nips nips2012 nips2012-345 knowledge-graph by maker-knowledge-mining

345 nips-2012-Topic-Partitioned Multinetwork Embeddings

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Author: Peter Krafft, Juston Moore, Bruce Desmarais, Hanna M. Wallach

Abstract: We introduce a new Bayesian admixture model intended for exploratory analysis of communication networks—speciﬁcally, the discovery and visualization of topic-speciﬁc subnetworks in email data sets. Our model produces principled visualizations of email networks, i.e., visualizations that have precise mathematical interpretations in terms of our model and its relationship to the observed data. We validate our modeling assumptions by demonstrating that our model achieves better link prediction performance than three state-of-the-art network models and exhibits topic coherence comparable to that of latent Dirichlet allocation. We showcase our model’s ability to discover and visualize topic-speciﬁc communication patterns using a new email data set: the New Hanover County email network. We provide an extensive analysis of these communication patterns, leading us to recommend our model for any exploratory analysis of email networks or other similarly-structured communication data. Finally, we advocate for principled visualization as a primary objective in the development of new network models. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract We introduce a new Bayesian admixture model intended for exploratory analysis of communication networks—speciﬁcally, the discovery and visualization of topic-speciﬁc subnetworks in email data sets. [sent-6, score-1.259]

2 Our model produces principled visualizations of email networks, i. [sent-7, score-0.839]

3 , visualizations that have precise mathematical interpretations in terms of our model and its relationship to the observed data. [sent-9, score-0.273]

4 We validate our modeling assumptions by demonstrating that our model achieves better link prediction performance than three state-of-the-art network models and exhibits topic coherence comparable to that of latent Dirichlet allocation. [sent-10, score-0.253]

5 We showcase our model’s ability to discover and visualize topic-speciﬁc communication patterns using a new email data set: the New Hanover County email network. [sent-11, score-1.719]

6 We provide an extensive analysis of these communication patterns, leading us to recommend our model for any exploratory analysis of email networks or other similarly-structured communication data. [sent-12, score-1.291]

7 Finally, we advocate for principled visualization as a primary objective in the development of new network models. [sent-13, score-0.282]

8 1 Introduction The structures of organizational communication networks are critical to collaborative problem solving [1]. [sent-14, score-0.368]

9 Although it is seldom possible for researchers to directly observe complete organizational communication networks, email data sets provide one means by which they can at least partially observe and reason about them. [sent-15, score-1.007]

10 As a result—and especially in light of their rich textual detail, existing infrastructure, and widespread usage—email data sets hold the potential to answer many important scientiﬁc and practical questions within the organizational and social sciences. [sent-16, score-0.147]

11 While some questions may be answered by studying the structure of an email network as a whole, other, more nuanced, questions can only be answered at ﬁner levels of granularity—speciﬁcally, by studying topic-speciﬁc subnetworks. [sent-17, score-0.994]

12 For example, breaks in communication (or duplicated communication) about particular topics may indicate a need for some form of organizational restructuring. [sent-18, score-0.45]

13 In order to facilitate the study of these kinds of questions, we present a new Bayesian admixture model intended for discovering and summarizing topic-speciﬁc communication subnetworks in email data sets. [sent-19, score-1.149]

14 There are a number of probabilistic models that incorporate both network and text data. [sent-20, score-0.146]

15 Although some of these models are speciﬁcally for email networks (e. [sent-21, score-0.708]

16 ’s author–recipient– topic model [2]), most are intended for networks of documents, such as web pages and the links between them [3] or academic papers and their citations [4]. [sent-24, score-0.259]

17 In contrast, an email network is more naturally viewed as a network of actors exchanging documents, i. [sent-25, score-1.044]

18 , actors are associated with nodes while documents are associated with edges. [sent-27, score-0.254]

19 In other words, an email network deﬁnes a multinetwork in which there may be multiple edges (one per email) between any pair of actors. [sent-28, score-0.937]

20 Instead, we take a complementary approach and focus on exploratory analysis. [sent-31, score-0.075]

21 Speciﬁcally, our goal is to discover and visualize topic-speciﬁc subnetworks. [sent-32, score-0.088]

22 If network modeling and visualization are undertaken separately, the resultant visualizations may not directly reﬂect the model and its relationship to the observed data. [sent-34, score-0.382]

23 Rather, these visualizations provide a view of the model and the data seen through the lens of the visualization algorithm and its associated assumptions, so any conclusions drawn from such visualizations can be biased by artifacts of the visualization algorithm. [sent-35, score-0.461]

24 , visualizations that have precise interpretations in terms of an associated network model and its relationship to the observed data, remains an open challenge in statistical network modeling [5]. [sent-38, score-0.559]

25 Addressing this open challenge was a primary objective in the development of our new model. [sent-39, score-0.045]

26 In order to discover and visualize topic-speciﬁc subnetworks, our model must associate each author– recipient edge in the observed email network with a topic, as shown in Figure 1. [sent-40, score-1.029]

27 Our model draws upon ideas from latent Dirichlet allocation (LDA) [6] to identify a set of corpus-wide topics of communication, as well as the subset of topics that best describe each observed email. [sent-41, score-0.239]

28 We model network structure using an approach similar to that of Hoff et al. [sent-42, score-0.111]

29 ’s latent space model (LSM) [7] so as to facilitate visualization. [sent-43, score-0.024]

30 Given an observed network, LSM associates each actor in the network with a point in K-dimensional Euclidean space. [sent-44, score-0.211]

31 If K = 2 or K = 3, these interaction probabilities, collectively known as a “communication pattern”, can be directly visualized in 2- or 3-dimensional space via the locations of the actor-speciﬁc points. [sent-46, score-0.044]

32 Our model extends this idea by associating a K-dimensional Euclidean space with each topic. [sent-47, score-0.034]

33 Observed author–recipient edges are explicitly associated with topics via the K-dimensional topic-speciﬁc communication patterns. [sent-48, score-0.42]

34 In the next section, we present the mathematical details of our new model and outline a corresponding inference algorithm. [sent-49, score-0.023]

35 We then introduce a new email data set: the New Hanover County (NHC) email network. [sent-50, score-1.326]

36 Although our model is intended for exploratory analysis, we test our modeling assumptions via three validation tasks. [sent-51, score-0.146]

37 1, we show that our model achieves better link prediction performance than three state-of-the-art network models. [sent-53, score-0.111]

38 We also demonstrate that our model is capable of inferring topics that are as coherent as those inferred using LDA. [sent-54, score-0.106]

39 Together, these experiments indicate that our model is an appropriate model of network structure and that modeling this structure does not compromise topic quality. [sent-55, score-0.253]

40 As a ﬁnal validation experiment, we show that synthetic data generated using our model possesses similar network statistics to those of the NHC email network. [sent-56, score-0.774]

41 4, we showcase our model’s ability to discover and visualize topic-speciﬁc communication patterns using the NHC network. [sent-58, score-0.393]

42 We give an extensive analysis of these communication patterns and demonstrate that they provide accessible visualizations of emailbased collaboration while possessing precise, meaningful interpretations within the mathematical framework of our model. [sent-59, score-0.492]

43 These ﬁndings lead us to recommend our model for any exploratory analysis of email networks or other similarly-structured communication data. [sent-60, score-1.053]

44 Finally, we advocate for principled visualization as a primary objective in the development of new network models. [sent-61, score-0.282]

45 2 Topic-Partitioned Multinetwork Embeddings In this section, we present our new probabilistic generative model (and associated inference algorithm) for communication networks. [sent-62, score-0.313]

46 For concreteness, we frame our discussion of this model in 2 terms of email data, although it is generally applicable to any similarly-structured communication data. [sent-63, score-0.901]

47 The generative process and graphical model are provided in the supplementary materials. [sent-64, score-0.032]

48 (d) (d) A single email, indexed by d, is represented by a set of tokens w(d) = {wn }N that comprise the n=1 text of that email, an integer a(d) ∈ {1, . [sent-65, score-0.119]

49 , A} indicating the identity of that email’s author, and a (d) set of binary variables y (d) = {yr }A indicating whether each of the A actors in the network is r=1 a recipient of that email. [sent-68, score-0.36]

50 For simplicity, we assume that authors do not send emails to themselves (d) (i. [sent-69, score-0.104]

51 Given a real-world email data set D = {{w(d) , a(d) , y (d) }}D , our d=1 model permits inference of the topics expressed in the text of the emails, a set of topic-speciﬁc K-dimensional embeddings (i. [sent-72, score-0.844]

52 , points in K-dimensional Euclidean space) of the A actors in the network, and a partition of the full communication network into a set of topic-speciﬁc subnetworks. [sent-74, score-0.489]

53 A symmetric Dirichlet prior with concentration parameter β is placed over Φ = {φ(1) , . [sent-76, score-0.022]

54 To capture the relationship between the topics expressed in an email and that email’s recipients, each topic t is also associated with a “communication pattern”: an A × A (t) matrix of probabilities P (t) . [sent-80, score-0.957]

55 Given an email about topic t, authored by actor a, element par is the probability of actor a including actor r as a recipient of that email. [sent-81, score-1.176]

56 Inspired by LSM [7], each communication pattern P (t) is represented implicitly via a set of A points in K-dimensional Euclidean (t) (t) (t) (t) (t) space S (t) = {sa }A and a scalar bias term b(t) such that par = pra = σ(b(t) − sa − sr ) a=1 (t) 2 2 with sa ∼ N (0, σ1 I) and b(t) ∼ N (µ, σ2 ). [sent-82, score-0.618]

57 1 If K = 2 or K = 3, this representation enables each topic-speciﬁc communication pattern to be visualized in 2- or 3-dimensional space via the locations of the points associated with the A actors. [sent-83, score-0.347]

58 In isolation, each point sa conveys no information; however, the distance between any two points has a precise and meaningful interpretation in the generative process. [sent-85, score-0.233]

59 Speciﬁcally, the recipients of any email associated with topic t are more likely to be those actors near to the email’s author in the Euclidean space corresponding to that topic. [sent-86, score-1.138]

60 Each email, indexed by d, has a discrete distribution over topics θ (d) . [sent-87, score-0.106]

61 A symmetric Dirichlet prior (d) with concentration parameter α is placed over Θ = {θ (1) , . [sent-88, score-0.022]

62 Each token wn is associated (d) (d) (d) (d) with a topic assignment zn , such that zn ∼ θ (d) and wn ∼ φ(t) for zn = t. [sent-92, score-0.765]

63 Our model does not include a distribution over authors; the generative process is conditioned upon their identities. [sent-93, score-0.032]

64 (d) The email-speciﬁc binary variables y (d) = {yr }A indicate the recipients of email d and thus the r=1 presence (or absence) of email-speciﬁc edges from author a(d) to each of the A − 1 other actors. [sent-94, score-0.867]

65 Consequently, there may be multiple edges (one per email) between any pair of actors, and D deﬁnes a multinetwork over the entire set of actors. [sent-95, score-0.163]

66 We assume that the complete multinetwork comprises T (d) topic-speciﬁc subnetworks. [sent-96, score-0.13]

67 In other words, each yr is associated with some topic t and therefore (t) (d) with topic-speciﬁc communication pattern P (t) such that yr ∼ Bern(par ) for a(d) = a. [sent-97, score-1.206]

68 A better approach, advocated (d) by Blei and Jordan, is to draw a topic assignment for each yr from the empirical distribution over (d) topics deﬁned by z . [sent-100, score-0.67]

69 By deﬁnition, the set of topics associated with edges will therefore be a subset of the topics associated with tokens. [sent-101, score-0.331]

70 One way of simulating this generative process is to associate (d) (d) each yr with a position n = 1, . [sent-102, score-0.477]

71 , max (1, N (d) ) and therefore with the topic assignment zn at (d) (d) that position2 by drawing a position assignment xr ∼ U(1, . [sent-105, score-0.496]

72 This (d) (t) (d) (d) indirect procedure ensures that yr ∼ Bern(par ) for a(d) = a, xr = n, and zn = t, as desired. [sent-109, score-0.658]

73 , N (d) = 0) convey information about the frequencies of communication between their authors and recipients. [sent-113, score-0.276]

74 As a result, we do not omit such emails from D; instead, we (d) (d) augment each one with a single, “dummy” topic assignment z1 for which there is no associated token w1 . [sent-114, score-0.336]

75 1 Inference For real-world data D = {w(d) , a(d) , y (d) }D , the tokens W = {w(d) }D , authors A = d=1 d=1 {a(d) }D , and recipients Y = {y (d) }D are observed, while Φ, Θ, S = {S (t) }T , B = {b(t) }T , t=1 t=1 d=1 d=1 Z = {z (d) }D , and X = {x(d) }D are unobserved. [sent-116, score-0.175]

76 In this section, we outline a Metropolis-within-Gibbs sampling algorithm that operates by sequentially (t) (d) (d) resampling the value of each latent variable (i. [sent-118, score-0.023]

77 , sa , bt , zn , or xr ) from its conditional posterior. [sent-120, score-0.395]

78 Count N (t) is the total number of tokens in W assigned to topic t by Z, of which N (v|t) are of type v and N (t|d) (d) belong to email d. [sent-122, score-0.848]

79 New values for discrete random variable xr may be sampled directly using (t) (d) P (x(d) = n | A, Y, S, B, zn = t, Z\d,n ) ∝ (pa(d) r ) r (d) yr (t) (1 − pa(d) r ) (d) 1−yr . [sent-123, score-0.639]

80 (t) New values for continuous random variables sa and b(t) cannot be sampled directly from their conditional posteriors, but may instead be obtained using the Metropolis–Hastings algorithm. [sent-124, score-0.147]

81 With (t) (t) (t) a non-informative prior over sa (i. [sent-125, score-0.147]

82 Likewise, with an improper, noninformative prior over b(t) (i. [sent-129, score-0.021]

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