 Award ID(s):
 1848596
 NSFPAR ID:
 10109798
 Date Published:
 Journal Name:
 Companion Proceedings of the 2019 World Wide Web Conference (WWW ’19 Companion)
 Page Range / eLocation ID:
 285 to 293
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

Graph clustering is a fundamental problem in social network analysis, the goal of which is to group vertices of a graph into a series of densely knitted clusters with each cluster well separated from all the others. Classical graph clustering methods take advantage of the graph topology to model and quantify vertex proximity. With the proliferation of rich graph contents, such as user profiles in social networks, and gene annotations in protein interaction networks, it is essential to consider both the structure and content information of graphs for highquality graph clustering. In this paper, we propose a graph embedding approach to clustering contentenriched graphs. The key idea is to embed each vertex of a graph into a continuous vector space where the localized structural and attributive information of vertices can be encoded in a unified, latent representation. Specifically, we quantify vertexwise attribute proximity into edge weights, and employ truncated, attributeaware random walks to learn the latent representations for vertices. We evaluate our attributeaware graph embedding method in realworld attributed graphs, and the results demonstrate its effectiveness in comparison with stateoftheart algorithms.more » « less

null (Ed.)In traditional graph learning tasks, such as node classification, learning is carried out in a closedworld setting where the number of classes and their training samples are provided to help train models, and the learning goal is to correctly classify unlabeled nodes into classes already known. In reality, due to limited labeling capability and dynamic evolving of networks, some nodes in the networks may not belong to any existing/seen classes, and therefore cannot be correctly classified by closedworld learning algorithms. In this paper, we propose a new openworld graph learning paradigm, where the learning goal is to not only classify nodes belonging to seen classes into correct groups, but also classify nodes not belonging to existing classes to an unseen class. The essential challenge of the openworld graph learning is that (1) unseen class has no labeled samples, and may exist in an arbitrary form different from existing seen classes; and (2) both graph feature learning and prediction should differentiate whether a node may belong to an existing/seen class or an unseen class. To tackle the challenges, we propose an uncertain node representation learning approach, using constrained variational graph autoencoder networks, where the label loss and class uncertainty loss constraints are used to ensure that the node representation learning are sensitive to unseen class. As a result, node embedding features are denoted by distributions, instead of deterministic feature vectors. By using a sampling process to generate multiple versions of feature vectors, we are able to test the certainty of a node belonging to seen classes, and automatically determine a threshold to reject nodes not belonging to seen classes as unseen class nodes. Experiments on realworld networks demonstrate the algorithm performance, comparing to baselines. Case studies and ablation analysis also show the rationale of our design for openworld graph learning.more » « less

Network embedding is an effective approach to learn the lowdimensional representations of vertices in networks, aiming to capture and preserve the structure and inherent properties of networks. The vast majority of existing network embedding methods exclusively focus on vertex proximity of networks, while ignoring the network internal community structure. However, the homophily principle indicates that vertices within the same community are more similar to each other than those from different communities, thus vertices within the same community should have similar vertex representations. Motivated by this, we propose a novel network embedding framework NECS to learn the Network Embedding with Community Structural information, which preserves the highorder proximity and incorporates the community structure in vertex representation learning. We formulate the problem into a principled optimization framework and provide an effective alternating algorithm to solve it. Extensive experimental results on several benchmark network datasets demonstrate the effectiveness of the proposed framework in various network analysis tasks including network reconstruction, link prediction and vertex classification.

Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and blocktridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistorcapacitorinductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to socalled nitedierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM statespace representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a nonsymmetric Lanczos algorithm written in Jsymmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nitedierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich datamanifolds), a nitedierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in portHamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible nonpositivity of conductors for the nonStieltjes case, we introduce an additional complex sdependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on KreinNudelman theory [5], that results in special datadriven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the threepoint second dierences: I. A twopoint positive denite problem in a semiinnite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graphLaplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go backmore » « less

Network alignment (NA) is a fundamental problem in many application domains – from social networks, through biology and communications, to neuroscience. The main objective is to identify common nodes and most similar connections across multiple networks (resp. graphs). Many of the existing efforts focus on efficient anchor node linkage by leveraging various features and optimizing network mapping functions with the pairwise similarity between anchor nodes. Despite the recent advances, there still exist two kinds of challenges: (1) entangled node embeddings, arising from the contradictory goals of NA: embedding proximal nodes in a closed form for representation in a single network vs. discriminating among them when mapping the nodes across networks; and (2) lack of interpretability about the node matching and alignment, essential for understanding prediction tasks. We propose dNAME (disentangled Network Alignment with Matching Explainability) – a novel solution for NA in heterogeneous networks settings, based on a matching technique that embeds nodes in a disentangled and faithful manner. The NA task is cast as an adversarial optimization problem which learns a proximitypreserving model locally around the anchor nodes, while still being discriminative. We also introduce a method to explain our semisupervised model with the theory of robust statistics, by tracing the importance of each anchor node and its explanations on the NA performance. This is extensible to many other NA methods, as it provides model interpretability. Experiments conducted on several public datasets show that dNAME outperforms the stateoftheart methods in terms of both network alignment precision and node matching ranking.more » « less