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Fig. 2. (a) The bipartite network G=(U,V,E), as well as its U-projection unimodal network (b) and V-projection unimodal network (c). In this figure, the circular nodes at the top represent authors and the square nodes at the bottom represent the topics. The edge weight in (b) and (c) is set as according to Definition-3. When bipartite networks are converted to unimodal networks, some information hidden in the topological structure of the network may lose their importance. To prevent this situation, weighted bipartite networks are used. Weighted networks are common in many areas, however, they are particularly important when representing the topological properties of the network in bipartite networks such as author-article relations, patient-disease, and actor-movie. In ¢ unimodal author-author network extracted from the bipartite network containing the authors and their publications, an edge weight represents the number of publications two authors have made collaboratively in the bipartite network. Weighted unimodal network projection is a technique used for obtaining a unimodal network from a two dimensional network; where the edge weight represents the number of common neighbors of the corners, and the network obtainec by using a weighted unimodal projection is called the weighted projection network. Mathematically it can be defined as follows: Ey = {(ui, u;)| Uj, Uj E U, Av; E V, VLE P(u;) fa) T(u,)}, Es = {(v;,v;)| Vj, V0; E V, Au; E U, Uj; E rv) N T(v;)}.

Figure 2 (a) The bipartite network G=(U,V,E), as well as its U-projection unimodal network (b) and V-projection unimodal network (c). In this figure, the circular nodes at the top represent authors and the square nodes at the bottom represent the topics. The edge weight in (b) and (c) is set as according to Definition-3. When bipartite networks are converted to unimodal networks, some information hidden in the topological structure of the network may lose their importance. To prevent this situation, weighted bipartite networks are used. Weighted networks are common in many areas, however, they are particularly important when representing the topological properties of the network in bipartite networks such as author-article relations, patient-disease, and actor-movie. In ¢ unimodal author-author network extracted from the bipartite network containing the authors and their publications, an edge weight represents the number of publications two authors have made collaboratively in the bipartite network. Weighted unimodal network projection is a technique used for obtaining a unimodal network from a two dimensional network; where the edge weight represents the number of common neighbors of the corners, and the network obtainec by using a weighted unimodal projection is called the weighted projection network. Mathematically it can be defined as follows: Ey = {(ui, u;)| Uj, Uj E U, Av; E V, VLE P(u;) fa) T(u,)}, Es = {(v;,v;)| Vj, V0; E V, Au; E U, Uj; E rv) N T(v;)}.

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Fig. 1. Prediction of links at time ¢+/ in bipartite network for an author-topic bipartite network at time f¢. In this figure, the circular nodes at the top represent authors and the square nodes at the bottom represent the topics, and the solid and dashed lines respectively represent already existent links and the prediction links between authors and topics. Fig. 1 shows prediction of links in an author-topic bipartite network. The solid and dashed line respectively denotes the fact that the author already studied the topic tag and the prediction that the author will study the topic tag. The main task of link prediction is to predict the possible links (dashed lines) in the author-topic network at time t+J/ according to the link information (solid lines) observed at time f.
Fig. 1. Prediction of links at time ¢+/ in bipartite network for an author-topic bipartite network at time f¢. In this figure, the circular nodes at the top represent authors and the square nodes at the bottom represent the topics, and the solid and dashed lines respectively represent already existent links and the prediction links between authors and topics. Fig. 1 shows prediction of links in an author-topic bipartite network. The solid and dashed line respectively denotes the fact that the author already studied the topic tag and the prediction that the author will study the topic tag. The main task of link prediction is to predict the possible links (dashed lines) in the author-topic network at time t+J/ according to the link information (solid lines) observed at time f.
Definition 4. (Strengthening of Bipartite Projection (SBP%)): From each of the U and V node par s forming G =(U,V,E) bipartite network, two unimodal networks, which are U-projection network G,, = (U, E, projection G, = (U,E,) are obtained. (A,B) € E,W: (A,B) > |T(A) NT(B)I. If W(A, B)>a, while the (A, B) is kept in the strengthening network SBP®, the edges whose W(A,B) < a weights are below the value are removed from the strengthening network (a: is the predetermined threshold value). This network which is the backbone of the unimodal network, in which strong node pairs are preserved pairs are removed, is obtained. For this case, more concrete analyzes can be made by using a weigh ie exnlained in Fio 2 he give and V edge o hreshol way, a strengthene and the weak nod function. This cas Fig. 3. (a) SBP tno Of the author-author projected network which is given in Fig. 2(a) for a@ = 1. (b) SBP ionic of the topic-topic projected network which is given in Fig. 2(c) for a =1. SBP no, and SBP ic strengthened network was constructed according to Definition 4.
Definition 4. (Strengthening of Bipartite Projection (SBP%)): From each of the U and V node par s forming G =(U,V,E) bipartite network, two unimodal networks, which are U-projection network G,, = (U, E, projection G, = (U,E,) are obtained. (A,B) € E,W: (A,B) > |T(A) NT(B)I. If W(A, B)>a, while the (A, B) is kept in the strengthening network SBP®, the edges whose W(A,B) < a weights are below the value are removed from the strengthening network (a: is the predetermined threshold value). This network which is the backbone of the unimodal network, in which strong node pairs are preserved pairs are removed, is obtained. For this case, more concrete analyzes can be made by using a weigh ie exnlained in Fio 2 he give and V edge o hreshol way, a strengthene and the weak nod function. This cas Fig. 3. (a) SBP tno Of the author-author projected network which is given in Fig. 2(a) for a@ = 1. (b) SBP ionic of the topic-topic projected network which is given in Fig. 2(c) for a =1. SBP no, and SBP ic strengthened network was constructed according to Definition 4.
The number of patterns covered by a PL, is directly related to the proximity of the edge nodes constituting it to each other in a bipartite network. The greater the number of patterns covered by the PL, the higher the probability of PL to occur in the future. Therefore, the number of patterns covered by PL can be used to measure the prediction probability of the notential link. Fig. 6. (a) The bipartite author-topic network, (b) The bipartite author-topic training network, (c) The bipartite author-topic test network. For example, in the bipartite network given in Fig. 6(a), the circular nodes at the top represent authors and the quare nodes at the bottom represent the topic tags the authors studied. T2,74 are the common study topics for the B ind E authors, (E,T1) and (£,7T3) are the potential links belonging to the PL set meeting the Definition-5 condition
The number of patterns covered by a PL, is directly related to the proximity of the edge nodes constituting it to each other in a bipartite network. The greater the number of patterns covered by the PL, the higher the probability of PL to occur in the future. Therefore, the number of patterns covered by PL can be used to measure the prediction probability of the notential link. Fig. 6. (a) The bipartite author-topic network, (b) The bipartite author-topic training network, (c) The bipartite author-topic test network. For example, in the bipartite network given in Fig. 6(a), the circular nodes at the top represent authors and the quare nodes at the bottom represent the topic tags the authors studied. T2,74 are the common study topics for the B ind E authors, (E,T1) and (£,7T3) are the potential links belonging to the PL set meeting the Definition-5 condition
The covered patterns by a potential link (PL) are the edges in the projection network. The A and B edges havin; common neighbor nodes in the G bipartite network are represented by the (A, B) edge in the G,, projection network Some topological information is lost when bipartite networks are converted to unimodal networks. Although th bipartite network given in Fig. 7(a) and Fig. 7(c) are different from each other, their projection networks are the sam as can be seen in Fig. 7(b) and Fig. 7(d). In such cases, there will be a serious topological information loss in th structure of the bipartite network, in order to deal with this problem, a weighted bipartite network is created to protec the network information. Since the number of common neighbors of the A and B nodes in Fig. 7(a) is lesser than th number of neighbors in Fig. 7(b). it is graded smaller. Fig. 7. Two different bipartite networks and theirs weighted projection networks. (b) The projection network of bipartite network which is given in (a). (d) The projection network of bipartite network which is given in (c).
The covered patterns by a potential link (PL) are the edges in the projection network. The A and B edges havin; common neighbor nodes in the G bipartite network are represented by the (A, B) edge in the G,, projection network Some topological information is lost when bipartite networks are converted to unimodal networks. Although th bipartite network given in Fig. 7(a) and Fig. 7(c) are different from each other, their projection networks are the sam as can be seen in Fig. 7(b) and Fig. 7(d). In such cases, there will be a serious topological information loss in th structure of the bipartite network, in order to deal with this problem, a weighted bipartite network is created to protec the network information. Since the number of common neighbors of the A and B nodes in Fig. 7(a) is lesser than th number of neighbors in Fig. 7(b). it is graded smaller. Fig. 7. Two different bipartite networks and theirs weighted projection networks. (b) The projection network of bipartite network which is given in (a). (d) The projection network of bipartite network which is given in (c).
Table 1: Classical neighborhood-based link prediction algorithms As can be understood from Equation 2, the smaller the degrees of the common neighbors of the A and B nodes, the greater the pattern weight. The probability of formation of each pattern element covered by a PL is equivalent to the total weight of the patterns it covers. The final score of the (A, p;) potential link that is predicted to be formed in the Gtrain = (U,V, E¢rqin) training network is as follows: In Table 1, some of the frequently used neighborhood-based link prediction algorithms are formulated, such as the degree of the node k,, A in the bipartite network (node degree=number of neighbors) and the neighbors of the (A), A node in the bipartite network.
Table 1: Classical neighborhood-based link prediction algorithms As can be understood from Equation 2, the smaller the degrees of the common neighbors of the A and B nodes, the greater the pattern weight. The probability of formation of each pattern element covered by a PL is equivalent to the total weight of the patterns it covers. The final score of the (A, p;) potential link that is predicted to be formed in the Gtrain = (U,V, E¢rqin) training network is as follows: In Table 1, some of the frequently used neighborhood-based link prediction algorithms are formulated, such as the degree of the node k,, A in the bipartite network (node degree=number of neighbors) and the neighbors of the (A), A node in the bipartite network.
The degrees of A and B nodes have a negative effect on the {A, B} pattern weight. For example, the degrees of the 4 and B nodes in Fig. 8(a) are respectively 2 and 1. In Fig. 8(b), the degrees of the A and B nodes are respectively 2 and 3. In Fig. 8(a), while the A author studied the T1 and T2 topics, the B authors only studied the T2 topic. However, in Fig. 8(b), they have carried out many different studies, and their only common study field is T2. Therefore, the study fields of the academicians in Fig. 8(b), are less similar than that of the authors in Fig. 8(a), thus, the {A, B} weight should be higher in Fig. 8(a).
The degrees of A and B nodes have a negative effect on the {A, B} pattern weight. For example, the degrees of the 4 and B nodes in Fig. 8(a) are respectively 2 and 1. In Fig. 8(b), the degrees of the A and B nodes are respectively 2 and 3. In Fig. 8(a), while the A author studied the T1 and T2 topics, the B authors only studied the T2 topic. However, in Fig. 8(b), they have carried out many different studies, and their only common study field is T2. Therefore, the study fields of the academicians in Fig. 8(b), are less similar than that of the authors in Fig. 8(a), thus, the {A, B} weight should be higher in Fig. 8(a).
Fig. 9. A section of the author-topic bipartite network. In this figure, the circular nodes which is colored in red at the top represent authors and the square nodes which is colored in blue at the bottom represent the topics. "author names, article title, keywords, abstract and reference list" are saved to our database. The collected information was only used in the academic study without any commercial purpose. The collected data is raw data. Since the network we will create from the raw data will have useless information, it was first examined with data processing techniques. For example, only the authors with one publication were filtered in the 2000-2016 time period. The standardization method mentioned in subsection 4.1 is applied for the topic titles. A bipartite network of author-topic title is created from the obtained database. In 2000-2016 G = (U,V,E) bipartite network, in 2000-2011 Gi-gin = (U,V, Etrain) and 2012-2016 Gres¢ = (U,V, Exest) bipartite networks are created. The G bipartite network consists of 67.677 authors and 122.852 topic nodes, and 1.260.559 links that these nodes create.
Fig. 9. A section of the author-topic bipartite network. In this figure, the circular nodes which is colored in red at the top represent authors and the square nodes which is colored in blue at the bottom represent the topics. "author names, article title, keywords, abstract and reference list" are saved to our database. The collected information was only used in the academic study without any commercial purpose. The collected data is raw data. Since the network we will create from the raw data will have useless information, it was first examined with data processing techniques. For example, only the authors with one publication were filtered in the 2000-2016 time period. The standardization method mentioned in subsection 4.1 is applied for the topic titles. A bipartite network of author-topic title is created from the obtained database. In 2000-2016 G = (U,V,E) bipartite network, in 2000-2011 Gi-gin = (U,V, Etrain) and 2012-2016 Gres¢ = (U,V, Exest) bipartite networks are created. The G bipartite network consists of 67.677 authors and 122.852 topic nodes, and 1.260.559 links that these nodes create.
Fig. 11. The comparison of the precision values at different thresholds of the algorithms
Fig. 11. The comparison of the precision values at different thresholds of the algorithms
Fig. 12. The comparison of the Precision-recall curves at different thresholds of the algorithms.
Fig. 12. The comparison of the Precision-recall curves at different thresholds of the algorithms.
In Fig. 10 and Fig. 11, the best prediction quality for each algorithm is obtained from the first version link prediction set (PL) obtained by the a = 8 threshold value of the proposed method. As can be seen in Fig. 10 and Fig. 11, the prediction quality of the algorithms decreases as the hreshold value increases. However, the potential link set grows as the threshold value becomes smaller as indicated in Table 2, and parallel to this, the run time and prediction quality of the algorithm increases. As the threshold value academic backgrounds are most similar to each other are ana increases, the relationships between the authors whose yzed by our method, and the topic suggestions are made. However, as can be seen in the above figures, this situation will actually have a negative effect, and then cause information loss. In Fig. 10, the AUC prediction quality in al value increases. It is clearly indicated by this tendency that algorithms tends to slightly decrease when the threshold here is hidden information in the network topology that can be used for prediction purposes. As the threshold value increases, the training set decreases, this results in a reduction in the number of node pairs with common neigh| bors, and thus, cause the difficulty of link prediction to increase. For this reason, links with high probability that do not exist in the network due to information loss cannot be predicted. This causes a decrease in the performance. The problem of choosing an appropriate threshold value is a major problem. As expressed in the study in [34], the most frequently observed edge weight is in the projection network. In our database this value is found as 10. The first results a = 10 were calculated according to the threshold value. It can be observed that, later, as the threshold value is exceeded, the prediction quality drops, however, the PL set decreases and run time increases, the prediction quality increases if it falls below the threshold value, however, the PL set grows and run time increases. As can be seen in Fig. the proposed algorithm in the a = 8 value, link prediction 10(a) and Fig. 11(a), according to the quality criterion of quality value is 0.98, according to the Precision quality criterion it is 1. Since the prediction quality has high values in the a = 8 threshold value, the method could not be tested for thresholds with lower values. Tha nasality Al the -avaAiatian palaalatad hy Dreanicotan. ranall aia axralivahaw matrin. an tha anatandial Lal eat Table 2: The number of potential link set created by our method according to threshold values
In Fig. 10 and Fig. 11, the best prediction quality for each algorithm is obtained from the first version link prediction set (PL) obtained by the a = 8 threshold value of the proposed method. As can be seen in Fig. 10 and Fig. 11, the prediction quality of the algorithms decreases as the hreshold value increases. However, the potential link set grows as the threshold value becomes smaller as indicated in Table 2, and parallel to this, the run time and prediction quality of the algorithm increases. As the threshold value academic backgrounds are most similar to each other are ana increases, the relationships between the authors whose yzed by our method, and the topic suggestions are made. However, as can be seen in the above figures, this situation will actually have a negative effect, and then cause information loss. In Fig. 10, the AUC prediction quality in al value increases. It is clearly indicated by this tendency that algorithms tends to slightly decrease when the threshold here is hidden information in the network topology that can be used for prediction purposes. As the threshold value increases, the training set decreases, this results in a reduction in the number of node pairs with common neigh| bors, and thus, cause the difficulty of link prediction to increase. For this reason, links with high probability that do not exist in the network due to information loss cannot be predicted. This causes a decrease in the performance. The problem of choosing an appropriate threshold value is a major problem. As expressed in the study in [34], the most frequently observed edge weight is in the projection network. In our database this value is found as 10. The first results a = 10 were calculated according to the threshold value. It can be observed that, later, as the threshold value is exceeded, the prediction quality drops, however, the PL set decreases and run time increases, the prediction quality increases if it falls below the threshold value, however, the PL set grows and run time increases. As can be seen in Fig. the proposed algorithm in the a = 8 value, link prediction 10(a) and Fig. 11(a), according to the quality criterion of quality value is 0.98, according to the Precision quality criterion it is 1. Since the prediction quality has high values in the a = 8 threshold value, the method could not be tested for thresholds with lower values. Tha nasality Al the -avaAiatian palaalatad hy Dreanicotan. ranall aia axralivahaw matrin. an tha anatandial Lal eat Table 2: The number of potential link set created by our method according to threshold values
it is possible to obtain fast and high-quality link prediction results from a large-scale bipartite Experimental results show that, through the proposed method, it is possible to obtain fast and high- quality link prediction results from a large-scale network created with real-world data.
it is possible to obtain fast and high-quality link prediction results from a large-scale bipartite Experimental results show that, through the proposed method, it is possible to obtain fast and high- quality link prediction results from a large-scale network created with real-world data.
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