M. Narasimha Murty

Sambaran Bandyopadhyay, Lokesh N, M. N. Murty

Attributed network embedding has received much interest from the research community as most of the networks come with some content in each node, which is also known as node attributes. Existing attributed network approaches work well when the network is consistent in structure and attributes, and nodes behave as expected. But real world networks often have anomalous nodes. Typically these outliers, being relatively unexplainable, affect the embeddings of other nodes in the network. Thus all the downstream network mining tasks fail miserably in the presence of such outliers. Hence an integrated approach to detect anomalies and reduce their overall effect on the network embedding is required. Towards this end, we propose an unsupervised outlier aware network embedding algorithm (ONE) for attributed networks, which minimizes the effect of the outlier nodes, and hence generates robust network embeddings. We align and jointly optimize the loss functions coming from structure and attributes of the network. To the best of our knowledge, this is the first generic network embedding approach which incorporates the effect of outliers for an attributed network without any supervision. We experimented on publicly available real networks and manually planted different types of outliers to check the performance of the proposed algorithm. Results demonstrate the superiority of our approach to detect the network outliers compared to the state-of-the-art approaches. We also consider different downstream machine learning applications on networks to show the efficiency of ONE as a generic network embedding technique. The source code is made available at https://github.com/sambaranban/ONE.

Govind Sharma, Aditya Challa, Paarth Gupta et al.

The problem of link prediction is of active interest. The main approach to solving the link prediction problem is based on heuristics such as Common Neighbors (CN) -- more number of common neighbors of a pair of nodes implies a higher chance of them getting linked. In this article, we investigate this problem in the presence of higher-order relations. Surprisingly, it is found that CN works very well, and even better in the presence of higher-order relations. However, as we prove in the current work, this is due to the CN-heuristic overestimating its prediction abilities in the presence of higher-order relations. This statement is proved by considering a theoretical model for higher-order relations and by showing that AUC scores of CN are higher than can be achieved from the model. Theoretical justification in simple cases is also provided. Further, we extend our observations to other similar link prediction algorithms such as Adamic Adar. Finally, these insights are used to propose an adjustment factor by taking into conscience that a random graph would only have a best AUC score of 0.5. This adjustment factor allows for a better estimation of generalization scores.

Shyni Thomas, M. Narasimha Murty

Multi Agent Path Finding (MAPF) requires identification of conflict free paths for agents which could be point-sized or with dimensions. In this paper, we propose an approach for MAPF for spatially-extended agents. These find application in real world problems like Convoy Movement Problem, Train Scheduling etc. Our proposed approach, Decentralised Multi Agent Path Finding (DeMAPF), handles MAPF as a sequence of pathplanning and allocation problems which are solved by two sets of agents Travellers and Routers respectively, over multiple iterations. The approach being decentralised allows an agent to solve the problem pertinent to itself, without being aware of other agents in the same set. This allows the agents to be executed on independent machines, thereby leading to scalability to handle large sized problems. We prove, by comparison with other distributed approaches, that the approach leads to a faster convergence to a conflict-free solution, which may be suboptimal, with lesser memory requirement.

Shyni Thomas, Dipti Deodhare, M. N. Murty

Path finding problems involve identification of a plan for conflict free movement of agents over a common road network. Most approaches to this problem handle the agents as point objects, wherein the size of the agent is significantly smaller than the road on which it travels. In this paper, we consider spatially extended agents which have a size comparable to the length of the road on which they travel. An optimal multi agent path finding approach for spatially-extended agents was proposed in the eXtended Conflict Based Search (XCBS) algorithm. As XCBS resolves only a pair of conflicts at a time, it results in deeper search trees in case of cascading or multiple (more than two agent) conflicts at a given location. This issue is addressed in eXtended Conflict Based Search with Awareness (XCBS-A) in which an agent uses awareness of other agents' plans to make its own plan. In this paper, we explore XCBS-A in greater detail, we theoretically prove its completeness and empirically demonstrate its performance with other algorithms in terms of variances in road characteristics, agent characteristics and plan characteristics. We demonstrate the distributive nature of the algorithm by evaluating its performance when distributed over multiple machines. XCBS-A generates a huge search space impacting its efficiency in terms of memory; to address this we propose an approach for memory-efficiency and empirically demonstrate the performance of the algorithm. The nature of XCBS-A is such that it may lead to suboptimal solutions, hence the final contribution of this paper is an enhanced approach, XCBS-Local Awareness (XCBS-LA) which we prove will be optimal and complete.

Sambaran Bandyopadhyay, Saley Vishal Vivek, M. N. Murty

Network (or graph) embedding is the task to map the nodes of a graph to a lower dimensional vector space, such that it preserves the graph properties and facilitates the downstream network mining tasks. Real world networks often come with (community) outlier nodes, which behave differently from the regular nodes of the community. These outlier nodes can affect the embedding of the regular nodes, if not handled carefully. In this paper, we propose a novel unsupervised graph embedding approach (called DMGD) which integrates outlier and community detection with node embedding. We extend the idea of deep support vector data description to the framework of graph embedding when there are multiple communities present in the given network, and an outlier is characterized relative to its community. We also show the theoretical bounds on the number of outliers detected by DMGD. Our formulation boils down to an interesting minimax game between the outliers, community assignments and the node embedding function. We also propose an efficient algorithm to solve this optimization framework. Experimental results on both synthetic and real world networks show the merit of our approach compared to state-of-the-arts.

Sambaran Bandyopadhyay, Manasvi Aggarwal, M. Narasimha Murty

Graph neural networks get significant attention for graph representation and classification in machine learning community. Attention mechanism applied on the neighborhood of a node improves the performance of graph neural networks. Typically, it helps to identify a neighbor node which plays more important role to determine the label of the node under consideration. But in real world scenarios, a particular subset of nodes together, but not the individual pairs in the subset, may be important to determine the label of the graph. To address this problem, we introduce the concept of subgraph attention for graphs. On the other hand, hierarchical graph pooling has been shown to be promising in recent literature. But due to noisy hierarchical structure of real world graphs, not all the hierarchies of a graph play equal role for graph classification. Towards this end, we propose a graph classification algorithm called SubGattPool which jointly learns the subgraph attention and employs two different types of hierarchical attention mechanisms to find the important nodes in a hierarchy and the importance of individual hierarchies in a graph. Experimental evaluation with different types of graph classification algorithms shows that SubGattPool is able to improve the state-of-the-art or remains competitive on multiple publicly available graph classification datasets. We conduct further experiments on both synthetic and real world graph datasets to justify the usefulness of different components of SubGattPool and to show its consistent performance on other downstream tasks.

Sambaran Bandyopadhyay, Manasvi Aggarwal, M. Narasimha Murty

Deep representation learning on non-Euclidean data types, such as graphs, has gained significant attention in recent years. Invent of graph neural networks has improved the state-of-the-art for both node and the entire graph representation in a vector space. However, for the entire graph representation, most of the existing graph neural networks are trained on a graph classification loss in a supervised way. But obtaining labels of a large number of graphs is expensive for real world applications. Thus, we aim to propose an unsupervised graph neural network to generate a vector representation of an entire graph in this paper. For this purpose, we combine the idea of hierarchical graph neural networks and mutual information maximization into a single framework. We also propose and use the concept of periphery representation of a graph and show its usefulness in the proposed algorithm which is referred as GraPHmax. We conduct thorough experiments on several real-world graph datasets and compare the performance of GraPHmax with a diverse set of both supervised and unsupervised baseline algorithms. Experimental results show that we are able to improve the state-of-the-art for multiple graph level tasks on several real-world datasets, while remain competitive on the others.

Sambaran Bandyopadhyay, Kishalay Das, M. Narasimha Murty

Network representation learning and node classification in graphs got significant attention due to the invent of different types graph neural networks. Graph convolution network (GCN) is a popular semi-supervised technique which aggregates attributes within the neighborhood of each node. Conventional GCNs can be applied to simple graphs where each edge connects only two nodes. But many modern days applications need to model high order relationships in a graph. Hypergraphs are effective data types to handle such complex relationships. In this paper, we propose a novel technique to apply graph convolution on hypergraphs with variable hyperedge sizes. We use the classical concept of line graph of a hypergraph for the first time in the hypergraph learning literature. Then we propose to use graph convolution on the line graph of a hypergraph. Experimental analysis on multiple real world network datasets shows the merit of our approach compared to state-of-the-arts.

Sambaran Bandyopadhyay, Anirban Biswas, M. N. Murty et al.

Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis community, which have mostly been unexplored in the network embedding space. For applications such as link prediction in homogeneous networks, vector representation (i.e., embedding) of an edge is derived heuristically just by using simple aggregations of the embeddings of the end vertices of the edge. Clearly, this method of deriving edge embedding is suboptimal and there is a need for a dedicated unsupervised approach for embedding edges by leveraging edge properties of the network. Towards this end, we propose a novel concept of converting a network to its weighted line graph which is ideally suited to find the embedding of edges of the original network. We further derive a novel algorithm to embed the line graph, by introducing the concept of collective homophily. To the best of our knowledge, this is the first direct unsupervised approach for edge embedding in homogeneous information networks, without relying on the node embeddings. We validate the edge embeddings on three downstream edge mining tasks. Our proposed optimization framework for edge embedding also generates a set of node embeddings, which are not just the aggregation of edges. Further experimental analysis shows the connection of our framework to the concept of node centrality.

Vijaikumar M, Shirish Shevade, M N Murty

Cross-Domain Collaborative Filtering (CDCF) provides a way to alleviate data sparsity and cold-start problems present in recommendation systems by exploiting the knowledge from related domains. Existing CDCF models are either based on matrix factorization or deep neural networks. Either of the techniques in isolation may result in suboptimal performance for the prediction task. Also, most of the existing models face challenges particularly in handling diversity between domains and learning complex non-linear relationships that exist amongst entities (users/items) within and across domains. In this work, we propose an end-to-end neural network model -- NeuCDCF, to address these challenges in a cross-domain setting. More importantly, NeuCDCF follows a wide and deep framework and it learns the representations combinedly from both matrix factorization and deep neural networks. We perform experiments on four real-world datasets and demonstrate that our model performs better than state-of-the-art CDCF models.

Anubhav Gupta, M. Narasimha Murty

Ranking in bibliographic information networks is a widely studied problem due to its many applications such as advertisement industry, funding, search engines, etc. Most of the existing works on ranking in bibliographic information network are based on ranking of research papers and their authors. But the bibliographic information network can be used for solving other important problems as well. The KDD Cup $2016$ competition considers one such problem, which is to measure the impact of research institutions, i.e. to perform ranking of research institutions. The competition took place in three phases. In this paper, we discuss our solutions for ranking institutions in each phase. We participated under team name "anu@TASL" and our solutions achieved the average NDCG@$20$ score of $0.7483$, ranking in eleventh place in the contest.

Geetha Manjunatha, M Narasimha Murty, Dinkar Sitaram

Most enterprise data is distributed in multiple relational databases with expert-designed schema. Using traditional single-table machine learning techniques over such data not only incur a computational penalty for converting to a 'flat' form (mega-join), even the human-specified semantic information present in the relations is lost. In this paper, we present a practical, two-phase hierarchical meta-classification algorithm for relational databases with a semantic divide and conquer approach. We propose a recursive, prediction aggregation technique over heterogeneous classifiers applied on individual database tables. The proposed algorithm was evaluated on three diverse datasets, namely TPCH, PKDD and UCI benchmarks and showed considerable reduction in classification time without any loss of prediction accuracy.