Dynamic Bipartite Graph Research Articles

An evolving learning style detection approach for online education using bipartite graph embedding

The increasingly widespread online education recently enabled a new form of teaching, learning, and overall educational outcome. However, the need of personalization is required as learners learn differently and learning follows a one-size-fits-all approach. Learning style is the most used personalization that plays an important role in learning. This learning style is a changeable trait that is influenced by the learner's behavior based on past experiences. As a result, knowing it over time helps to point learners in the right direction, motivate them, and enhance their learning outcomes. Research done so far does not take into account the changes in the behavior of learners, and the behavioral data is at large volume, making the existing approaches fail to capture and extract the behavior of learners efficiently. Inspired by these constraints, we propose an incremental learning style detection approach for online education with a bipartite graph embedding technique. We first construct a dynamic bipartite graph to represent the incremental interaction between learners and learning resources while learning. Then, introduce a dynamic bipartite graph embedding to learn the low dimensional representation of the constructed graph from the current and previous time. Finally, the low dimensional features are mapped to the selected Felder-Silverman learning style model (FSLSM) dimension each time to identify and group similar learners using the k-means clustering algorithm. The proposed approach can be integrated into different educational systems. Extensive experiments conducted using three datasets from 2015 KDD Cup courses demonstrate the effectiveness of our approach. Average of 93.19%, 95.76%, and 98.48% are achieved across the three datasets in accuracy compared to the existing approaches.

Efficient Core Maintenance in Large Bipartite Graphs

As an important cohesive subgraph model in bipartite graphs, the (α, β)-core (a.k.a. bi-core) has found a wide spectrum of real-world applications, such as product recommendation, fraudster detection, and community search. In these applications, the bipartite graphs are often large and dynamic, where vertices and edges are inserted and deleted frequently, so it is costly to recompute (α, β)-cores from scratch when the graph has changed. Recently, a few works have attempted to study how to maintain (α, β)-cores in the dynamic bipartite graph, but their performance is still far from perfect, due to the huge size of graphs and their frequent changes. To alleviate this issue, in this paper we present efficient (α, β)-core maintenance algorithms over bipartite graphs. We first introduce a novel concept, called bi-core numbers, for the vertices of bipartite graphs. Based on this concept, we theoretically analyze the effect of inserting and deleting edges on the changes of vertices' bi-core numbers, which can be further used to narrow down the scope of the updates, thereby reducing the computational redundancy. We then propose efficient (α, β)-core maintenance algorithms for handling the edge insertion and edge deletion respectively, by exploiting the above theoretical analysis results. Finally, extensive experimental evaluations are performed on both real and synthetic datasets, and the results show that our proposed algorithms are up to two orders of magnitude faster than the state-of-the-art approaches.

Stateful Posted Pricing with Vanishing Regret via Dynamic Deterministic Markov Decision Processes

An online problem called dynamic resource allocation with capacity constraints (DRACC) is introduced and studied in the realm of posted price mechanisms. This problem subsumes several applications of stateful pricing, including but not limited to posted prices for online job scheduling and matching over a dynamic bipartite graph. Because existing online learning techniques do not yield vanishing regret for this problem, we develop a novel online learning framework over deterministic Markov decision processes with dynamic state transition and reward functions. Following that, we prove, based on a reduction to the well-studied problem of online learning with switching costs, that if the Markov decision process admits a chasing oracle (i.e., an oracle that simulates any given policy from any initial state with bounded loss), then the online learning problem can be solved with vanishing regret. Our results for the DRACC problem and its applications are then obtained by devising (randomized and deterministic) chasing oracles that exploit the particular structure of these problems. Funding: The work of Y. Emek was supported in part by the Israel Science Foundation [Grant 1016/17]. The work of R. Lavi was partially supported by the Israel Science Foundation [Grant 2560/17] and the National Natural Science Foundation of China [Grant 2560/17]. The work of R. Niazadeh was supported by the University of Chicago Booth School of Business. The work of Y. Shi was partially supported at the Technion by the Council for Higher Education [fellowship], and at Shandong University by the Science Fund Program of Shandong Province for Distinguished Oversea Young Scholars [Grant 2023HWYQ-006].

AoI-Based Temporal Attention Graph Neural Network for Popularity Prediction and Content Caching

Along with the fast development of network technology and the rapid growth of network equipment, the data throughput is sharply increasing. To handle the problem of backhaul bottleneck in cellular network and satisfy people’s requirements about latency, the network architecture, like the information-centric network (ICN) intends to proactively keep limited popular content at the edge of network based on predicted results. Meanwhile, the interactions between the content (e.g., deep neural network models, Wikipedia-alike knowledge base) and users could be regarded as a dynamic bipartite graph. In this paper, to maximize the cache hit rate, we leverage an effective dynamic graph neural network (DGNN) to jointly learn the structural and temporal patterns embedded in the bipartite graph. Furthermore, in order to have deeper insights into the dynamics within the evolving graph, we propose an age of information (AoI) based attention mechanism to extract valuable historical information while avoiding the problem of message staleness. Combining this aforementioned prediction model, we also develop a cache selection algorithm to make caching decisions in accordance with the prediction results. Extensive results demonstrate that our model can obtain a higher prediction accuracy than other state-of-the-art schemes in two real-world datasets. The results of hit rate further verify the superiority of the caching policy based on our proposed model over other traditional ways.

Anonymous Edge Representation for Inductive Anomaly Detection in Dynamic Bipartite Graph

The activities in many real-world applications, such as e-commerce and online education, are usually modeled as a dynamic bipartite graph that evolves over time. It is a critical task to detect anomalies inductively in a dynamic bipartite graph. Previous approaches either focus on detecting pre-defined types of anomalies or cannot handle nodes that are unseen during the training stage. To address this challenge, we propose an effective method to learn anonymous edge representation (AER) that captures the characteristics of an edge without using identity information. We further propose a model named AER-AD to utilize AER to detect anomalies in dynamic bipartite graphs in an inductive setting. Extensive experiments on both real-life and synthetic datasets are conducted to illustrate that AER-AD outperforms state-of-the-art baselines. In terms of AUC and F1, AER-AD is able to achieve 8.38% and 14.98% higher results than the best inductive representation baselines, and 6.99% and 19.59% than the best anomaly detection baselines.

DynHEN: A heterogeneous network model for dynamic bipartite graph representation learning

Learning node representations in graphs is a widespread problem in node classification and link prediction. Current research has focused on static heterogeneous, homogeneous networks, and dynamic homogeneous networks. However, many existing graphs, such as citation and social networks, are heterogeneous. Therefore, it is still a great challenge to obtain heterogeneous information in a dynamic heterogeneous graph to assist node representation learning. In this paper, we propose a Dynamic HEterogeneous Network (DynHEN) for user-item bipartite networks. It is a discrete dynamic graph neural network model that can be used directly for node representation learning by utilizing dynamic heterogeneous graphs. Specifically, DynHEN takes a bipartite graph at each time step as input, gets the corresponding embedding by capturing the deep heterogeneous information of the nodes while fusing the temporal information. To illustrate the effectiveness of heterogeneous information for graph representation learning, we compare with the current SOTA methods in the two type experiments of link prediction and node classification, and achieve outstanding results.

DBGE: Employee Turnover Prediction Based on Dynamic Bipartite Graph Embedding

The issue of employee turnover is always critical for companies, and accurate predictions can help them prepare in time. Most past studies on employee turnover have focused on analyzing impact factors or using simple network centrality measures. In this paper, we study the problem from a completely new perspective by modeling users’ historical job records as a dynamic bipartite graph. Specifically, we propose a bipartite graph embedding method with temporal information called dynamic bipartite graph embedding (DBGE) to learn the vector representation of employees and companies. Our approach not only considers the relations between employees and companies but also incorporates temporal information embedded in consecutive work records. We first define the Horary Random Walk on a bipartite graph to generate a sequence for each vertex in chronological order. Then, we employ the skip-gram model to obtain a temporal low-dimensional vector representation for each vertex and apply machine learning methods to predict employee turnover behavior by combining embedded features with employees’ basic information. Experiments on a real-world dataset collected from one of China’s largest online professional social networks show that the features learned through DBGE can significantly improve turnover prediction performance. Moreover, experiments on public Amazon and Taobao datasets show that our approach achieves better performance in the link prediction and visualization task than other graph embedding methods that do not consider temporal information.

Input and State Observability of Network Systems With Time-Varying Topology

We aim to study the problem of reconstructing the initial state as well as the sequence of unknown inputs [input and state observability (ISO)] for linear network systems having time-varying topology. Evolution of such systems can be represented by a collection of graphs $\lbrace \mathcal {G}_{k}\rbrace$ . We find conditions under which the system with a pattern of fixed zeros imposed by $\lbrace \mathcal {G}_{k}\rbrace$ is ISO: 1) for almost all choices of edge weights in $\lbrace \mathcal {G}_{k}\rbrace$ (structural ISO) and 2) for all nonzero choices of edge weights in $\lbrace \mathcal {G}_{k}\rbrace$ (strongly structural ISO). We introduce two suitable descriptions of the whole collection of graphs $\lbrace \mathcal {G}_{k}\rbrace$ called the dynamic graph and dynamic bipartite graph. Two equivalent characterizations of structural ISO are then stated in terms of the existence of linking and matching of a suitable size in the dynamic graph and in the dynamic bipartite graph, respectively. For strongly structural ISO, we provide a sufficient condition and a necessary condition, both concerning the existence of a uniquely restricted matching of a suitable size in the dynamic bipartite graph and in a subgraph of it. When there is no direct feedthrough of the input on the measurements, the two conditions can be merged to give rise to a necessary and sufficient condition.

Incremental Maintenance of Maximal Bicliques in a Dynamic Bipartite Graph

We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1) Near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set, and an (2) Incremental algorithm for enumerating the change in the set of maximal bicliques. For the case when a constant number of edges are added to the graph, our algorithm is “change-sensitive”, i.e., its time complexity is proportional to the magnitude of change in the set of maximal bicliques. To our knowledge, this is the first incremental algorithm for enumerating maximal bicliques in a dynamic graph, with a provable performance guarantee. Our algorithm is easy to implement, and experimental results show that its performance exceeds that of baseline implementations by orders of magnitude.

Reconfigurable interlocking furniture

Reconfigurable assemblies consist of a common set of parts that can be assembled into different forms for use in different situations. Designing these assemblies is a complex problem, since it requires a compatible decomposition of shapes with correspondence across forms, and a planning of well-matched joints to connect parts in each form. This paper presents computational methods as tools to assist the design and construction of reconfigurable assemblies, typically for furniture. There are three key contributions in this work. First, we present the compatible decomposition as a weakly-constrained dissection problem, and derive its solution based on a dynamic bipartite graph to construct parts across multiple forms; particularly, we optimize the parts reuse and preserve the geometric semantics. Second, we develop a joint connection graph to model the solution space of reconfigurable assemblies with part and joint compatibility across different forms. Third, we formulate the backward interlocking and multi-key interlocking models, with which we iteratively plan the joints consistently over multiple forms. We show the applicability of our approach by constructing reconfigurable furniture of various complexities, extend it with recursive connections to generate extensible and hierarchical structures, and fabricate a number of results using 3D printing, 2D laser cutting, and woodworking.

Competition for foundation patronage and the differential effects of prestige on the grant market success of social movement organisations

Extant models of the financial patronage of Social Movement Organisations (SMOs) by private foundations exclusively use population density to account for competition. However, density fails to reveal how SMOs win grants whilst neglecting the strategic decision-making of foundation-investors. Here I recast patronage as a mutualistic network represented by a dynamic bipartite graph wherein SMOs and foundations cooperate across class whilst SMOs compete within class for financial support. A SMO's competitiveness rests with its position in a network-based prestige hierarchy and a foundation's propensity to invest is mediated by its structural position within the grant market. While previous research has predicted a positive monotonic relationship between status and patronage, using Stochastic Actor-Oriented Models I find a tendency for status-based disassortativity in the mutualistic system such that high-status foundations prefer to invest in low-status SMOs. I attribute this counterintuitive finding to foundations’ preferences for grantees that can innovate around social problems. Relative to their peripheral counterparts, well-funded SMOs may suffer a rigidity of goals due to the risk of alienating an existing support-base through organisational change. Data consist of 3261 grants given from 2003 to 2007 by 136 private foundations to 66 professional SMOs with nonprofit status loosely mobilised against the notion of anthropogenic climate change.

AN INDIVIDUAL-BASED NETWORKED MODEL WITH PROBABILISTIC RELOCATION OF PEOPLE AND VECTORS AMONG LOCATIONS FOR SIMULATING THE SPREAD OF INFECTIOUS DISEASES

Eubank et al. propose to study the spread of infectious disease in large urban environments using dynamic bipartite graph modeling the contact pattern, and computer simulations to estimate the evolution of epidemics. Eubank's approach requires a detailed knowledge of individuals, daily routine. In our work we would generalize the model by introducing a stochastic relocation of people and vectors among locations, thanks to distribution functions. Computer simulations are used to produce the infection and death processes. Finally, the paper presents two case studies. The first case study emphasizes the effect of using probabilistic relocation in a particular social network, while the second discusses how vector-borne diseases could be taken into account.

The modified Hopfield architecture applied in dynamic programming problems and bipartite graph optimization

Artificial neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements that are shown to be extremely effective in computation. This paper presents a modified Hopfield architecture, which has equilibrium points representing the solution of the problems considered, i.e, dynamic programming problems and bipartite graph optimization. The internal parameters of the network have been computed using the valid-subspace technique. This method allows us to define a subspace, which contains only those vectors that represent feasible solutions to the problem analyzed. It has also been demonstrated that with appropriately set parameters, the network confines its output to this subspace, thus ensuring convergence to a valid solution. Simulation results and comparative analyses with other methods are presented to validate the proposed approach.

On-Line Load Balancing and Network Flow

In this paper we study two problems that can be viewed as on-line games on a dynamic bipartite graph. The first problem is on-line load balancing with preemption. A centralized scheduler must assign tasks to servers, processing on-line a sequence of task arrivals and departures. Each task is restricted to run on some subset of the servers. The scheduler attempts to keep the load well-balanced. If preemptive reassignments are disallowed, Azar et al. [3] proved a lower bound of Ω(n 1/2 ) on the ratio between the maximum load achieved by an on-line algorithm and the optimum off-line maximum load. We show that this ratio can be greatly reduced by an efficient scheduler using only a small amount of rescheduling. We then apply these ideas to network flow. Cheriyan and Hagerup [6] introduced an on-line game on a bipartite graph as a fundamental step in improving algorithms for computing the maximum flow in networks. They described a randomized strategy to play the game. King et al. [11] studied a modified version of this game, called ``node kill,'' and gave a deterministic strategy. We obtain an improved deterministic algorithm for the node kill game (and hence for maximum flow) in all but the sparsest graphs. The running time achieved is O(mn log m/n n+n 2 log 2+e n) , compared with King et al.'s O(mn+n 2+e ) . These problems combine a demand for good competitive ratios with more traditional requirements of implementation efficiency. Our solutions deal with the tradeoffs between these measures.