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- 1. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference Modeling Relationship Strength in Online Social Networks Rongjing Xiang, Jennifer Neville, Monica Rogati Presented by Minsu Ko ryan0802@owl-nest.com http://owl-nest.com/lab/ WWW ’10 Proceedings of the 19th international conference on World wide web 2011. 6. 6. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 2. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference0.1 Index 1. Introduction 2. Latent Variable Model 2.1. Model speciﬁcation 2.2. Inference 3. Experiments 3.1 LinkedIn Data 3.1.1 Dataset 3.1.2 Evaluation 3.2 Facebook Data 3.2.1 Dataset 3.2.2 Evaluation 4. Related Work 5. Conclusion and Future work OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 3. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (1) Previous Work and Research Tendency Previous works (McPherson 2001, Liben-Nowell 2003, Neville 2005, Taskar 2003) analyzing social networks have mainly focused on binary friendship relations (e.g., friends or not). Network connectivity and attribute similarity can improve link prediction models. Relational ties can improve behavior prediction in tasks such as fraud detection and viral marketing. Relational patterns of homophily can improve predictive models of both link structure and behaviour. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 4. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference Homophily / Transitivity Homophily : The tendency for relationships to form between people of similar characteristics. Transitivity : The tendency for relationships to form if there is a common friend to act as a “bridge” between two people. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 5. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (2) Starting Point, The low cost of link formation can lead to networks with heterogeneous relationship strengths. (e.g., acquaintances and best friends mixed together) Binary indicators provide only a coarse representation of relationship information. Treating all relationships as equal will increase the level of noise in the learned models and likely lead to degradation in performance. → Prune away spurious relationships and highlight stronger relationships. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 6. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (3) GOAL : to propose a model to infer relationship strength Based on proﬁle similarity and interaction activity with the goal of automatically distinguishing strong relationships from weak ones. Focused on developing a richer model that can represent the full spectrum of relationship strength. A development of an unsupervised model to estimate relationship strength from interaction activity (e.g., communication, tagging) and user similarity. More speciﬁcally, → A Link-based Latent Variable Model OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 7. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (4) Fortunately, Online Social Networks (OSNs) consist of more than just a record of social network ties. The system can be used to identify which linked members are close friends/colleagues, as opposed to acquaintances. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 8. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (5) For instance, 1 LinkedIn users can request write recommendations for other users in the system. → Users will only write recommendations for those with whom they are most familiar. 2 Facebook users have a Wall page as part of their proﬁle, where friends can post messages. → Users communicate more frequently with friends due to resource constraints. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 9. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 10. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 11. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (6) From the modeling perspective, the characteristic of this model is that, It distinguishes interaction acitivity from users’ proﬁle data to improve model accuracy. Integrate these two types of information to be the hidden eﬀect of user proﬁle similarities, as well as the hidden cause of the interactions between users. Focus on modeling link strength rather than link existence. Unsupervised approach, inﬀering a continuous-valued measure of relationship strength for OSNs. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 12. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (7) The approach of this paper, naturally leads to a latent variable model which captures the causality of the underlying social process. takes discriminative approach to modeling the proﬁle similarities, and a generative approach to the interactions. is scalable, implements a principled optimization scheme to infer the parameter values and the relationship strengths for a set of user pairs. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 13. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference1. Introduction (8) Immediate implications for social science applications Link prediction Item recommendation Newfeeds People search Visualization OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 14. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2. Latent Variable Model (1) The stronger the tie, the higher the similarity. In OSNs, we can model the relationship strength as a hidden eﬀect of nodal proﬁle similarities. (e.g., schools, companies, online groups, geographic locations, etc.) The stronger the relationship, the higher likelihood that a certain type of interaction. The relationship strength as the hidden cause of user interactions. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 15. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2. Latent Variable Model (2) Formally, The proﬁle vectors of two individuals : x (i) , x (j) (ij) The occurrences of m diﬀerent interactions : yt , t = 1, 2, . . . , m The latent relationship strength variable : z (ij) 1 We model the inﬂuence of x (i) and x (j) on z (ij) , as well as the (ij) inﬂuence of z (ij) on yt , t = 1, 2, . . . , m 2 ‘z’ summarizes the similarities and interactions between a pair of people. 3 Its value is not directly observed in the data. → latent variable 4 Estimation for each pair of people to maximize the overall observed data likelihood. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 16. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2. Latent Variable Model (3) Hybrid of discriminative and generative models The upper part : discriminative (p(Z |X )) The lower part : generative (p(Y |Z )) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 17. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2. Latent Variable Model (4) This model represents . . . The likely causal relationships among these variables by modeling the conditional dependencies. The joint distribution decomposes as follows: m (ij) P(z (ij) , y (ij) |x (i) , x (j) ) = P(z (ij) |x (i) , x (j) ) P(yt |z (ij) ) (1) t=1 OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 18. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2. Latent Variable Model (5) In general, This model can be applied to infer either directed or undirected relationship strengths, depending on the way how we specify the proﬁle similarity and the interactions for each pair. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 19. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (1) Gaussian distribution to model the conditional probability of the relationship strength given proﬁle similarities. A set of similarity measures taken on pairs of nodes i,j ⇒ sk (x (i) , x (j) ), (k = 1, 2, . . . , n) Then, the dependency between z ij and x (i) , x (j) : P(z (ij) |x (i) , x (j) ) = N(w T s(x (j) , x (j) ), v ) (2) A similarity vector calculated based on x (i) and x (j) ⇒ s An n-dimensional weight vector to be estimated ⇒ w The variance in Gaussian model ⇒ v (conﬁgured to be 0.5 in the experiments) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 20. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (2) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 21. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (3) The proposed model, (ij) The probability distribution of each yt is conditionally independent given z (ij) . The variable may denote whether a user i has posted on j’s wall. To increase the accuracy of the model, (ij) (ij) (ij) A set of auxiliary variables at1 , at2 , . . . , atlt for each interaction t. We could moderate the eﬀect of relationship strength on interactions with a speciﬁc user. For example, the total number of pictures that a user has tagged represents their intrinsic tendency. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 22. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (4) Logistic Function (ij) To model the conditional probability of yt given z (ij) and (ij) at : (ij) (ij) P(yt = 1|z (ij) , at ) (3) 1 = (ij) (ij) (ij) +θt2 at2 +...+θtl atl +θtl+1 z (ij) +b) 1 + e −(θt1 at1 The set of parameters to be estimated ⇒ θt = [θt1 , θt2 , . . . , θtl , θtl+1 ]T OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 23. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (5) To make the notation more compact, (ij) at Deﬁne, u(ij) = t z (ij) (ij) (ij) 1 P(yt = 1|ut ) = T (ij) (4) 1+ e −(θt ut +b) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 24. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (6) To avoid over-ﬁtting, L2 regularizers on the parameters w and θ (Gaussian priors) λw wT w) P(w ) ∝ e −( 2 (5) T −( λθ θt θt ) P(θt ) ∝ e 2 , t = 1, 2, . . . , m (6) N samples of user pairs : D = {(i1 , j1 ), (i2 , j2 ), . . . , (iN , jN )} Based on Eq. (1), the joint probability is as follows: P(D|w , θ)P(w , θ) = P(z (ij) , y (ij) |x (i) , x (j) , w , θ) P(w )P(θ) (7) (i,j)∈D m (ij) = P(z (ij) |x (i) , x (j) , w ) P(yt |z (ij) , θt )P(w )P(θt ) (i,j)∈D t=1 m T (ij m − 2v (w T s (ij) −z(ij))2 1 e −(θt u(ij)+b)(1−yt ) λw wT w) λθ θ T θ ) ∝ e T (ij) · e −( 2 e −( 2 t t 1+e −(θt ut +b) (i,j)∈D t=1 t=1 OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 25. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.1 Model speciﬁcation (7) Tikhonov Regularization (Golub 1999) λ : a positive constant chosen to control the size of the solution vector. L : a matrix that deﬁnes a (semi)norm on the solution. : represents the ﬁrst or second derivative operator. If L is the identity matrix, then the Tikhonov problem is said to be in standard form. min{||Ax − b||2 + λ||Lx||2 2 2 (AT A + λLT L)x = AT b OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 26. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (1) Estimation of a latent variable model Latent variable as a parameter ˆ ˆˆ Point estimates w , θ, z that maximize the likelihood ˆ P(y , z , w , θ|x) ˆ ˆ Logarithm of Eq. (7) to get the data log-likelihood: In Eq. (8), the function L is concave. 1 L(z ({(i,j)∈D}) , w , θt ) = − (w T s (ij) − z(ij))2 (8) 2v (ij)∈D m T (ij) (ij) (ij) + T −(1 − yt )(θt ut + b) − log 1 + e −(θt ut +b) (ij)∈D t=1 m λw T λθ T − w w− θ θt + C 2 t=1 2 t OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 27. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (2) Gradient-based method L(z (ij) , w , θt ) To optimize over the parameters w , θt (t = 1, 2, . . . , m), and z (ij) , (ij) ∈ D to ﬁnd the maximum of L Coordinate-wise gradients to ﬁnd argmax(L(z (ij) , w , θt )): Coordinate-wise : manipulating each coordinate independently with the only criterion being that it improves the objective function. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 28. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (3) z:latent relation strength, θ:set of parameters, w :weight vector ∂L 1 (ij) 1 (ij) = (w T x (ij) − z (ij) ) + m yt − T θt,lt+1 (9) ∂z v t=1 1+ e −(θt ut (ij)+b) ∂L (ij) 1 (ij) = yt − T ut − λ θ θt (10) ∂θt (ij)∈D 1+ e −(θt ut (ij)+b) ∂L 1 = (z (ij) − w T s (ij) )s (ij) − λw w (11) ∂w v (ij)∈D OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 29. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (4) The learning algorithm : a coordinate ascent optimization Update w , z (ij) , θt iteratively until convergence Use of the Newton-Raphson updates in each iteration: ∂L ∂2L z (ij)new = z (ij)old − / (ij) ∂(z (ij) )2 (12) ∂z new old ∂L ∂2L θt = θt − / T (13) ∂θt ∂θ(t) ∂θt For w, the root of (11) can be found analytically as in usual ridge regression: w new = (λw I + S T S)−1 S T z (14) S = [s(i1 j1 ), s(i2 j2 ), . . . , s(iN jN )]T , z = [z(i1 j1 ), z(i2 j2 ), . . . , z(iN jN )]T OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 30. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (5) where the 2nd order derivatives are given by: T (ij) m ∂2L 1 θt,li+1 e −(θt 2 ut +b) =− − T u (ij) +b) (15) ∂(z (ij) )2 v t=1 (1 + e −(θt t )2 T (ij) ∂2L e −(θt ut +b) (ij) (ij)T T =− T (ij) ut ut − λθ I (16) ∂(θt )∂θt 1+e −(θt ut +b) (ij)∈D OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 31. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (6) The learning algorithm Algorithm : While not converged: 1: For each Newton-Raphson step: For t=1,. . . ,m: update θt according to Eq. (13). 2: For each Newton-Raphson step: For (i, j) ∈ D: update z (ij) according to Eq. (12). 3: Update w according to Eq. (14). OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 32. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference2.2 Inference (7) For a new pair of users (i, j), the learned model can be applied in two ways. (ij) (ij) 1 If user attributes (x (i) , x (j) ), their interactions (y1 , . . . , yt ) are known, → z (ij) in step 2. 2 More common scenario: When the interaction data are unobserved, just apply Eq. (2) to infer z (ij) . The interaction data are usually sparse, temporal and diﬃcult to obtain. 3 Hybrid model Generative : The overall model will not suﬀer much from missing interaction data. Discriminative : Treat user background information and interaction equally. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 33. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3. Experiments - 3.1 LinkedIn Data LinkedIn data (www.linkedin.com) Business-oriented social networking site More than 50 million users worldwide Business proﬁle, connections search member, proﬁles and job postings, communication, recommendations, form/join groups OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 34. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.1.1 Dataset (1) Sample pairs for evaluations 100 users as seed nodes up to 2 links away in the connection graph (within its two-hop neighborhood) 100,000 sample pairs OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 35. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.1.1 Dataset (2) Proﬁle and connection similarity features (ij) (ij) (ij) s (ij) = [s1 s2 . . . s8 ]T H class HH 1 0 si H H s1 same school otherwise s2 same company otherwise s3 same geographical region otherwise s4 same industry otherwise s5 same job title otherwise s6 same functional area otherwise s7 normalized counts of common groups otherwise s8 normalized counts of common connections otherwise OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 36. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.1.1 Dataset (3) LinkedIn interaction features For yi . Auxiliary feature : total number of nodes ki HH class HH 1 0 yi H y1 connection otherwise y2 recommendation otherwise y3 viewed proﬁle otherwise y4 address book otherwise OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 37. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.1.2 Evaluation (1) For the ﬁrst set of evaluations, job, functional area, geographical region similarity feature How well the estimated relationship strengths identify pairs of users? Compare the rankings using relationship strength to several alternative rankings: 1 Recommendation links 2 Proﬁle-view links 3 Address-book links 4 Connection links 5 Interaction count : by the total count (ij) 6 Proﬁle similarity : by the overall similarity k sk OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 38. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.1.2 Evaluation (2) using all features correlation with historical proﬁle co-viewing The relationship strengths are approximating the way that humans perceive relationships among people. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 39. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2 Facebook Data Facebook data (www.facebook.com) Popular online social network site Over 250 million members worldwide Personal proﬁle page (views, interests, group memberships, friends) User’s interaction : posting on each others’ wall, tagging each other in pictures OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 40. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.1 Dataset (1) Sample pairs for evaluations ﬁve public Purdue Facebook users as seed nodes within three hops of the seed nodes (total sample : 4500 nodes) 144,712 sample pairs OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 41. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.1 Dataset (2) Proﬁle and connection similarity features (ij) (ij) (ij) s (ij) = [s1 s2 s3 ]T PP for i,j logarithm of the normalized counts PP si PP PP s1 of common networks s2 of common groups s3 of common friends Table : Facebook proﬁle and connection similarity features OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 42. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.1 Dataset (3) Additional similarity features (ij) (ij) y1 , y2 HH class H 1 0 yi HH y1 i has posted on j’s wall otherwise y2 i has tagged j in a picture otherwise Table : Facebook interaction features OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 43. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.1 Dataset (4) During learning phase, No use of the user proﬁle attributes. The reasons of the information limitation, 1 For accurate evaluation (later use). 2 Unlisted attributes (gender : 44%, political views : 27%) 3 The information is often not public. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 44. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (1) Used proposed model for evaluation to estimate the relationship strengths to compare the weighted graph formed by the estimated relationship strengths to the following 4 grphas formed from the observed data: 1 Friendship graph : all friendship links between users. 2 Top-friend graph : all top-friend nominations. 3 Wall graph : edges corresponding to wall posting activities. 4 Picture graph : edges corresponding to picture-tagging activities. Evaluation in 2 diﬀerent ways: 1 Measure the increase in autocorrelation on the induced graph. 2 Measure the accuracy improvement over several collective classiﬁcation tasks. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 45. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (2) Autocorrelation improvement The autocorrelation (Jensen 2002) of a random process describes the correlation between values of the process at diﬀerent points in time. A mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. T 1 T [yt − y ][yt−τ − y ] ¯ ¯ t=τ+1 p (τ) = ˆ T , τ = t2 − t1 1 T (y − y )2 ¯ t=τ+1 OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 46. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (3) Autocorrelation improvement Chi-square statistic Eij : the expected occurrence, Oij : the observed occurrence Scale the chi-square statistics to the range [-1(perfect negative), 1(perfect positive)] Oij − Eij χ2 = Eij i∈K j∈K Corrected contingency coeﬃcient: N : the number of linked pairs (scaling factor, N is also scaled.) K χ2 CC = (K − 1)(N + χ2 ) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 47. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (4) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 48. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (5) Results in ﬁgure 4, Vary the number of links in the network by theresholding the link strength. Randomly drop links to assess the autocorrelation on networks with the same density. Tradeoﬀ between link density and autocorrelation. Increased sparsity will hamper the ability of the predictive models. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 49. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (6) Classiﬁcation improvement Further exploration of the utility of the weighted graph formed from relationship strength Binary classiﬁcation task based on its most frequent value. 1 Gender 2 Relationship Status 3 Political Views 4 Religious Views OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 50. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (7) Semi-supervised Gaussian Random Field (Zhu 2003) Similar unlabeled examples should be given the same classiﬁcation. Labeled data items - boundary points, Unlabeled points - interior points OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 51. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (8) GRF in the evaluation Assumption : autocorrelation is present in the graph and propagates information from the labeled portion of the graph to infer the values for unlabeled nodes. Modify each link w (i, j) in the 4 directed graphs to be max{w (i, j), w (j, i)} (Undirected graphs as input) If w (i, j) = w (j, i), approximate by choosing max value. Vary the proportion of labeled nodes from 30% to 90%. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 52. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (9) OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 53. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference3.2.2 Evaluation (10) Results in ﬁgure 5, Averaged over 5 runs with diﬀerent random selections of labeled instances. Omit : Wall graph, Picture graph The top-friend graph : highest autocorrelation but lowest performance. why? Insuﬃcient density Strength of the proposed approach : 1 Maintain the density of the full friendship graph but signiﬁcantly increase the autocorrelation levels. 2 Combine the natural heuristics (interaction-count, proﬁle-similarity) in a single representation of overall relationship strength. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 54. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference4. Related Work The recent growth and popularity of OSNs lead to a surge in research focused on . . . Modeling networks and their properties. Link prediction. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 55. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work Reference5. Conclusion and Future Work Conclusion A latent variable model for the relationship strength estimation in OSN. The intrinsic causality of social interactions. Downweighted/Highlighted → Increase accuracy. Future Work Plan to develop alternative inference procedures which maximize the observed data likelihood by integrating over all possible values of the latent variable. Consider alternative ways to specify the model - Kernels in deﬁning proﬁle similarities for learning automatically. Nonlinear classiﬁcation or regression instead of the generalized linear model for the interaction dependencies. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 56. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work ReferenceReference [1] M. McPherson, L. Smith-Lovin, J. Cook. Birds of a feather: Homophily in social networks. Annual In: Review of Sociology, 27(1):415–444, 2001. [2] X. Zhu, Z. Ghahramani, J. Laﬀerty. Semi-supervised learning using gaussian ﬁelds and harmonic functions In: ICML ’03, 2003. [3] Gene H. Golub, Per Christian Hansen, Dianne P. O’Leary. Tikhonov Regularization and Total Least Squares In: Journal SIAM Journal on Matrix Analysis and Applications archive. Volume 21 Issue 1, Aug. 1999. [4] D. Liben-Nowell, J. Kleinberg. The link prediction problem for social networks In: CIKM ’03, 2003. [5] J. Neville, O. Simsek, D. Jensen, J. Komoroske, K. Palmer, H. Goldberg. Using relational knowledge discovery to prevent securities fraud In: KDD ’05, 2005. OwlNest Corp. Modeling Relationship Strength in Online Social Networks
- 57. Index Introduction Latent Variable Model Experiments Related Work Conclusion and Future Work ReferenceReference [6] B. Taskar, M. F. Wong, P. Abbeel, D. Koller. Link prediction in relational data In: NIPS ’03, 2003. [7] David Jensen, Jennifer Neville. Linkage and Autocorrelation Cause Feature Selection Bias in Relational Learning In: Proceeding ICML ’02 Proceedings of the Nineteenth International Conference on Machine Learning. 2002. OwlNest Corp. Modeling Relationship Strength in Online Social Networks

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