Efficient $m$-closest entity matching over heterogeneous information networks

Highlights

• A novel m-closest entity matching problem over HINs is devised.

• Pruning abilities at both the non-spatial and spatial layers are explored.

• Our approach can achieve much better performance than the baseline methods.

Abstract

This work investigates a novel $m$-closest entity ($m$CE) matching problem over geographic heterogeneous information networks (Geo-HINs). That is, given a Geo-HIN $G$ and $m$ query graphs $\{q_1,q_2,\dots ,q_m\}$, $m$CE matching aims to find a group of geographic entities (geo-entities) whose patterns match the query graphs $\{q_1,q_2,\dots ,q_m\}$ correspondingly, for which the maximum distance between any geo-entity pair (i.e., the diameter) in the group is minimized. As a fundamental problem, the $m$CE matching can be applied for many scenarios, e.g., travel itinerary recommendation and city planning. The existing works have not simultaneously considered the characteristics of patterns matching and spatial search so that they cannot solve our problem, which is computationally expensive. To solve this problem efficiently, we propose a unified framework named $Fuzzy-Exact$ framework to process entity matching and spatial search comprehensively, in which pruning abilities at non-spatial and spatial layers are cooperatively explored. Two mutually adaptive auxiliary data structures named $Arc-Tree$ and $Arc-Forest$ are devised to maintain the intermediate search results which are exploited to enhance the search process between non-spatial and spatial layers. Experimental results demonstrate that our algorithm can outperform the baseline methods by 2 orders of magnitude on runtime.

Introduction

Heterogeneous information networks (HINs) [1] are formed by multiple typed entities and multiple typed links to model various data, such as social networks, biology, and knowledge graphs. With the prevalence of location based service, plenty of entities in HINs are generated with location related links to identify their geographic info. For example, restaurants or hotels (entities) in Yelp network usually associate with location attributes to store their geographic coordinates. In social networks, such as Twitter, user entities usually contain check-in info and the micro-blogs are labeled with geo-tags. A Geo-HIN is a HIN, where at least one type of entity have geographic location attribute (named geo-entity). Fig. 1 shows a Geo-HIN example of Yelp network, which consists of eight geo-entities (i.e., $e_1,\dots ,e_8$). Each geo-entity $e_i$ links to node $l_i$ denoting the location of $e_i$. Here a geo-entity $e_i$ can be restaurant, hotel, park, or any object with location info. Besides, there are several types of non-geographic entities (non-geo-entities) in Fig. 1, such as user, feature, grade and so on. In this paper, we study the $m$-closest entity ($m$CE) matching problem over Geo-HINs. Below is a motivating example.

Example 1

Fig. 1 illustrates a Geo-HIN of Yelp network. $u_1$ is a customer of Yelp who requests a travel itinerary planning for an unfamiliar city. Fig. 2 shows three query graphs $\{q_1,q_2,q_3\}$ to express the requirements of $u_1$. In specific, the query graphs contain following contents “find a kids-friendly ($t_1$) restaurant $e_x$ which is rated with five stars ($g_1$) and marked by seafood ($f_1$)”, “find a kids-friendly ($t_1$) hotel $e_y$ which has been booked by $u_1$'s friend $u_2$ and tagged with swimming pool ($f_2$)”, and “find a kids-friendly ($t_1$) and indoor ($f_3$) scenic spot $e_z$ that has been visited by $u_1$'s friend $u_2$ and is rated with five stars”. Through graph matching, we have $e_x=\{e_2,e_5\}$, $e_y=\left\{e_3\right\}$, and $e_z=\left\{e_4\right\}$. Among the combination results of $e_x$, $e_y$, and $e_z$ (i.e., $\{e_2,e_3,e_4\}$, $\{e_5,e_3,e_4\}$), $m$CE may recommend $\{e_5,e_3,e_4\}$ to $u_1$ as the geo-diameter is minimized.

The $m$-closest entity ($m$CE) matching problem over Geo-HINs can be further formulate as: given a Geo-HIN $G$ and $m$ query graphs in $\{q_1,q_2,\dots ,q_m\}$ where each query graph describes the pattern of a geo-entity, the $m$CE matching aims to find a group of geo-entities matching with the patterns of query graphs $\{q_1,q_2,\dots ,q_m\}$ correspondingly such that the diameter of the geo-entity group is minimized. Here the diameter of a group (aka geo-diameter) is defined as the largest geo-distance between any pair of geo-entities in the group.

Applications. The $m$CE matching can be used in many applications. As discussed in Example 1, it provides considerate travel itinerary planning to meet sophisticated requirements from users. This function is popular in tourist oriented APPs such as Wanderlog and Ctrip. Besides, for city planning, the locations of public facilities should be carefully considered. Given the specified public facilities, $m$CE matching can be used to evaluate the setting according to the POI group within a smallest range. Similar to travel planning, $m$CE matching can also be used to evaluate Internet of Things (IoT) system and location-based service system for recommending proper objects or users. Moreover, it is observed that when each query graph is as simplified as possible, e.g., just including geo-entity, $m$CE matching problem is equal to $m$CK query problem [2]. Thus, $m$CE matching may extend the applications of the $m$CK query.

Existing Studies. To the best of our knowledge, this is the first work to study the $m$-closest entities ($m$CE) matching over Geo-HINs. The most related work to $m$CE matching is $m$-closest keywords ($m$CK) query [2], an important type of the spatial keyword query studied in several existing works (e.g.,[2], [3], [4]). However, $m$CK query is located at the spatial database, which aims to find a group of objects that cover all keywords and guarantee the geo-diameter of the group is minimized. Our $m$CE matching is a more complex problem than the existing $m$CK query. The reason is that the $m$CK query solves the $m$-closest problem involving keywords and locations, and $m$CE matching need to address the complex relations between subgraphs matching and locations. For instance, in Example 1, $m$CE will return a POI that contains a kid-friendly swimming pool while $m$CK can only ensure the POI contains a swimming pool and is a kid-friendly place. Note that the relationship between the swimming pool and kid-friendly keywords cannot be represented by $m$CK, which will lead to the resulting swimming pool may be for adults only and it is not expected by the users. Moreover, all keywords are independent and the relationship between them cannot be explicitly specified in the $m$CK query, which leads to it cannot precisely represent the user demand and the query answer may deviate far from user expectation. In regard to this limitation, we will empirically discuss in Section 5.2. In contrast to the $m$CK, $m$CE matching can provide more semantic information and make query requirements more general. Thus, it is necessary to pursuit ingenious method to integrate the process of subgraph matching and spatial search for $m$CE matching.

Challenges and Our Solution. The challenges lie in two folds. The first challenge is that the pattern matching of entities and $m$-closest searching among candidate entities are two relatively independent tasks. To improve query efficiency, a novel cooperated framework should be devised to exploit the intermediate search results of these two search processes. However, the related existing studies mainly focus on the queries that have both textual and spatial constraints [5], [6], [7], [8], [9], [10]. To the best of our knowledge, this is the first work to study the query that considers both entity pattern matching and spatial constraints. Compared with keywords, entity pattern matching can describe richer semantic information, while it also brings higher query complexity. Thus, it is important but hard to efficiently answer the queries that consider both entity pattern matching and spatial constraints.

The second challenge is that on account of subgraph matching and $m$-closest search which are both NP-hard [11] [2]. The search space will increase exponentially with the increasing number of vertices in query graphs, and no algorithm that can find the exact answer in polynomial time. In existing studies, the general solution is to return an approximate answer to avoid the large time cost [2], [12], [13], [14], [15]. However, for approximate solutions, we may sacrifice some properties on the result such as a relaxed spatial constraint or partially matched entities. Moreover, the result of early termination of the exact algorithm in the hard case can be considered as an approximate solution. As the $m$CE problem is studied for the first time, the investigation of exact algorithm is significant.

To address this new and practical problem, we propose an efficient $Fuzzy-Exact$ framework to process entity matching and spatial search comprehensively. The cooperation of pruning strategies at both the non-spatial and spatial layers are explored to improve the efficiency of $m$CE matching. Specifically, we design a fuzzy mechanism to avoid exhaustive checking whether each geo-entity is actually eligible. Moreover, two auxiliary data structures named $Arc-Tree$ and $Arc-Forest$ are introduced to maintain the intermediate search results and then facilitate the search process.

Contributions. The principal contributions in this paper are summarized as follows.

• To our best knowledge, this is the first attempt to investigate the $m$-closest entity matching problem over geographic heterogeneous information networks. Inspired by real-world applications, $m$CE matching considers both the pattern matching and spatial search, which makes the problem more general than $m$CK.

• A novel $Fuzzy-Exact$ framework is proposed, where the pruning abilities at non-spatial and spatial layers are cooperatively explored by integrating a fuzzy mechanism. Two mutually adaptive data structures named $Arc-Tree$ and $Arc-Forest$ are introduced to enhance the search process and make the framework more scalable.

• Extensive experimental results demonstrate the efficiency and scalability of the proposed framework on five real-world datasets with up to ten million vertices. Our techniques can achieve 2 orders of magnitude improvements on runtime compared with baselines.