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Network representations have been shown to improve performance within a variety of tasks, including classification, clustering, and link prediction. However, most models either focus on moderate-sized, homogeneous networks or require a significant amount of auxiliary input to be provided by the user. Moreover, few works have studied network representations in real-world heterogeneous social networks with ambiguous social connections and are often incomplete. In the present work, we investigate the problem of learning low-dimensional node representations in heterogeneous professional social networks (HPSNs), which are incomplete and have ambiguous social connections. We present a general heterogeneous network representation learning model called Star2Vec that learns entity and person embeddings jointly using a social connection strength-aware biased random walk combined with a node-structure expansion function. Experiments on LinkedIn's Economic Graph and publicly available snapshots of Facebook's network show that Star2Vec outperforms existing methods on members' industry and social circle classification, skill and title clustering, and member-entity link predictions. We also conducted large-scale case studies to demonstrate practical applications of the Star2Vec embeddings trained on LinkedIn's Economic Graph such as next career move, alternative career suggestions, and general entity similarity searches. 

One of the principal goals of graph modeling is to capture the building blocks of network data in order to study various physical and natural phenomena. Recent work at the intersection of formal language theory and graph theory has explored the use of graph grammars for graph modeling. However, existing graph grammar formalisms, like Hyperedge Replacement Grammars, can only operate on small tree-like graphs. The present work relaxes this restriction by revising a different graph grammar formalism called Vertex Replacement Grammars (VRGs). We show that a variant of the VRG called Clustering-based Node Replacement Grammar (CNRG) can be efficiently extracted from many hierarchical clusterings of a graph. We show that CNRGs encode a succinct model of the graph, yet faithfully preserves the structure of the original graph. In experiments on large real-world datasets, we show that graphs generated from the CNRG model exhibit a diverse range of properties that are similar to those found in the original networks. 

Representation learning is popular for its power of learning latent feature vectors (i.e., embeddings) to represent data units from a complex type of data (e.g., languages, networks, behaviors). The embeddings preserve specific structure and thus improve the performance of predictive models. In this work, we develop a new representation learning method in the chemistry domain. Given a large set of compounds of inorganic crystals, the method learns the embeddings of atoms so that the predictive models can place them into the periodic table correctly. Our method preserves not only the compounds' compositions but also their structures such as crystal system, point group, and space group. Experiments demonstrate the effectiveness of the proposed method, compared to the state-of-the-art method (in PNAS 2018). One interesting result is that given 20 atoms with known positions in the periodic table, our method can achieve an accuracy of 0.70, while the baseline makes only 0.54, on filling the remaining 14 hidden atoms into the table. This shows that the atomic embeddings we generated preserve useful information and can be extended for scientific exploration. 

An enormous amount of real-world data exists in the form of graphs. Oftentimes, interesting patterns that describe the complex dynamics of these graphs are captured in the form of frequently reoccurring substructures. Recent work at the intersection of formal language theory and graph theory has explored the use of graph grammars for graph modeling and pattern mining. However, existing formulations do not extract meaningful and easily interpretable patterns from the data. The present work addresses this limitation by extracting a special type of vertex replacement grammar, which we call a KT grammar, according to the Minimum Description Length (MDL) heuristic. In experiments on synthetic and real-world datasets, we show that KT-grammars can be efficiently extracted from a graph and that these grammars encode meaningful patterns that represent the dynamics of the real-world system. 

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. Recent work at the intersection of formal language theory and graph theory has found that a Probabilistic Hyperedge Replacement Grammar (PHRG) can be extracted from a tree decomposition of any graph. However, because the extracted PHRG is directly dependent on the shape and contents of the tree decomposition, rather than from the dynamics of the graph, it is unlikely that informative graph-processes are actually being captured with the PHRG extraction algorithm. To address this problem, the current work adapts a related formalism called Probabilistic Synchronous HRG (PSHRG) that learns synchronous graph production rules from temporal graphs. We introduce the PSHRG model and describe a method to extract growth rules from the graph. We find that SHRG rules capture growth patterns found in temporal graphs and can be used to predict the future evolution of a temporal graph. We perform a brief evaluation on small synthetic networks that demonstrate the prediction accuracy of PSHRG versus baseline and state of the art models. Ultimately, we find that PSHRGs seem to be very good at modelling dynamics of a temporal graph; however, our prediction algorithm, which is based on string parsing and generation algorithms, does not scale to practically useful graph sizes.