Personalized PageRank Research Articles

Parallelizing approximate single-source personalized PageRank queries on shared memory

Given a directed graph G, a source node s, and a target node t, the personalized PageRank (PPR) $$\pi (s,t)$$ measures the importance of node t with respect to node s. In this work, we study the single-source PPR query, which takes a source node s as input and outputs the PPR values of all nodes in G with respect to s. The single-source PPR query finds many important applications, e.g., community detection and recommendation. Deriving the exact answers for single-source PPR queries is prohibitive, so most existing work focuses on approximate solutions. Nevertheless, existing approximate solutions are still inefficient, and it is challenging to compute single-source PPR queries efficiently for online applications. This motivates us to devise efficient parallel algorithms running on shared-memory multi-core systems. In this work, we present how to efficiently parallelize the state-of-the-art index-based solution FORA, and theoretically analyze the complexity of the parallel algorithms. Theoretically, we prove that our proposed algorithm achieves a time complexity of $$O(W/P+\log ^2{n})$$, where W is the time complexity of sequential FORA algorithm, P is the number of processors used, and n is the number of nodes in the graph. FORA includes a forward push phase and a random walk phase, and we present optimization techniques to both phases, including effective maintenance of active nodes, improving the efficiency of memory access, and cache-aware scheduling. Extensive experimental evaluation demonstrates that our solution achieves up to 37$$\times $$ speedup on 40 cores and 3.3$$\times $$ faster than alternatives on 40 cores. Moreover, the forward push alone can be used for local graph clustering, and our parallel algorithm for forward push is 4.8$$\times $$ faster than existing parallel alternatives.

Realtime top-k personalized pagerank over large graphs on GPUs

Given a graph G , a source node s ∈ G and a positive integer k , a top- k Personalized PageRank (PPR) query returns the k nodes with the highest PPR values with respect to s , where the PPR of a node v measures its relevance from the perspective of source s. Top- k PPR processing is a fundamental task in many important applications such as web search, social networks, and graph analytics. This paper aims to answer such a query in realtime , i.e., within less than 100ms, on an Internet-scale graph with billions of edges. This is far beyond the current state of the art, due to the immense computational cost of processing a PPR query. We achieve this goal with a novel algorithm kPAR, which utilizes the massive parallel processing power of GPUs. The main challenge in designing a GPU-based PPR algorithm lies in that a GPU is mainly a parallel computation device, whereas PPR processing involves graph traversals and value propagation operations, which are inherently sequential and memory-bound. Existing scalable PPR algorithms are mostly described as single-thread CPU solutions that are resistant to parallelization. Further, they usually involve complex data structures which do not have efficient adaptations on GPUs. kPAR overcomes these problems via both novel algorithmic designs (namely, adaptive forward push and inverted random walks ) and system engineering (e.g., load balancing) to realize the potential of GPUs. Meanwhile, kPAR provides rigorous guarantees on both result quality and worst-case efficiency. Extensive experiments show that kPAR is usually 10x faster than parallel adaptations of existing methods. Notably, on a billion-edge Twitter graph, kPAR answers a top-1000 PPR query in 42.4 milliseconds.

A Structural Result for Personalized PageRank and its Algorithmic Consequences

Many systems, such as the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example is Personalized PageRank (PPR), which assigns to each node v a vector whose i-th entry describes the importance of the i-th node from the perspective of v. PPR has proven useful in many applications, such as recommending who users should follow on social networks (if this i-th entry is large, v may be interested in following the i-th user). Unfortunately, computing n PPR vectors exactly for a graph of n nodes has complexity O(n^3), which is infeasible for many graphs of interest. In this work, we devise a scheme to estimate all n PPR vectors with bounded l_1 error and complexity O(n c ), where c < 2 depends on the degrees of the graph at hand, the desired error tolerance, and a parameter that defines PPR. This improves upon existing methods, the best of which have complexity O(n 2 łog n) in our setting. Our complexity guarantee holds with high probability, for certain choices of the PPR parameter, and for a certain class of random graphs (roughly speaking, the sparse directed configuration model with heavy-tailed in-degrees); our accuracy guarantee holds with probability 1 and for arbitrary graphs and PPR parameters. The complexity result arises as a consequence of our main (structural) result, which shows that the dimensionality of the set of PPR vectors scales sublinearly in n with high probability, for the same class of random graphs and for a notion of dimensionality similar to matrix rank. It is this coupling of the PPR vectors for the nodes on a common underlying graph that allows for estimating them faster. Hence, at a high level, our scheme is analogous to (but distinct from) low-rank matrix approximation. We also note that our scheme is similar to one that was proposed in [Jeh and Widom 2003] but lacked accuracy and complexity guarantees, so another contribution of our paper is to address this gap in the literature.

A Survey on Personalized PageRank Computation Algorithms

Personalized PageRank (PPR) is an important variation of PageRank, which is a widely applied popularity measure for Web search. Unlike the original PageRank, PPR is a node proximity measure that represents the degree of closeness among multiple nodes within a graph. It is also widely applied to diverse domains, such as information retrieval, recommendations, and knowledge discovery, due to its theoretical simplicity and flexibility. However, computing PPR in large graphs using naive algorithms such as iterative matrix multiplication and matrix inversion is not fast enough for many of these applications. Therefore, devising efficient PPR algorithms has been one of the most important subjects in large-scale graph processing. In this paper, we review the algorithms for efficient PPR computations, organizing them into five categories based on their core ideas. Along with detailed explanations including recent advances and their applications, we provide a multifaceted comparison of the algorithms.

Piping “personalized Page Rank” Algorithm from the Analytic Hierarchy Process(AHP) – A Case study

Piping “personalized Page Rank” Algorithm from the Analytic Hierarchy Process(AHP) – A Case study

Bootstrapped Graph Diffusions

Graph-based semi-supervised learning (SSL) algorithms predict labels for all nodes based on provided labels of a small set of seed nodes. Classic methods capture the graph structure through some underlying diffusion process that propagates through the graph edges. Spectral diffusion, which includes personalized page rank and label propagation, propagates through random walks. Social diffusion propagates through shortest paths. These diffusions are linear in the sense of not distinguishing between contributions of few "strong" relations or many "weak'' relations. Recent methods such as node embeddings and graph convolutional networks (GCN) attained significant gains in quality for SSL tasks. These methods vary on how the graph structure, seed label information, and other features are used, but do share a common thread of nonlinearity that suppresses weak relations and re-enforces stronger ones. Aiming for quality gain with more scalable methods, we revisit classic linear diffusion methods and place them in a self-training framework. The resulting bootstrapped diffusions are nonlinear in that they re-enforce stronger relations, as with the more complex methods. Surprisingly, we observe that SSL with bootstrapped diffusions not only significantly improves over the respective non-bootstrapped baselines but also outperform state-of-the-art SSL methods. Moreover, since the self-training wrapper retains the scalability of the base method, we obtain both higher quality and better scalability.

Bootstrapped Graph Diffusions

Graph-based semi-supervised learning (SSL) algorithms predict labels for all nodes based on provided labels of a small set of seed nodes. Classic methods capture the graph structure through some underlying diffusion process that propagates through the graph edges. Spectral diffusion, which includes personalized page rank and label propagation, propagates through random walks. Social diffusion propagates through shortest paths. These diffusions are linear in the sense of not distinguishing between contributions of few "strong" relations or many "weak" relations. Recent methods such as node embeddings and graph convolutional networks (GCN) attained significant gains in quality for SSL tasks. These methods vary on how the graph structure, seed label information, and other features are used, but do share a common thread of nonlinearity that suppresses weak relations and reenforces stronger ones. Aiming for quality gain with more scalable methods, we revisit classic linear diffusion methods and place them in a self-training framework. The resulting bootstrapped diffusions are nonlinear in that they re-enforce stronger relations, as with the more complex methods. Surprisingly, we observe that SSL with bootstrapped diffusions not only significantly improves over the respective non-bootstrapped baselines but also outperform state-of-the-art SSL methods. Moreover, since the self-training wrapper retains the scalability of the base method, we obtain both higher quality and better scalability.

Mining heterogeneous terrorist attack network using personalized PageRank

Mining heterogeneous terrorist attack network using personalized PageRank

An intelligent approach to design of E-Commerce metasearch and ranking system using next-generation big data analytics

The purpose of this research work is to explore various limitations of conventional search and page ranking systems in an E-Commerce environment. The key objective is to assist customers in making an online purchase decision by providing personalized page ranking order of E-Commerce web links in response to E-Commerce query by analyzing the customer preferences and browsing behavior. This research work first employs an orderly and category wise literature review. The findings reveal that conventional search systems have not evolved to support big data analysis as required by modern E-Commerce environment. This work aims to develop and implement second-generation HDFS- MapReduce based innovative page ranking algorithm, i.e. Relevancy Vector (RV) algorithm. This research equips the customer with a robust metasearch tool, i.e. IMSS-AE to easily understand personalized search requirements and purchase preferences of customer. The proposed approach can well satisfy all critical parameters such as scalability, partial failure support, extensibility as expected from next-generation big data processing systems. An extensive and comprehensive experimental evaluation shows the efficiency and effectiveness of proposed RV page ranking algorithm and IMSS-AE tool over and above other popular search engines.

An Integrated Approach for Identifying Topical Experts in Microblogs

In the recent times, usage of Social Networking and Micro-blogging sites by the people has increased exponentially. Identifying the right topical experts in a particular domain is a tedious task as huge amount of data being processed. The existing approaches limited in accuracy, which leads to providing irrelevant results. Furthermore, few deal with syntactic similarity and not the semantic analysis. In this paper, we introduce an integrated approach which combines focus crawling, semantic analysis and personalized page ranking algorithm to provide top-k ranked results for a topic. Twitter data is taken as input and the twitter lists are extracted to construct the endorsement graph. Links in the graph are weighted using personalized PageRank. Since social network itself has a huge chunk of data, it is obvious for the endorsement graph to have quite large number of nodes. To increase the scalability and performance, focused crawling is applied before the PageRank calculation. The semantic similarity is calculated between the given input query and the Twitter list name/description to yield better results. We compare the results with Twitter’s WTF (Who To Follow) algorithm to showcase that the proposed system provides more obvious and serendipitous topical experts.

Collective List-Only Entity Linking: A Graph-Based Approach

List-only entity linking (EL) is the task of mapping ambiguous mentions in texts to target entities in a group of entity lists. Different from traditional EL task, which leverages rich semantic relatedness in knowledge bases to improve linking accuracy, the list-only EL can merely take advantage of co-occurrences information in entity lists. State-of-the-art work utilizes co-occurrences information to enrich entity descriptions which are further used to calculate local compatibility between mentions and entities to determine results. Nonetheless, entity coherence is also deemed to play an important part in EL, which is yet currently neglected. In this paper, in addition to local compatibility, we take into account global coherence among entities. Specifically, we propose to harness co-occurrences in entity lists for mining both explicit and implicit entity relations. The relations are then integrated into an entity graph, on which personalized PageRank is incorporated to compute entity coherence. The final results are derived by combining local mention-entity similarity and global entity coherence. The experimental studies validate the superiority of our method. Our proposal not only improves the performance of the list-only EL, but also opens up the bridge between the list-only EL and conventional EL solutions.

A novel framework to facilitate personalized web search in a dual mode

Now days, web search engines provide good services in terms of retrieval and presentation of the information to the user. A foremost difficulty in the modern and ever growing web is the lack of user interest adaption in the process of web search. All users are presented with the same set of search engine result pages (SERPs) for a given input query string, since it follows the keyword based search. The limitation of keyword based search is (i) uncertain user needs and (ii) improper query selection. If the programmer is searching for a query “switch”, it refers to the switch statement of a programming language and for an electrical engineer, the context of search is the physical house hold switch component. In addition to that a user may fall short in choosing the proper query for search that best articulate their information need. Hence, it is evident that keyword searches have tough time to distinguish the user context over the query. A typical approach to focus on this challenge is a personalized web search strategy where the results are retrieved based on the user interest and preferences. The three different major search modules are: (i) building user profiles (ii) re-ranking the SERPs in personal mode and (iii) re-ranking the SERPs in group mode. The proposed work stands for contributing in the field of user profile construction and personalized page ranking. A new method of user model representation termed as Preference Network is constructed. The proposed system can work in both initialization and maintenance mode to build a new or update an existing model. Both the short term and long term interest are utilized to rank the SERPs. The user interest score and group interest score are computed dynamically.

Parallel personalized pagerank on dynamic graphs

Personalized PageRank (PPR) is a well-known proximity measure in graphs. To meet the need for dynamic PPR maintenance, recent works have proposed a local update scheme to support incremental computation. Nevertheless, sequential execution of the scheme is still too slow for highspeed stream processing. Therefore, we are motivated to design a parallel approach for dynamic PPR computation. First, as updates always come in batches, we devise a batch processing method to reduce synchronization cost among every single update and enable more parallelism for iterative parallel execution. Our theoretical analysis shows that the parallel approach has the same asymptotic complexity as the sequential approach. Second, we devise novel optimization techniques to effectively reduce runtime overheads for parallel processes. Experimental evaluation shows that our parallel algorithm can achieve orders of magnitude speedups on GPUs and multi-core CPUs compared with the state-of-the-art sequential algorithm.

Local Higher-Order Graph Clustering.

Local graph clustering methods aim to find a cluster of nodes by exploring a small region of the graph. These methods are attractive because they enable targeted clustering around a given seed node and are faster than traditional global graph clustering methods because their runtime does not depend on the size of the input graph. However, current local graph partitioning methods are not designed to account for the higher-order structures crucial to the network, nor can they effectively handle directed networks. Here we introduce a new class of local graph clustering methods that address these issues by incorporating higher-order network information captured by small subgraphs, also called network motifs. We develop the Motif-based Approximate Personalized PageRank (MAPPR) algorithm that finds clusters containing a seed node with minimal motif conductance, a generalization of the conductance metric for network motifs. We generalize existing theory to prove the fast running time (independent of the size of the graph) and obtain theoretical guarantees on the cluster quality (in terms of motif conductance). We also develop a theory of node neighborhoods for finding sets that have small motif conductance, and apply these results to the case of finding good seed nodes to use as input to the MAPPR algorithm. Experimental validation on community detection tasks in both synthetic and real-world networks, shows that our new framework MAPPR outperforms the current edge-based personalized PageRank methodology.

Quantifying the web browser ecosystem

Contrary to the assumption that web browsers are designed to support the user, an examination of a 900,000 distinct PCs shows that web browsers comprise a complex ecosystem with millions of addons collaborating and competing with each other. It is possible for addons to “sneak in” through third party installations or to get “kicked out” by their competitors without user involvement. This study examines that ecosystem quantitatively by constructing a large-scale graph with nodes corresponding to users, addons, and words (terms) that describe addon functionality. Analyzing addon interactions at user level using the Personalized PageRank (PPR) random walk measure shows that the graph demonstrates ecological resilience. Adapting the PPR model to analyzing the browser ecosystem at the level of addon manufacturer, the study shows that some addon companies are in symbiosis and others clash with each other as shown by analyzing the behavior of 18 prominent addon manufacturers. Results may herald insight on how other evolving internet ecosystems may behave, and suggest a methodology for measuring this behavior. Specifically, applying such a methodology could transform the addon market.

Supporting inter-topic entity search for biomedical Linked Data based on heterogeneous relationships

ObjectiveThe keyword-based entity search restricts search space based on the preference of search. When given keywords and preferences are not related to the same biomedical topic, existing biomedical Linked Data search engines fail to deliver satisfactory results. This research aims to tackle this issue by supporting an inter-topic search—improving search with inputs, keywords and preferences, under different topics. MethodsThis study developed an effective algorithm in which the relations between biomedical entities were used in tandem with a keyword-based entity search, Siren. The algorithm, PERank, which is an adaptation of Personalized PageRank (PPR), uses a pair of input: (1) search preferences, and (2) entities from a keyword-based entity search with a keyword query, to formalize the search results on-the-fly based on the index of the precomputed Individual Personalized PageRank Vectors (IPPVs). ResultsOur experiments were performed over ten linked life datasets for two query sets, one with keyword-preference topic correspondence (intra-topic search), and the other without (inter-topic search). The experiments showed that the proposed method achieved better search results, for example a 14% increase in precision for the inter-topic search than the baseline keyword-based search engine. ConclusionThe proposed method improved the keyword-based biomedical entity search by supporting the inter-topic search without affecting the intra-topic search based on the relations between different entities.

Toward Efficient Hub-Less Real Time Personalized PageRank

In the era of big data, reduced models capable of reducing big data graph to estimate personalized PageRank are limited. Personalized PageRank is a page rank calculation where random jumps are only allowed to a subset of start nodes. The resources of current process of calculation of personalized PageRank are highly prohibitive, thus in this paper we propose a novel fast accurate and less resource intensive algorithm to the personalized PageRank problem. FAST Personalized PageRank is utilized to find the target node set. Using the mentioned target set, the algorithm gives an estimation of the closeness of any pair of nodes in the graph. As the time taken by the estimation of personalized PageRank is directly proportional to the network size, in this paper a node reduction method is used to prune the graph. In this pruning model, most popular nodes also known as hubs are found using personalized page vector. To decrease the entropy and reduce the number of alternate paths to the target nodes, popular nodes are identified and flagged. The flagged nodes are, then, given a lower priority in the computation. This way the redundant path will being ignored in the computation process. After pruning the graph, estimation results achieve an improved time complexity. In our experiment, we compare our result with the benchmark FAST personalized PageRank approach. Our algorithm significantly reduces the computation time and outperforms the benchmark FAST personalized PageRank algorithm in highly dense graphs.

HubPPR

Personalized PageRank (PPR) computation is a fundamental operation in web search, social networks, and graph analysis. Given a graph G , a source s, and a target t, the PPR query Π( s, t ) returns the probability that a random walk on G starting from s terminates at t. Unlike global PageRank which can be effectively pre-computed and materialized, the PPR result depends on both the source and the target, rendering results materialization infeasible for large graphs. Existing indexing techniques have rather limited effectiveness; in fact, the current state-of-the-art solution, BiPPR, answers individual PPR queries without pre-computation or indexing, and yet it outperforms all previous index-based solutions. Motivated by this, we propose HubPPR, an effective indexing scheme for PPR computation with controllable tradeoffs for accuracy, query time, and memory consumption. The main idea is to pre-compute and index auxiliary information for selected hub nodes that are often involved in PPR processing. Going one step further, we extend HubPPR to answer top- k PPR queries, which returns the k nodes with the highest PPR values with respect to a source s , among a given set T of target nodes. Extensive experiments demonstrate that compared to the current best solution BiPPR, HubPPR achieves up to 10x and 220x speedup for PPR and top- k PPR processing, respectively, with moderate memory consumption. Notably, with a single commodity server, HubPPR answers a top- k PPR query in seconds on graphs with billions of edges, with high accuracy and strong result quality guarantees.

A local dynamic method for tracking communities and their evolution in dynamic networks

The analysis of communities and their evolutionary behaviors in dynamic networks is a challenging topic. Although a growing body of work on this topic is emerging, there are few methods which can reveal and track meaningful communities over time and can also deal with large networks efficiently. In this paper, we propose a method to track dynamic communities and their evolutionary behaviors. The main idea behind our method is to discover dynamic communities by exploring the local views of nodes that change. Moreover, based on the discovered dynamic communities, the global community structure can be derived by updating the historical community structure and the evolutionary behaviors of communities can also be tracked. To discover the dynamic communities, we apply the technique of approximate personalized PageRank vector; to track the evolutionary behaviors of the communities, we introduce a partial evolutionary graph. We compare the proposed method with several existing methods by performing experiments on nine synthetic networks and one real network. The experimental results show that the proposed method performs well on discovering communities as well as tracking their evolution in dynamic networks, and spends much less running time than the existing methods.

Optimized relativity search: node reduction in personalized page rank estimation for large graphs

This paper proposes an algorithm called optimized relativity search to reduce the number of nodes in a graph when attempting to decrease the running time for personalized page rank (PPR) estimation. Even though similar estimations have been done, this method significantly increases the speed of computation, making it a feasible candidate for large graph solutions, such as search engines and friend recommendation techniques used in social media. In this study, the weighted page rank method was combined with the Monte-Carlo technique and a local update algorithm over a reduced map space; this algorithm was developed to achieve a more accurate and faster search method than FAST PPR. The experimental results showed that for nodes with a high degree of incoming nodes, the speed of estimation was twice as fast compared to FAST PPR, at the expense of a little accuracy.