and the second node divided by the sum of all the weights of the connections that originate from the second node and multiplied by the first coupling strength of the corresponding labeled connection; or

(ii) the second coupling strength of the connection between the nodes across layers of the multilayer network that represent the same entity; and

provide one or more media content recommendations based on the random walk model.

3. The system according to claim 1 , wherein an entity has one or more roles, and wherein each role represents a function performable, by the entity, with respect to connected entities.

4. The system according to claim 1 , wherein each labeled connection also has a temporal attribute.

5. The system according to claim 1 , wherein providing the one or more media content recommendations comprises:

(i) sequencing the plurality of nodes in the multilayer network;

(ii) grouping the plurality of nodes in the multilayer network;

(iii) constructing representations of the plurality of nodes in the multilayer network;

(iv) embedding the plurality of nodes in the multilayer network; or

(v) any combination of (i), (ii), (iii) and (iv).

6. The system according to claim 1 , wherein the one or more processors further perform:

automated selection and output of data corresponding to the one or more entities.

7. The system according to claim 1 , wherein the one or more processors further perform:

automated selection and output of data corresponding to the one or more entities from the context in which the data has been generated and stored based on entity relationships or node relationships with other entities or nodes.

8. The system according to claim 1 , wherein the one or more processors further:

automatically select the data and cause the data to be locally stored within a computer, thereby enabling access to the data via the computer.

9. The system according to claim 1 , wherein the one or more processors further:

automatically select the data and transmit the data to a computer, thereby enabling access to the data by the computer.

10. The system according to claim 2 , wherein an entity can have one or more roles, and wherein each role represents a function performable, by the entity, with respect to connected entities.

11. The system according to claim 2 , wherein a probability of visiting a second node of the plurality of nodes from a first node of the plurality of nodes is equal to an entry in the supra-adjacency matrix having a column number of the supra-adjacency matrix corresponding to the first node and a row number of the supra-adjacency matrix corresponding to the second node multiplied by the salience of the entry and divided by the sum of all the entries of the sum of all the entries of the column corresponding to the first node, each entry of the column multiplied by its corresponding salience, thereby constructing a rate matrix of a random walk on the supra-adjacency matrix.

12. A system for performing random walks on knowledge graphs, comprising:

a memory; and

one or more processors to:

(A) receive a plurality of knowledge graphs, each knowledge graph;

(x) having:

(i) a plurality of entities, each entity having an entity type; and

(ii) a plurality of labeled connections representing the relationships of the plurality of entities, each labeled connection having:

 (i) a label; and

 (ii) a pair of specified entity types including a first entity type and a second entity type;

(y) connecting a plurality of pairs of entities of the specified entity types; and

(z) being weighted or unweighted;

(B) generate, for each entity type, a unique ordering of all the entities belonging to that entity type;

(C) generate, for each labeled connection;

(1) a monolayer network, wherein each entity of the specified entity types is represented by a node, and wherein a labeled connection having a distinct pair of specified entity types is a bipartite monolayer network and a labeled connection having a non-distinct pair of specified entity types is a unipartite monolayer network, thereby generating a plurality of monolayer networks;

(2) an adjacency matrix for each monolayer network having:

a number of columns:

 (i) equal to the number of entities of the first entity type; and

 (ii) each column representing an entity of the first entity type in the unique ordering of the entities; and

a number of rows:

 (i) equal to the number of entities of the second entity type; and

 (ii) each row representing an entity of the second entity type in the unique ordering of the entities,

wherein each entry of the adjacency matrix has;

 (i) a zero value if the entities represented by the column and row do not have a connection of the labeled connection; and

 (ii) a non-zero value if the entities represented by the column and row do have a connection of the labeled connection, the non-zero value corresponding to the weight of the connection if the monolayer network is weighted and one (1) if the connection of the labeled connection is an unweighted connection;

(3) one role for each of the specified entity types, wherein each role represents a function performable, by the entity, with respect to connected entities, and wherein all entities of that entity type inherit the role;

(4) an activity array for each role, the activity array having a length equal to the number of entities of each distinct specified entity type, wherein the position of the entity in the activity array corresponds to the position of the entity in the unique ordering of the entities of the entity type, and wherein the value of each entry in the activity array corresponds to a function of a degree or a weighted degree in the monolayer network associated to the role; and

(5) a coupling matrix, for every role, having a number of columns and a number of rows equal to the number of entities of the entity type, each column and row representing each entity in the same ordering as the unique ordering as in the activity array and containing in a main diagonal of the coupling matrix the activity array corresponding to the role and zeros everywhere else;

(D) generate, for a subset of the plurality of monolayer networks:

a multilayer network wherein, each layer of the multilayer network corresponds to the monolayer network of each of the labeled connections in the subset of the monolayer networks of labeled connections, and wherein nodes that represent the same entity in different layers of the multilayer network are connected to each other;

a supra-adjacency matrix of the multilayer network having:

(i) a block structure determined by the roles that appear in the subset of the plurality of monolayer networks;

(ii) an equal number of columns and row blocks; and

(iii) one block for each role, each of the blocks having a size equal to the number of entities of the entity type associated to the role,

each role in the block-columns of the supra-adjacency matrix is a source-role, and each role in the block-rows of the supra-adjacency matrix is a target-role, wherein:

(i) the adjacency matrices of the unipartite monolayer networks from the labeled connections between entities of the same entity type are placed on the block of the supra-adjacency matrix corresponding to the intersection of the block column and block row corresponding to the same role;

(ii) the adjacency matrices of the bipartite monolayer networks from the labeled connections between entities of different entity types are placed on two locations of the supra-adjacency matrix including:

 (A) one in the block column of a first role and block row of a second role; and

 (B) transposed in the block column of the second role and the block row of the first role; and

(iii) a plurality of weighted directed interlayer connections between all nodes that represent the same entity in different roles, each weighted directed interlayer connection being represented, for every ordered pair of roles that belong to the same entity type in the supra-adjacency matrix by the coupling matrix of a target role that is placed in the block column of a source role and the block row of the target role;

(E) receive a plurality of coupling saliences (non-negative, real numbers), each of the coupling saliences corresponding to a non-empty block of the supra-adjacency matrix;

(F) construct a random walk model on the multilayer network; and

(G) provide one or more media content recommendations based on the random walk model.

13. The system according to claim 12 , wherein the pair of specified entity types is the same entity types or distinct entity types.

14. The system according to claim 12 , wherein the value of each entry in the activity array corresponds to:

(i) an in-degree or out-degree;

(ii) the weighted degree; or

(iii) a combination of (i) and (ii).

15. The system according to claim 12 , wherein a weighted directed interlayer connection is provided if the entry corresponding to the target node in the activity array of its role is greater than zero.

16. The system according to claim 12 , wherein empty blocks of the supra-adjacency matrix are assigned a salience equal to zero.

17. A computer implemented method for performing random walks on knowledge graphs, comprising:

receiving a plurality of knowledge graphs,

for each knowledge graph:

constructing a multilayer network having:

unipartite layers, wherein the unipartite layers comprise connections that origination from and terminate at the same node;

bipartite layers, wherein the bipartite layers comprise connections that originate from and terminate at different nodes; and

interlayer connections that:

(i) connect nodes of the unipartite layers and the bipartite layers that represent the same entity;

(ii) are directed; and

(iii) are weighted with a weight that depends on an activity of a target node in the unipartite layer or the bipartite layer in which the target node resides;

processing a random walk model of the multilayer network that takes into account saliencies of the interlayer connections and intralayer connections of the nodes; and

providing one or more media content recommendations based on the random walk model.

18. A computer implemented method for performing random walks on knowledge graphs, comprising:

receiving a plurality of knowledge graphs, each knowledge graph having a plurality of entities and a collection of types of labeled connections representing the relationships of the plurality of entities, each labeled connection being weighted or unweighted and each entity having:

(i) an entity type; and

(ii) a set of connections with other entities in the knowledge graph;

generating, for each type of labeled connection, a monolayer network, wherein each entity of the entity types connected by the labeled connection is represented by a node, thereby generating a plurality of monolayer networks;

assembling the plurality of monolayer networks into a multilayer network, wherein each layer of the multilayer network corresponds to one of the plurality of monolayer networks, wherein two or more nodes that represent the same entity are linked by an interlayer connection;

receiving a first plurality of coupling strengths, each of the first coupling strengths corresponding to one of the labeled connections;

receiving a second plurality of coupling strengths, each second coupling strength corresponding to the connections between nodes across layers of the multilayer network that represent the same entity;

constructing a random walk model on the multilayer network, wherein a probability of visiting a first node of the plurality of nodes from a second node of the plurality of nodes is proportional to:

(i) the weight of the labeled connection between the first node and the second node divided by the sum of all the weights of the connections that originate from the second node and multiplied by the first coupling strength of the corresponding labeled connection; or

(ii) the second coupling strength of the connection between the nodes across layers of the multilayer network that represent the same entity; and

providing one or more media content recommendations based on the random walk model.

19. The computer implemented method according to claim 18 , wherein an entity can have one or more roles, and wherein each role represents a function performable, by the entity, with respect to connected entities.

20. A computer implemented method for performing random walks on knowledge graphs, comprising:

(A) receiving a plurality of knowledge graphs, each knowledge graph;

(x) having:

(i) a plurality of entities, each entity having an entity type; and

(ii) a plurality of labeled connections representing the relationships of the plurality of entities, each labeled connection having:

(i) a label; and

(ii) a pair of specified entity types including a first entity type and a second entity type;

(y) connecting a plurality of pairs of entities of the specified entity types; and

(z) being weighted or unweighted;

(B) generating, for each entity type, a unique ordering of all the entities belonging to that entity type;

(C) generating, for each labeled connection;

(1) a monolayer network, wherein each entity of the specified entity types is represented by a node, and wherein a labeled connection having a distinct pair of specified entity types is a bipartite monolayer network and a labeled connection having a non-distinct pair of specified entity types is a unipartite monolayer network, thereby generating a plurality of monolayer networks;

(2) an adjacency matrix for each monolayer network having:

a number of columns:

(i) equal to the number of entities of the first entity type; and

(ii) each column representing an entity of the first entity type in the unique ordering of the entities; and

a number of rows:

(i) equal to the number of entities of the second entity type; and

(ii) each row representing an entity of the second entity type in the unique ordering of the entities,

wherein each entry of the adjacency matrix has;

(i) a zero value if the entities represented by the column and row do not have a connection of the labeled connection; and

(ii) a non-zero value if the entities represented by the column and row do have a connection of the labeled connection, the non-zero value corresponding to the weight of the connection if the monolayer network is weighted and one (1) if the connection of the labeled connection is an unweighted connection;

(3) one role for each of the specified entity types, wherein each role represents a function performable, by the entity, with respect to connected entities, and wherein all entities of that entity type inherit the role;

(4) an activity array for each role, the activity array having a length equal to the number of entities of each distinct specified entity type, wherein the position of the entity in the activity array corresponds to the position of the entity in the unique ordering of the entities of the entity type, and wherein the value of each entry in the activity array corresponds to a function of a degree or a weighted degree in the monolayer network associated to the role; and

(5) a coupling matrix, for every role, having a number of columns and a number of rows equal to the number of entities of the entity type, each column and row representing each entity in the same ordering as the unique ordering as in the activity array and containing in a main diagonal of the coupling matrix the activity array corresponding to the role and zeros everywhere else;

(D) generate, for a subset of the plurality of monolayer networks:

a multilayer network wherein, each layer of the multilayer network corresponds to the monolayer network of each of the labeled connections in the subset of the monolayer networks of labeled connections, wherein nodes that represent the same entity in different layers of the multilayer network are connected to each other;

a supra-adjacency matrix of the multilayer network having;

(i) a block structure determined by the roles that appear in the subset of the plurality of monolayer networks;

(ii) an equal number of columns and row blocks; and

(iii) one block for each role, each of the blocks having a size equal to the number of entities of the entity type associated to the role,

each role in the block-columns of the supra-adjacency matrix is a source-role, and each role in the block-rows of the supra-adjacency matrix is a target-role, wherein:

(i) the adjacency matrices of the unipartite monolayer networks from the labeled connections between entities of the same entity type are placed on the block of the supra-adjacency matrix corresponding to the intersection of the block column and block row corresponding to the same role;

(ii) the adjacency matrices of the bipartite monolayer networks from the labeled connections between entities of different entity types are placed on two locations of the supra-adjacency matrix including:

(A) one in the block column of a first role and block row of a second role; and

(B) transposed in the block column of the second role and the block row of the first role; and

(iii) a plurality of weighted directed interlayer connections between all nodes that represent the same entity in different roles, each weighted directed interlayer connection being represented, for every ordered pair of roles that belong to the same entity type in the supra-adjacency matrix by the coupling matrix of a target role that is placed in the block column of a source role and the block row of the target role;

(E) receiving a plurality of coupling saliences (non-negative, real numbers), each of the coupling saliences corresponding to a non-empty block of the supra-adjacency matrix;

(F) constructing a random walk model on the multilayer network; and

(G) providing one or more media content recommendations based on the random walk model.

Assignments (1)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Sep 13, 2021
From: BEGUERISSE-DÍAZ, MARIANO; HOFFMANN, TILL ALEXIS; KORKINOF, DIMITRIOS
To: SPOTIFY AB
Reel/Frame 057461/0896 →
Continuity (2)
Provisional Application 63031857 · May 29, 2020
Related Publication 20210374555A1 · Dec 2, 2021
References Cited (74)
US 8433670B2 · Chidlovskii · 2013 [cited by examiner]
US 10349134B2 · Hamiti et al. · 2019 [cited by applicant]
US 10546507B2 · Popat et al. · 2020 [cited by applicant]
US 20160086498A1 · Popat et al. · 2016 [cited by applicant]
US 20180332347A1 · Hamiti et al. · 2018 [cited by applicant]
US 20190392330A1 · Martineau et al. · 2019 [cited by applicant]
WO 2020065906 · 2020 [cited by applicant]
Ning, Nianwen, Bin Wu, and Chengcheng Peng. “Representation learning based on influence of node for multiplex network.” In 2018 IEEE Third International Conference on Data Science in Cyberspace (DSC), pp. 865-872. IEEE,… [cited by examiner]
Ai, Qingyao, et al., “Learning Heterogeneous Knowledge Base Embeddings for Explainable Recommendation”, Algorithms, vol. 11, No. 137 (2018), 16 pages. [cited by applicant]
Amburg, Ilya, et al., “Clustering in graphs and hypergraphs with categorical edge labels”, arXiv:1910.09943v2 [cs.SI] Feb. 17, 2020, 13 pages. [cited by applicant]
Beguerisse-Diaz, M., et al., “Competition for popularity in bipartite networks”, Chaos, 20 (2010), p. 043101, https://doi.org/10.1063/1.3475411, 12 pages. [cited by applicant]
Bell, R.M., et al., “Modeling Relationships at Multiple Scales to Improve Accuracy of Large Recommender Systems”, KDD'07, San Jose, CA, USA, Aug. 12-15, 2007, San Jose, CA, 10 pages. [cited by applicant]
Bellomarini, L., et al., “The Vadalog System: Datalog-based Reasoning for Knowledge Graphs”, Proc. VLDB Endow., vol. 11, No. 9 (2018), pp. 975-987, https://doi.org/10.14778/3213880.3213888. [cited by applicant]
Bergstra, J. et al., “Random Search for Hyper-Parameter Optimization”, Journal of Machine Learning Research, 13 (2012), pp. 281-305. [cited by applicant]
Carass, A., et al. , “Evaluating White Matter Lesion Segmentations with Refined Sorensen-Dice Analysis”, Scientific Reports, 10 (2020), pp. 1-19. [cited by applicant]
Chang, Yan-Shuo, et al., “Refined Spectral Clustering via Embedded Label Propagation”, Neural Computation, 29 (2017), pp. 3381-3396, https://doi.org/10.1162/neco a 01022. [cited by applicant]
Chaudhari, S., et al., “An Entity Graph Based Recommender System”, AI Communications, 30 (2017), pp. 141-149. [cited by applicant]
Chen, X., et al., “A review: Knowledge reasoning over knowledge graph”, Expert Systems with Applications, 141 (2020), p. 112948, https://doi.org/10.1016/j.eswa.2019.12948, 21 pages. [cited by applicant]
Covington, P., et al., “Deep Neural Networks for YouTube Recommendations”, in Rec. Sys., Sep. 15-19, 2016, Boston, MA, USA, https://doi.org/10.1145/2959100.2959190, pp. 191-198. [cited by applicant]
Cramer, H., et al., “Assessing and Addressing Algorithmic Bias in Practice”, Interactions, 25 (Nov./Dec. 2018), pp. 58-63. [cited by applicant]
De Domenico, M. et al., “Navigability of interconnected networks under random failures”, PNAS, Jun. 10, 2014, vol. 111, No. 23, pp. 8351-8356, https://doi.org/10.1073/pnas.1318469111. [cited by applicant]
Del Corso, G., et al., “Fast PageRank Computation via a Sparse Linear System”, Internet Mathematics, vol. 2, No. 3 (2005), pp. 251-273. [cited by applicant]
Desrosiers, C., et al., “A Comprehensive Survey of Neighborhood-based Recommendation Methods”, Chapter 4, Recommender Systems Handbook, Eds. F. Ricci et al., DOI 10.1007/978-0-387-85820-3_4, Springer Science and Busines… [cited by applicant]
Dong, X. L., “Challenges and Innovations in Building a Product Knowledge Graph,” in KDD, Aug. 19-23, 2018, London, UK, p. 2869. [cited by applicant]
Dong, X.L., et al., “Knowledge Vault: A Web-Scale Approach to Probabilistic Knowledge Fusion”, in KDD, 2014, 10 pages. [cited by applicant]
Dong, Y. et al., “Metapath2vec: Scalable Representation Learning for Heterogeneous Networks”, in KDD, Aug. 13-17, 2017, Halifax, NS, Canada, pp. 135-144, https://doi.org/10.1145/3097983. 3098036. [cited by applicant]
Ebert, R., “Amores perros”, Apr. 13, 2001, https://www.rogerebert.com/reviews/amores-perros-2001, 16 pages. [cited by applicant]
Ehrlinger, Lisa et al., “Towards a Definition of Knowledge Graphs”, Semantics (Posters, Demos, SUCCESS), 48, Sep. 13-14, 2016, 4 pages. [cited by applicant]
Eksombatchai, C., et al., “Pixie: A System for Recommending 3+ Billion Items to 200+ Million Users in Real-Time”, in WWW, 2018, pp. 1775-1784. [cited by applicant]
Gilotte, A., et al., “Offline A/B testing for Recommender Systems”, in WSDM, 5-9 Feb. 5-9, 2018, Marina Del Rey, CA, USA, pp. 198-206. [cited by applicant]
Gleich, David, “PageRank Beyond the Web”, SIAM Review, vol. 57, No. 3 (2015), pp. 321-363. [cited by applicant]
Gope, J., et al., “A Survey on Solving Cold Start Problem in Recommender Systems”, in Int. Conf. on Computing, Communication & Automation (ICAA), 2017, 6 pages. [cited by applicant]
Gruson, A., et al., “Offline Evaluation to Make Decisions About Playlist Recommendation Algorithms”, Session 7: E-Commerce and Recommendation, in WSDM, Feb. 11-15, 2019, Melbourne, Aus., pp. 420-428. [cited by applicant]
Guo, L., et al., “Learning to Exploit Long-term Relational Dependencies in Knowledge Graphs”, Proceedings of the 36th International Conference on Machine Learning, Long Beach, CA, PMLR 97, 2019, 13 pages. [cited by applicant]
Harper, F., et al., “The Movielens Datasets: History and Context”, ACM Transactions on Interactive Intelligent Systems (tiis), vol. 5, No. 4, (2015), 20 pages. [cited by applicant]
Higham D., et al., “The Sleekest Link Algorithm”, Mathematics Today, vol. 39, Dec. 2003, pp. 192-197. [cited by applicant]
Hug, N., “Surprise, a Python library for recommender systems”, 2020 Jour. Open Source Software (JOSS), 5(52), 3 pages. [cited by applicant]
Jaderberg, M., et al,. “Population based training of neural networks”, arXiv preprint arXiv:1711.09846, 2017, 21 pages. [cited by applicant]
Kivelä, M., et al., “ Multilayer networks.” Journal of Complex Networks (2014) 2, 203-271. [cited by applicant]
Lambiotte, R. et al., “From networks to optimal higher-order models of complex systems”, Nature Physics, 15(4) (2019), pp. 313-320. [cited by applicant]
Lu,, L., et al., Recommender Systems, Physics Reports, 519 (2012), pp. 1-49, https://doi.org/https://doi.org/10.1016/j.physrep.2012.02.006. [cited by applicant]
Martin, T., et al., “Localization and centrality in networks”, 2014 Phys. Rev. E, 90.052808, https://doi.org/10.1103/PhysRevE.90.052808, 8 pages. [cited by applicant]
Masuda, N., et al., “Random walks and diffusions on networks.” Physics Reports 716-717 (2017) 1-58. [cited by applicant]
McInerney, J., et al., “Explore, Exploit, and Explain: Personalizing Explainable Recommendations with Bandits”, in Rec. Sys., Oct. 2-7, 2018, Vancouver, BC, Canada, pp. 31-39. [cited by applicant]
Monti, F., et al., “Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks”, in NIPS, Proceedings of the 34th International Conference on Machine Learning, 2017, Long Beach, CA, pp. 3697-3707. [cited by applicant]
Mu, R., et al., “Collaborative Filtering Recommendation Algorithm Based on Knowledge Graph”, Hindawi, Mathematical Problems in Engineering, vol. 2018, Article ID 9617410, https://doi.org/10.1155/2018/9617410, 15 pages (… [cited by applicant]
Newman, M.E.J., “The Structure and Function of Complex Networks.” SIAM Review, vol. 45, No. 2, 2003, pp. 167-256. [cited by applicant]
Nikolakopoulos, A., et al., “Personalized Diffusions for Top-N Recommendation”, In Proceedings of the 13th ACM Conference on Recommender Systems, Rec Sys '19, Sep. 16-19, 2019, 9 pages. [cited by applicant]
Page, L., et al., “The PageRank Citation Ranking: Bringing Order to the Web”, in WWW, Jan. 29, 1998, 17 pages. [cited by applicant]
Rosvall, M., et al., “Memory in network flows and its effects on spreading dynamics and community detection”, Nature Communications, 5(1) (2014), pp. 1-13. [cited by applicant]
Salha, G., et al., “Keep It Simple: Graph Autoencoders Without Graph Convolutional Networks”, 33rd Conference on Neural Information Processing Systems, arXiv:1910.00942, (2019), https:/arxiv.org/abs/1910. 00942, 18 page… [cited by applicant]
Seneta, E., “Non-negative Matrices and Markov Chains”, Springer Series in Statistics, Springer-Verlag, New York, 1981, ISBN 038790598-37, 22 pages. [cited by applicant]
Shi, Yue, et al., “Collaborative Filtering beyond the User-Item Matrix: A Survey of the State of the Art and Future Challenges”, ACM Comput. Surv., vol. 47, No. 1, Article 3, Apr. 2014, https://doi.org/10.1145/2556270, … [cited by applicant]
Sun, Zhu, et al., “Recurrent Knowledge Graph Embedding for Effective Recommendation”, In Proceedings of the 12th ACM Conference on Recommender Systems, RecSys '18, Vancouver, BC, Canada, Oct. 2-7, 2018, pp. 297-305. URL… [cited by applicant]
Szomszor, M., et al., “Folksonomies, the Semantic Web, and Movie Recommendation”, in 4th European Semantic Web Conf., Jun. 7, 2007, 15 pages. [cited by applicant]
Takács, G., et al., “Matrix factorization and neighbor based algorithms for the Netflix prize problem”, In Proceedings of the 2008 ACM Conference on Recommended Systems, RecSys '08, pp. 267-274, New York, NY, USA, 2008,… [cited by applicant]
Taylor, Dane, “Multiplex Markov Chains: Convection Cycles and Optimality”, arXiv, 2004. 12820 (2020), https://arxiv.org/abs/2004, 2820, 12 pages. [cited by applicant]
The Movie Database (TMDb), 2008, https://www.themoviedb.org/ (accessed Jun. 1, 2021), 33 pages. [cited by applicant]
Toni, T., et al., “Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems.” Journal of the Royal Society Interface, 6(31):187-202, 2009. [cited by applicant]
Vig, J., et al., “The Tag Genome: Encoding Community Knowledge to Support Novel Interaction”, ACM Trans. Interact. Intell. Syst., vol. 2, No. 3, Article 13, Sep. 2012, https://doi.org/10.1145/2362394.2362395, 45 pages. [cited by applicant]
Wang, Z., et al., “Graph-based Recommendation on Social Networks”, in 2010 12th Int. Asia-Pacifc Web Conf., 2010 IEEE, pp. 116-122, https://doi.org/10.1109/APWeb.2010.60. [cited by applicant]
Xian, Y., et al., “Reinforcement Knowledge Graph Reasoning for Explainable Recommendation”, in SIGIR, Jul. 21-25, 2019, Paris, France, 10 pages. [cited by applicant]
Yang, S., et al., “Fast Top-K Search in Knowledge Graphs”, in 32nd Int. Conf. on Data Engineering (ICDE), 2016, pp. 990-1001. [cited by applicant]
Ying, Rex, et al., “Graph Convolutional Neural Networks for Web-Scale Recommender Systems”, in KDD, Aug. 19-23, 2018, 10 pages. [cited by applicant]
Yu, Xiao, et al., “Personalized Entity Recommendation: A Heterogeneous Information Network Approach”, In Proceedings of the 7th ACM International Conference on Web Search and Data Mining, WSDM 2014, pp. 283-292, https:/… [cited by applicant]
Zheng, G., et al., “DRN: A Deep Reinforcement Learning Framework for News Recommendation”, in WWW, Apr. 23-27, 2018, pp. 167-176, https://doi.org/10.1145/3178876.3185994. [cited by applicant]
Dewancker, Ian, et al., “Bayesian optimization primer”, 2015, SIGOPT Research, 4 pages. [cited by applicant]
Diestel, R., “Graph Theory”, (Graduate Texts in Mathematics), Springer, 2017 ISBN 978-3-662-53621-6, 448 pages. [cited by applicant]
Hogan, A., et al., “Knowledge Graphs”, arXiv:2003.02320, (2021), https://arxiv.org/abs/2003.02320, 136 pages. [cited by applicant]
Manning, C. D., et al., “An Introduction to Information Retrieval”, CUP, 2009 Online Edition, Cambridge, 569 pages. [cited by applicant]
Poursabzi-Sangdeh, F., et al., “Manipulating and Measuring Model Interpretability”, CHI, May 8-13, 2021, Yokohama, JP, arXiv, 1802.07810, 67 pages. [cited by applicant]
Ricci, F., et al., “Recommender Systems Handbook”, Springer, 2010. ISBN 0387858199, 9780387858197, 845 pages. [cited by applicant]
Rossi, A., et al., “Knowledge Graph Embedding for Link Prediction: A Comparative Analysis”, arXiv, 2002.00819 (2020), 41 pages. [cited by applicant]
Siroker D., et al., “A/B Testing: The Most Powerful Way to Turn Clicks Into Customers”, Wiley, 2013, 21 pages. [cited by applicant]
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