82 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA …nikos/TKDE_LKS.pdf · The ﬁrst challenge of our LKS...

Location Aware Keyword Query SuggestionBased on Document Proximity

Shuyao Qi, Dingming Wu, and Nikos Mamoulis

Abstract—Keyword suggestion in web search helps users to access relevant information without having to know how to preciselyexpress their queries. Existing keyword suggestion techniques do not consider the locations of the users and the query results; i.e.,the spatial proximity of a user to the retrieved results is not taken as a factor in the recommendation. However, the relevance of searchresults in many applications (e.g., location-based services) is known to be correlated with their spatial proximity to the query issuer. Inthis paper, we design a location-aware keyword query suggestion framework. We propose a weighted keyword-document graph, whichcaptures both the semantic relevance between keyword queries and the spatial distance between the resulting documents and the userlocation. The graph is browsed in a random-walk-with-restart fashion, to select the keyword queries with the highest scores assuggestions. To make our framework scalable, we propose a partition-based approach that outperforms the baseline algorithm by up toan order of magnitude. The appropriateness of our framework and the performance of the algorithms are evaluated using real data.

Index Terms—Query suggestion, spatial databases

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1 INTRODUCTION

KEYWORD suggestion (also known as query suggestion)has become one of the most fundamental features of

commercial web search engines. After submitting a key-word query, the user may not be satisfied with theresults, so the keyword suggestion module of the searchengine recommends a set of m keyword queries that aremost likely to refine the user’s search in the right direc-tion. Effective keyword suggestion methods are based onclick information from query logs [1], [2], [3], [4], [5], [6],[7] and query session data [8], [9], [10], or query topicmodels [11]. New keyword suggestions can be deter-mined according to their semantic relevance to the origi-nal keyword query.

However, to our knowledge, none of the existingmethods provide location-aware keyword query suggestion(LKS), such that the suggested queries retrieve documentsnot only related to the user information needs but alsolocated near the user location. This requirement emergesdue to the popularity of spatial keyword search [12], [13],[14], [15], [16]. Google processed a daily average of 4.7 bil-lion queries in 2011,1 a substantial fraction of which havelocal intent and target spatial web objects (i.e., points ofinterest with a web presence having locations as well as text

descriptions) or geo-documents (i.e., documents associatedwith geo-locations). Furthermore, 53 percent of Bing’smobile searches in 2011 have a local intent.2

In this paper, we propose the first Location-aware Key-word query Suggestion framework. We illustrate the benefitof LKS using a toy example. Consider five geo-documentsd1-d5 as listed in Fig. 1a. Each document di is associatedwith alocation di:! as shown in Fig. 1b. Assume that a user issues akeyword query kq ¼ “seafood” at location !q, shown inFig. 1b. Note that the relevant documents d1–d3 (containing“seafood”) are far from !q. A location-aware suggestion is“lobster”, which can retrieve nearby documents d4 and d5 thatare also relevant to the user’s original search intention. Previ-ous keyword query suggestion models (e.g., [5]) ignore theuser location and would suggest “fish”, which again fails toretrieve nearby relevant documents. Note that LKS has a dif-ferent goal and therefore differs from other location-awarerecommendationmethods (e.g., auto-completion/instant sea-rch [17], [18], tag recommendation [19]). Section 5 provides adetailed discussion about the differences between LKS andthese models, while in Section 4 we experimentally show thatan adaptation of themethod in [19] is less effective than LKS.

The first challenge of our LKS framework is how to effec-tively measure keyword query similarity while capturingthe spatial distance factor. In accordance to previous querysuggestion approaches [2], [3], [4], [5], [6], [7], [9], [10], LKSconstructs and uses a keyword-document bipartite graph(KD-graph for short), which connects the keyword querieswith their relevant documents as shown in Fig. 1c. Differentto all previous approaches which ignore locations, LKSadjusts the weights on edges in the KD-graph to capture notonly the semantic relevance between keyword queries, butalso the spatial distance between the document locationsand the query issuer’s location !q. We apply the populargraph distance measure, Personalized PageRank (PPR) a.k.a.

1. http://www.statisticbrain.com/google-searches

" S. Qi is with the Department of Computer Science, the University of HongKong, Hong Kong. E-mail: [email protected].

" N. Mamoulis is with the Department of Computer Science andEngineering, University of Ioannina. E-mail: [email protected].

" D. Wu is with the College of Computer Science & Software Engineering,Shenzhen University, China, and the Department of Computer Science,University of Hong Kong, Hong Kong. E-mail: [email protected].

Manuscript received 12 Mar. 2015; revised 31 July 2015; accepted 1 Aug.2015. Date of publication 6 Aug. 2015; date of current version 3 Dec. 2015.Recommended for acceptance by W. Wang.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TKDE.2015.2465391

2. http://searchengineland.com/microsoft-53-percent-of-mobile-searches-have-local-intent-55556

82 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 28, NO. 1, JANUARY 2016

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random walk with restart (RWR) distance [20] on the KD-graph, starting from the user supplied query kq, to find theset of m keyword queries with the highest semantic rele-vance to kq and spatial proximity to the user location !q.RWR on a KD-graph has been considered superior to alter-native approaches [6] and has been a standard techniqueemployed in previous (location-independent) keywordquery suggestion studies [4], [5], [6], [7], [9], [10].

The second challenge is how to compute the suggestionsefficiently. Performing keyword suggestion instantly isimportant for the applicability of LKS in practice. However,RWR search has a high computational cost on large graphs.Previous work on scaling up RWR search require pre-com-putation and/or graph segmentation [20], [21], [22], [23],[24] and require that the transition probabilities betweennodes (i.e., the edge weights) are known beforehand. How-ever, the edge weights of our KD-graph are unknown inadvance, hindering the application of all these approaches.To the best of our knowledge, no existing technique canaccelerate RWR when edge weights are unknown apriori(or they are dynamic). To address this issue, we present anovel partition-based algorithm (PA) that greatly reducesthe cost of RWR search on such a dynamic bipartite graph.In a nutshell, our proposal divides the keyword queries andthe documents into partitions and adopts a lazy mechanismthat accelerates RWR search. PA and the lazy mechanismare generic techniques for RWR search, orthogonal to LKS,therefore they can be applied to speed up RWR search inother large graphs.

In summary, the contributions of this paper are:

" We design the first ever Location-aware Keywordquery Suggestion framework, for suggestions rele-vant to the user’s information needs that also retrieverelevant documents close to the query issuer’slocation.

" We extend the state-of-the-art Bookmark ColoringAlgorithm (BCA) [25] for RWR search to computethe location-aware suggestions. In addition, we pro-pose a partition-based algorithm (PA) that greatlyreduces the computational cost of BCA.

" We conduct an empirical study that demonstratesthe usefulness of location-aware keyword query sug-gestion. We also show experimentally that PA is twotimes to one order of magnitude faster than BCA.

The rest of the paper is organized as follows. LKS isintroduced in Section 2. Our partition-based algorithm ispresented in Section 3. We evaluate the effectiveness of LKS

and the performance of PA in Section 4. Related work isreviewed in Section 5 and we conclude in Section 6.

2 LKS FRAMEWORK

Consider a user-supplied query q with initial input kq; kqcan be a single word or a phrase. Assuming that the queryissuer is at location !q, two intuitive criteria for selectinggood suggestions are: (i) the suggested keyword queries(words or phrases) should satisfy the user’s informationneeds based on kq and (ii) the suggested queries can retrieverelevant documents spatially close to !q. The proposed LKSframework captures these two criteria.

2.1 Initial Keyword-Document GraphWithout loss of generality, we consider a set of geo-docu-mentsD such that each document di 2 D has a point locationdi:!.

3 Let K be a collection of keyword queries from a querylog. LKS first constructs an initial keyword-document graph(KD-graph), which is what a classic keyword suggestionapproach that does not consider locations would use [4], [5],[6], [7], [9], [10]. This directed weighted bipartite graphG ¼ ðD;K;EÞ between D and K captures the semantics andtextual relevance between the keyword query and documentnodes; i.e., the first criterion of location-aware suggestion. If adocument di is clicked by a user who issued keyword querykj in the query log, E contains an edge e from kj to di and anedge e0 from di to kj. The weights of edges e and e0 are thesame and equal to the number of clicks on document di, givenkeyword query kj [1]. Therefore, the direct relevance betweena keyword query and a clicked document is captured by theedge weight. Furthermore, the semantic relevance betweentwo keyword queries is captured by their proximity in thegraphG (e.g., computed as their RWRdistance). Any updatesin the query log and/or the document database can be easilyapplied on the KD-graph; for a new query/document, weadd a new node to the graph; for new clicks, we only need toupdate the corresponding edge weights accordingly. As anexample, Fig. 1a shows five documents d1-d5 and three key-word queries k1–k3. The corresponding KD-graph is shownin Fig. 1c. For the ease of presentation, the edge weights arenormalized (i.e., divided by the maximum number of clicksin the log for any query-document pair).

Fig. 1. LKS example.

3. If a document relates to multiple locations, we can model it asmultiple documents, each referring to a single location. Location-independent documents can also be included in our framework byturning off the location awareness component for them.

QI ET AL.: LOCATION AWARE KEYWORD QUERY SUGGESTION BASED ON DOCUMENT PROXIMITY 83

2.2 Location-Aware Edge Weight AdjustmentIn order to satisfy the second criterion of location-awaresuggestion (i.e., location awareness), we propose to adjustthe edge weights in the KD-graph based on the spatial rela-tionships between the location of the query issuer and thenodes of the KD-graph. Note that this edge adjustment isquery-dependent and dynamic. In other words, differentadjustment is used for each different query independently.

We now outline the details of the edge weights adjust-ment. Recall that a user-supplied query q consists of twoarguments: an input keyword query kq (a word or a phrase)and a query location !q. Given q, the weight wðeÞ of theedge e from a keyword query node ki to a document nodedj is adjusted by the following function:

~wðeÞ ¼ b% wðeÞ þ ð1' bÞ % ð1' distð!q; dj:!ÞÞ; (1)

where wðeÞ is the initial weight of e in the KD-graph, ~wðeÞ isthe adjusted edge weight, distð!q; dj:!Þ is the euclidean dis-tance between the query issuer’s location !q and documentdj, and parameter b 2 ½0; 1) is used to balance the impor-tance between the original (i.e., click-based) weight and thedistance of dj to the query location. Euclidean distances arenormalized to take values in ½0; 1). This keyword-to-docu-ment edge weight adjustment increases the weights of thedocuments that are close to the user’s location.

Let DðkiÞ be the set of documents connected to a key-word query ki 2 K in the KD-graph. DðkiÞ may containmultiple documents and the locations of them form a spatialdistribution. We propose to adjust the weights of the edgespointing to ki by the minimum distance between !q and thelocations of documents in DðkiÞ. 4 Such an adjustmentfavors keyword query nodes which have at least one rele-vant document close to the query issuer’s location !q. Spe-cifically, the weight wðe0Þ of the edge e0 from a documentnode dj to a keyword query node ki is adjusted as follows:

~wðe0Þ ¼ b% wðe0Þ þ ð1' bÞ % ð1'mindistð!q; DðkiÞÞÞ; (2)

where mindistð!q; DðkiÞÞ is the minimum euclidean dis-tance5 between !q and any document inDðkiÞ.

For example, Fig. 1b shows the locations of the five docu-ments of Fig. 1a and a query location !q; Fig. 1d includes the(approximate) euclidean distances between !q and thefive documents. Fig. 2 illustrates how the edge weightsfrom keyword query nodes to document nodes (Fig. 2a)and from document nodes to keyword query nodes(Fig. 2b) are adjusted based on the query location, assum-ing b ¼ 0:5. Take the edge from k1 to d1 as a concreteexample. Its weight is calculated using Equation (1)where distð!q; d1:!Þ ¼ 1. The weight of the edge from d1to k1 is computed using Equation (2) where Dðk1Þ ¼fd1; d2g and mindistð!q; Dðk1ÞÞ ¼ 0:9.

We remark that the original KD-graph G is constructedonly once in advance (as in previous work [4], [5], [6], [7],

[9], [10]). In addition, any update operations on the KD-graph (discussed in Section 2.1) are independent to our edgeweight adjustment strategy, which is query-dependent.Given a user-supplied query q, the adjusted graph Gq isdynamically derived from G based on the query location !q,used to compute suggestions for q, and then dropped. Dur-ing this process, Gq is maintained separately and G is notchanged, so that concurrent or follow up queries are notaffected. As we will discuss in Section 3.1, only a small por-tion of edges, relevant to the current query, are adjusted andcached, hence the adjustment is conducted efficiently andon-demand, during the keyword query suggestion process.

2.3 Location-Aware Keyword Query SuggestionWe denote by Gq the KD-graph G after adjusting the edgeweights, based on the query location !q. Gq captures thetwo criteria of selecting suggestions, i.e., relevance to kq andcloseness to !q. Thus, keyword queries close to kq in Gq arelikely to be relevant to kq and, at the same time, they resultin documents close to the query issuer. In order to find theset of keyword queries for recommendation, we computefor all keyword queries a graph proximity score withrespect to kq, based on the random walk with restart process(typically used to measure graph proximity). Intuitively, theRWR score of a node v in graph Gq models the probabilitythat a random surfer starting from kq will reach v. At eachstep of the walk, the surfer either moves to an adjacent nodewith a probability 1' a (the next node depends on theweight of the corresponding edge), or ‘teleports’ to kq with aprobability a. The top-m keyword nodes in Gq with thehighest scores (excluding kq) are the suggestions.

Formally, let ~c be a column vector recording the RWR

scores of all keyword queries in K based on Gq. ~c is com-puted by [26]:

~c ¼ ð1' aÞMTDKM

TKD

~cþ a~cq: (3)

MDK is a document-by-keyword matrix and MKD is a key-word-by-document matrix, storing the edge weights in Gq;

both matrices are row-normalized. ~cq is the initial score vec-tor having zeros at all positions except the position of kq,where it has 1. Since the user-supplied query kq also gets anRWR score, in the end we compute the top-m keywordqueries other than kq.

Example 1. Consider query q with initial input kq ¼“seafood” and location !q ¼ ð0:2; 0:2Þ against the

Fig. 2. Location-aware edge weight adjustment.

4. Since the locations of past query issuers are not always available(e.g., due to privacy constraints), in this paper, we focus on the casewhere only document locations are known. Therefore, the edge adjust-ments for keyword-to-document edges and document-to-keywordedges are performed differently.

5. The effect of using the average distance toDðkiÞ is similar.


documents of Fig. 1a. The locations of the documents and!q are shown in Fig. 1b. The KD-graph G is shown inFig. 1c and the adjusted edge weights based on !q arepresented in Fig. 2. The top-1 suggestion for q is “lobster”according to Equation (3) given a ¼ 0:5. Note that“lobster” retrieves documents d4 and d5 that are close tothe query location, which cannot be achieved by“seafood”. Also queries “lobster” and “seafood” aresemantically relevant.

3 ALGORITHMS

In this section, we introduce a baseline algorithm (BA) forlocation-aware suggestions (Section 3.1). Then, we proposeour efficient partition-based algorithm (Section 3.2).

3.1 Baseline Algorithm (BA)We extend the popular Bookmark-Coloring Algorithm [25]to compute the RWR-based top-m query suggestions as abaseline algorithm. BCA models RWR as a bookmark coloringprocess. Starting with one unit of active ink injected intonode kq, BA processes the nodes in the graph in descendingorder of their active ink. Different from typical personalizedPageRank problems [27], [28] where the graph is homoge-neous, our KD-graph Gq has two types of nodes: keywordquery nodes and document nodes. As opposed to BCA, BAonly ranks keyword query nodes; a keyword query noderetains a portion of its active ink and distributes 1' a portionto its neighbor nodes based on its outgoing adjusted edgeweights, while a document node distributes all its active inkto its neighbor nodes.

In our implementation, the weight of each edge e isadjusted based on !q online, at the time when the sourcenode of e is distributing ink. This means that the edgeweight adjustment which we propose in Section 2.2 is doneduring BA (i.e., Gq needs not be computed and materializedbefore BA starts). Moreover, a node may be processed sev-eral times; thus, the adjusted weights of its outgoing edgesare cached after the node is first processed, for later usage.A node can distribute ink when its active ink exceeds athreshold ". Algorithm BA terminates when either (i) theink retained at the top-mth keyword query node is morethan the ink retained at the top-ðmþ 1Þth keyword querynode plus the sum of the active ink of all nodes [27] or (ii)the active ink of each node is less than " (typically, " ¼ 10'5).

Algorithm 1 is a pseudo code of BA. Priority queue Qmaintains the nodes to be processed in descending order oftheir active ink (line 1). Q initially contains one entry, i.e., theuser-supplied keywords kq with active ink 1 (line 2). Priority

queue C, initially empty, stores the candidate suggestions indescending order of their retained ink (line 1). The sum of theactive ink of all nodes AINK is set to 1 (line 3). Terminationconditions (i) and (ii) are checked at lines 4 and 8, respectively.The processing of a keyword query node involves retaining aportion of its active ink (line 13) and distributing 1' a portionto its neighbor document nodes based on the adjusted edgeweights (lines 19-23). The total active ink AINK is modifiedaccordingly (line 14). As soon as a keyword query node hassome retained ink, it enters C. The processing of a documentnode involves distributing all its active ink to neighbor key-word query nodes according to the adjusted edge weights(lines 19-23). The algorithm returns the top-m candidate sug-gestions other than kq inC as the result (line 24).

Algorithm 1. Baseline Algorithm (BA)

Input: GðD;K;EÞ, q ¼ ðkq;!qÞ,m, "Output: C1 PriorityQueue Q ;, C ;;2 Add kq to Qwith kq:aink 1;3 AINK 1;4 while Q 6¼ ; and Q:top:aink * " do5 Deheap the first entry top from Q;6 tm ¼ the top-m entry from C;7 tm0 ¼ the top-ðmþ 1Þ entry from C;8 if tm:rink > tm0:rinkþAINK then9 break10 distratio ¼ 1 ;11 if top is a keyword query node then12 distratio ¼ 1' a ;13 top:rink top:rinkþ top:aink% a;14 AINK AINK ' top:aink% a;15 if there exist a copy t of top in C then16 Remove t from C;17 top:rink top:rinkþ t:rink;18 Add top to C;19 for each node v connected to top in G do20 v:aink top:aink% distratio% ~wðtop; vÞ;21 if there exists a copy v0 of v in Q then22 Remove v0 from Q; v:aink v:aink þ v0:aink;23 Add v to Q;24 return the top-m entries (excluding kq) in C;

Example 2. Fig. 3 shows the steps of BA (for m ¼ 1, " ¼ 0:1and a ¼ 0:5), when applied to the adjusted KD graph ofour running example (see Example 1 and Figs. 1 and 2).The number next to each node indicates its amount ofactive ink. The numbers in rounded rectangles are theamount of retained ink. Initially, one unit amount of inkis injected into node k2, i.e., the keyword query kq ¼

Fig. 3. Illustration of Algorithm BA.


“seafood” supplied by the user. In the first iteration, nodek2 retains 0.5 amount of ink and distributes 0.5 amount ofink to its neighbor document nodes d1–d3 according to theadjusted edge weights. In the second iteration, d3 distrib-utes its active ink of amount 0.325 to its neighbor keywordquery nodes k2 and k3. BA terminates at the sixth iterationwhere the active ink of each node is smaller than ". Thetop-1 suggestion (excluding user query k2) is k3 ¼“lobster”, with the largest amount of retained ink (0.098).

3.2 Partition-Based AlgorithmAlgorithm BA can be slow for several reasons. First, at eachiteration, only one node is processed; thus, the active inkdrops slowly and the termination conditions are met aftertoo many iterations. Second, given the large number of iter-ations, the overhead of maintaining queue Q is significant.Finally, the nodes distribute their active ink to all theirneighbors, even if some of them only receive a smallamount of ink. To improve the performance of BA, in thissection, we propose a partition-based algorithm that dividesthe keyword queries and the documents in the KD-graph G

into groups. Let PK ¼ fPKi g be the partitions of the key-

word queries and PD ¼ fPDi g be the document partitions.

Algorithm PA follows the basic routine of algorithm BA,but with the following differences:

1) Node-partition graphs. PA uses two directed graphsGKP and GDP constructed offline from the KD-graph

G and partitions PK and PD. In graph GKP , a key-word query node ki connects to a document partitionPD if ki connects inG to at least one document in PD.Similarly, in graph GDP , a document node dj con-nects to a keyword partition PK if dj connects in G toat least one keyword query node ki. As an example,in Fig. 4, the document partitions are PD

1 ¼ fd1; d2gand PD

2 ¼ fd3; d4; d5g and the keyword query parti-tions are PK

1 ¼ fk1g and PK2 ¼ fk2; k3g. The edge

weights are defined based on graph Gq, computedduring the execution of PA. Each edge weight shownin Fig. 4 indicates the portion of the ink to be distrib-uted to a partition P from a node v that is the sum ofthe adjusted weights of the edges from node v to thenodes in P according to Gq.

2) Ink distribution. In PA, each node distributes its activeink to its neighbor partitions (contrast this to BA,where each node distributes its active ink to each ofits neighbor nodes). The priority queue used in BAmaintains the nodes that will distribute ink, but thepriority queue used in PA records the partitions thatwill be processed. The ink received by a partition isnot spread to the nodes inside the partition until thispartition reaches the head of the priority queue. Thebenefit is that a partition may receive ink from thesame node several times while waiting in the queue,so that the nodes in this partition receive ink in batchwhen this partition reaches the head of the queue. Inalgorithm PA, the active ink drops fast and the ter-mination conditions may be fulfilled early. Thus, thenumber of iterations needed is largely reduced andso is the cost spent for maintaining the priorityqueue Q. Moreover, since the number of partitions ismuch smaller than that of nodes, the size of queue Qis much smaller compared to that used in BA, sooperations on it are fast as well. As an example, inFig. 5, in algorithm BA, node k2 distributes its activeink to each of its three neighbor nodes d1–d3. How-ever, in algorithm PA, the active ink of k2 is only dis-tributed to two recipients: partitions PD

1 and PD2 ; an

underlying document node will not receive the ink,until its partition reaches the top of the queue.

3) Lazy distribution mechanism. In BA, a node distributesink aggressively, i.e., each of its neighbor nodesreceives ink no matter how much it is. On the otherhand, in algorithm PA, we adopt a lazy distributionmechanism that relies on threshold ". If the amount ofthe ink to be distributed from a node v to a partition Pis smaller than ", P does not receive the ink immedi-ately; instead, the ink is accumulated (i.e., buffered)at v. Later, if at some point the ink accumulated at vfor partition P exceeds ", P receives it. Overall, thislazy distribution mechanism delays the distributionof small amounts of ink across the graph that wouldotherwise result in many updates, reducing thecomputational cost significantly. As a toy example inFig. 5b, the amount of ink (0.07) to be distributedfrom node k2 to partition PD

1 waits at k2 when " ¼ 0:1.Algorithm 2 is a pseudocode for PA. Priority queue Q

maintains the partitions to be processed in descendingorder of their keys (line 1). A partition waiting in the queuemay have received ink from multiple nodes. Let P:ainkvi bethe ink received by partition P from node vi. The key of Pin the queue is the maximum value of P:ainkvi . Priorityqueue C stores the candidate suggestions in descendingorder of their retained ink, initialized as empty (line 1). Qinitially contains one entry referring to the keyword query

Fig. 4. Node-partition graphs.

Fig. 5. Ink distribution methods.


partition P containing the user supplied keywords withactive ink 1 (line 2). The sum of the active ink of all nodesAINK is set to 1 (line 3). The termination conditions are thesame as those of algorithm BA (lines 4 and 8). For a partitionPt being processed, PA firstly spreads its received ink to Pt’snodes (line 10). When processing a keyword query parti-tion, each keyword query node v inside retains a portion ofits active ink (line 15). The ranking of this keyword querynode in C is updated and the active ink AINK is modified(line 16). For each document partition Pi connected from vin GKP , if the amount of accumulated ink for Pi at v exceeds", partition Pi receives the ink. Otherwise, the ink is accumu-lated at v for Pi (lines 24-32). Similarly, when processing adocument partition, for each document node v inside thepartition, the lazy ink distribution mechanism is applied.As before, the only difference is that document nodes donot retain any ink. The algorithm finally returns the top-mcandidate suggestions in C as the result (line 33).

Note that the partitioning is done offline, and thus it doesnot add any cost to the online query suggestion process. InPA, the cost of maintaining the partition information (interms of both the memory usage and the CPU cost) is negli-gible when the number of partitions is small (e.g., 16-64 asshown in our experiments).

Example 3. We illustrate algorithm PA (for m ¼ 1, " ¼ 0:1,and a ¼ 0:5) using our running example (kq ¼ “seafood”and !q ¼ ð0:2; 0:2Þ). Fig. 4 shows the node-partitiongraphs. Fig. 6 shows how the scores (ink) of the keywordqueries are computed. Initially, partition PK

2 contains theuser supplied keyword k2 having active ink 1. In the firstiteration, partition PK

2 is processed. Each keyword querynode inside partition PK

2 retains a portion of its activeink. In this example, k2 retains 0.5 amount of ink. Docu-ment partitions PD

1 and PD2 connected from k2 according

to graph GKP receive 0.175 and 0.325 amount of ink,respectively. In the second iteration, document partitionPD2 is processed. Each node inside PD

2 first receives theink from k2 and then distributes ink to the connected key-word query partition PK

2 according to graph GDP . In thethird iteration, partition PK

2 is processed. Each nodeinside PK

2 receives the ink from d3. After that, node k3accumulates ink for partition PD

2 , since the amount of ink

for PD2 is 0.097 (< "). Similarly, node k2 accumulates ink

for partitions PD1 and PD

2 . In the fourth iteration, partitionPD1 is processed. For each node inside PD

1 , the ink to bedistributed does not exceed threshold ", so that d1 and d2accumulate ink for partitions PK

1 and PK2 . In the end, the

top-1 suggestion is keyword query k3 ¼ “lobster”.

Algorithm 2. PA

Input: GðD;K;EÞ, GKP , GDP , q ¼ ðkq;!qÞ,m, "Output: C1 PriorityQueue Q ;, C ; ;2 Add partition P 3 kq to Qwith P:aink 1;3 AINK 1;4 while Q 6¼ ; and Q:top:ainkvi * " do5 Deheap the top entry Pt from Q;6 tm ¼ the top-m entry from C;7 tm0 ¼ the top-ðmþ 1Þ entry from C;8 if tm:rink > tm0:rinkþAINK then9 break;10 Spread the active ink to nodes in Pt;11 for each node v in partition Pt do12 distratio ¼ 1 ;13 if v is a keyword query node then14 distratio = 1' a ;15 v:rink v:rinkþ v:aink% a;16 AINK AINK ' v:aink% a;17 if there exist a copy t of v in C then18 Remove t from C;19 v:rink v:rinkþ t:rink;20 Add v to C;21 Get partition set P connected from v in GKP ;22 else23 Get partition set P connected from v in GDP ;24 for each partition Pi in P do25 ink v:aink% distratio% ~wðv; PiÞ;26 if inkþ v:acc:Pi * " then27 Pi:aink inkþ v:acc:Pi;28 if there exist a copy P 0i of Pi in Q then29 Remove P 0i from Q;

Pi:aink Pi:ainkþ P 0i :aink;30 Add Pi to Q;31 else32 Accumulate ink at node v for Pi (v:acc:Pi);33 return the top-m entries (excluding kq) in C;

Fig. 6. Illustration of Algorithm PA.


Partitioning methods. We consider four partitioning meth-ods for keyword query/document nodes, to be empiricallyevaluated in Section 4.

Random partitioning. Keyword queries are evenly andrandomly partitioned into a predetermined number of par-titions. The same is done for the documents.

Spatial partitioning. First, a regular grid is used to partitionthe euclidean space of document locations. The documentswhose locations lie in the same grid cell form a partition. Thekeyword queries are partitioned according to the documentpartitions. The idea is inspired by the duality of word and docu-ment clustering [29]. Specifically, let PD ¼ fPD

1 ; PD2 ; . . . ; PD

n gbe the document partitions. We initialize N empty keywordquery partitions PK ¼ fPK

1 ; PK2 ; . . . ; PK

N g. According tograph GKP , which connects keywords to document parti-tions, each keyword query node ki is connected to a set ofdocument partitions P ðkiÞ ¼ fPD

i g. Let PDj be the document

partition connected from ki with the highest edge weight,i.e., argmaxPD

j 2P ðkiÞwðki; PDj Þ. Keyword query node ki is

added to partition PKj that has the same subscript j as parti-

tion PDj . In the end, some of the keyword query partitions in

PK might be empty, and thus are removed.Textual partitioning. Each document d is associated to a

vector d:c where each dimension refers to a keyword queryk connected to d in the KD-graph G and the value of thisdimension is the edge weight wðd; kÞ. Let cos ðdi:c; dj:cÞ bethe cosine similarity between the vectors of documents diand dj. A clustering algorithm, e.g., k-means, is applied onthe document vectors using the cosine similarity, so that thedocument partitions are obtained. The keyword queries arepartitioned based on the document partitions in the sameway as in the spatial partitioning method.

Hybrid partitioning. Let fHðdi; djÞ ¼ g % cos ðdi:c; dj:cÞ þð1' gÞ % distðdi:!; dj:!Þ be a hybrid distance between docu-ments di and dj, considering both their euclidean distanceand cosine similarity. A clustering algorithm, e.g., k-means,is applied on the documents using the hybrid distance, sothat the document partitions are obtained. The keywordqueries are partitioned as in the previous methods.

4 EMPIRICAL STUDY

We conducted extensive experiments to evaluate the effec-tiveness and efficiency of LKS. Section 4.1 presents ourexperimental setup. The effectiveness of our LKS frame-work compared to query suggestion that does not considerlocations is evaluated in Section 4.2. The runtime perfor-mance of algorithms BA and PA is evaluated in Section 4.3.

4.1 SetupTwo datasets AOL and TWEET are used in our evaluation.AOL is based on a real query log of the AOL searchengine [30]. Each record in the log contains a keywordquery, the time when the query was submitted, and a URLclicked. Since the locations of the URLs are not readily avail-able in the query log, we geo-located the URL domains withthe help of the Freegeoip6 project and removed the URLs

without any geo information. In addition, we cleaned thequery log by removing the keyword queries without clickinformation and with frequency less than 3. We added anedge between a keyword query node ki and a URL node dj ifthere exist records containing both ki and dj in the query log.The edge weight was defined by the number of records con-taining both ki and dj (i.e., the click count). At last, the con-structed KD-graph G has 629,875 keyword query nodes,496,221 document nodes (URLs), and 2,778,050 edges. Data-set TWEET is based on 3,198,266 tweets published inside theNew York area, collected using Twitter’s Streaming API.7

Each tweet has a text message and a location where the tweetis posted. Following the methodology in [31], we extractedphrases of length 1 to 10 from the text messages and usedthem tomodel the keyword queries. Only the phrases endingwith either a noun or an adjective andwith frequency at least3 are kept, in order to reduce the number of noisy queries.We add an edge between a keyword query node ki and atweet node dj if dj contains keywords ki. The edge weight isthe tf-idf score of ki w.r.t. dj. Afterwards, documents with noconnected keyword query nodes are removed. Finally, theconstructed KD-graph has 781,465 keyword queries,1,482,064 documents (tweets), and 12,078,958 edges.

From each dataset, we randomly selected 100 keywordqueries and used them as a workload. For each query, theuser location is considered to be the location of a randomlyselected document from those that contain the query key-words. The reasoning behind this is that the query locationdistribution typically tends to follow the distribution of thedocuments that contain the query.

All tested methods were implemented using Java. Theexperiments were run on a machine with Intel Corei7-3770 3.40 GHz and 16 GB main memory. Our LKSframework and the algorithms are evaluated under vari-ous parameter settings, as shown in Table 1. For eachparameter, we used a wide range of values in order totest their effects. The number of suggestions m is fixed to5 (the performance of the evaluated algorithms is not sen-sitive to it). Finally, the default partitioning method forPA is Spatial Partitioning.

4.2 Effectiveness of the LKS FrameworkIn this section, we assess the effectiveness of LKS using realexamples, a user study, and quantitative measurements.These evaluation metrics verify whether the keyword

TABLE 1Parameters

Description Parameter Values Default Value

Number of partitions N 1,4,16,64,256 16RWR probability a 0.2,0.35,0.5,

0.65,0.80.5

Edge weight adjustmentparam.

b 0,0.25,0.5,0.75,1

0.5

Threshold (%10'5) " 0.1,0.5,1,5,10

1

Number of documents(M)

jDj 0.5, 1, 1.5,2, 2.5

1.5

6. http://freegeoip.net 7. https://dev.twitter.com/docs/api/streaming


suggestions are (i) semantically relevant to the originalquery and (ii) able to find documents that are close to thequery location.

4.2.1 Case Study

We first demonstrate the effectiveness of considering theuser location in query suggestion, by showcasing queryexamples on the TWEET data set. Consider a user-suppliedkeyword query with kq ¼ “airport”. Figs. 7 and 8 show thetop-1 suggestion for kq considering two different query loca-tions !q and using various values of b. In all plots, the trian-gle denotes the query location, the crosses denote theprocessed documents by the PA algorithm (i.e., the documentsthat distribute ink during the course of the algorithm), andthe circles are the retrieved document by the suggested key-words close to the query location (located within 10kmfrom the query location). When b ¼ 1, LKS ignores thequery location; thus, no matter where the query location is,the suggestion for the user supplied keyword “airport” isalways “LaGuardia Airport” (the most relevant phrase to“airport” when disregarding location data) as shown inFigs. 7a and 8a. When the query location is close to LaGuar-dia Airport, the suggested keywords “LaGuardia Airport”can retrieve some relevant documents nearby (the circles inFig. 7a). However, when the query location is close to

Newark, there are no relevant documents around related tothe suggestion (no circle in Fig. 8a).

When 0 < b < 1 (b ¼ 0:5 in this example), the sugges-tion depends on the query location. Keywords “LaGuardiaAirport” are suggested when the query is issued nearLaGuardia (Fig. 7b), while “Newark Liberty International Air-port” is the top suggestion when the query location is closeto Newark (Fig. 8b). Each of the two suggestions can retrieverelevant documents (circles) close to the correspondingquery location. When b ¼ 0, the suggestion only depends onthe query location and can fetch relevant documents nearbyas shown in Figs. 7c and 8c. However, sometimes the sug-gestion is less specific (i.e., less relevant) compared to thecase of b ¼ 0:5, e.g., “Newark Liberty International Airport”versus “Newark Liberty”. This is because the spatial-only rec-ommendation favors the queries havingmore relevant docu-ments close to the query location, regardless of their textualrelevance. When the query location is near JFK, “John FKennedy International Airport” and “Kennedy International”are reported when b is set to 0.5 and 1.0, respectively. Weomit the details due to space constraints.

We also observe that for small b values, fewer documentsare involved in the computation (crosses) because moreweights are given to the nearby documents. For example,the number of crosses is 2,296, 2,177, and 822 in Figs. 8a and8b, and c, respectively. Moreover, small b results in more

Fig. 7. User Supplied Keyword kq ¼ “airport” , Query Location !q near LaGuardia Airport.

Fig. 8. User Supplied Keyword kq ¼ “airport” , Query Location !q near Newark Liberty International Airport.


general query suggestions, which retrieve more nearbydocuments. As an example, the number of circles is 600 and630 in Figs. 8b and c, respectively.

A case where LKS is especially useful is when there areno (or very few) relevant documents near the user location.LKS recommends to the user alternative query keywords,which match the user’s intention and at the same time findnearby documents. For example, Fig. 9 present the top rec-ommendation to kq ¼ “prada” on our AOL dataset for vari-ous b values. When the location information is ignored(b ¼ 1, Fig. 9a), query “prada store” is recommended, whichhowever retrieves no nearby document. LKS with b ¼ 0:5(Fig. 9b) recommends a different brand “gucci”, which canretrieve three related documents. Finally, when the model isover-biased to the location factor (b ¼ 0, Fig. 9c), the sugges-tion “handbags” retrieves even more (8) nearby documents,which however is less irrelevant to kq.

4.2.2 User Study

As an additional way to test the effectiveness of LKS, we ran-domly selected 100 AOL queries with b ¼ 0 (suggestionbased on location only), b ¼ 0:5 (our LKS model) and b ¼ 1(previous work, i.e., location-independent models), and dis-tributed them to seven colleagues. To ensure the fairness ofthe user study, the participants were not informed about thedetails of this project and the respective b setup of the threescenarios. For each input query, we showed the participants(1) the top suggestion and (2) the top-5 documents retrievedby spatial keyword search using the boolean range querymodel [32], so that they are within 0.1 distance to the userlocation and are ranked by their relevance to the suggestion.Then, we asked the participants to suggest two scores, (1)SK : how relevant (in 0-5) the suggestion is to the originalinput keyword, and (2) SD: for each document, judge if it isrelated to the initial query intent (0 or 1 for each document,in case fewer than five documents are within 0.1 distance,set the remaining slots to 0, which represents a penalty ifthe suggestion still cannot retrieve at least five nearbyresults). SD is the sum of these five binary values. SK veri-fies textual relevance of the suggestion. On the other hand,SD verifies usefulness of the suggestion by the relevance ofthe retrieved nearby documents (i.e., verifies the user’sintention both semantically and spatially). The average SK

and SD scores are presented in Fig. 10, showing the supe-riority of LKS. Note that document relevance SD is low atb ¼ 1 (previous work) because without location informa-tion, the suggested keywords may fail to find five nearbydocuments; SD is also low at b ¼ 0 because althoughmany documents are retrieved, they are not very relevantto the initial input.

4.2.3 Quantitative Study

Designing quantitative evaluation metrics for LKS is chal-lenging, because it is hard to establish the ground truth forsuggestions. Considering the two criteria of good sugges-tions, we evaluate (i) the semantic relevance of the sug-gested keyword queries (together with their retrievednearby documents) w.r.t. the user’s initial query and (ii) thenumber of nearby documents retrieved by the query sug-gestions. As a competitor to our LKS framework, we imple-mented the influence tag co-occurrence (INF) methodproposed in [19]. INF is designed to employ both spatialand textual information into tag recommendation for Flickrand has been shown to be more effective than alternativeapproaches [19]. Given a photo p published at p:loc and atag t, the task is to retrieve k tag recommendations to t. Theidea is that if a tag t0 co-occurs with t in a photo p0, they areconsidered textually relevant. In the meantime, if p0 is closeto p (i.e., distðp0:loc; p:locÞ is small), the relevance between t0

and t is even higher. In INF, the relevance between t andt0 is defined according to a influence score

infðt; t0Þ ¼P

p02P\P 0 2''distðp0 ;pÞ

r

jP[P 0j . Here P and P 0 are the sets of

photos containing tag t and t0, respectively, and r is a

Fig. 9. Suggestions to query kq ¼ “ prada” , !q ¼ ð0:75; 0:7Þ.

Fig. 10. User study on AOL.


parameter to adjust the importance of spatial distance. 8 Toapply INF in keyword suggestion, we consider the co-occurrence of keywords in the same document and exploit asimilar relevance function.

We first report the average number of nearby documentsretrieved by (a) the original query, (b) the queries suggestedby INF, and (c) the queries suggested by our LKS frame-work, over the workload of TWEET when varying parame-ters a (in Equation (3)) and b (in Equation (1)). Fig. 11a plotsthe number of documents retrieved by the original inputand the keyword queries suggested by INF or LKS, within aratio r of the maximum euclidean distance between anypair of documents (r ¼ f0:05; 0:1g). The queries suggestedby INF can retrieve some more nearby locations. However,the number of documents retrieved by the LKS-suggestedqueries is significantly higher than that of either the originalinput, or the INF suggested keyword queries, for all a val-ues, showing the value of LKS w.r.t. the location criterion.Obviously, for larger r values more documents are retr-ieved. Also, the number of documents decreases as aincreases. The reason is that for small a values, the distrib-uted ink reaches more documents compared to the casewhere a is large. Hence, more document nodes near thequery location participate in the ink distribution processand more relevant queries are reached and included in thetop-m ranking. As special cases, when a ¼ 1, no keywordqueries can be returned because all the ink is retained bythe original query, while when a ¼ 0, no restart is involvedin the random walk, hence the result is independent of theinput. Fig. 11b reports the number of documents retrievedby the original input and the keyword queries suggested byINF or LKS when varying b. The number of documentsretrieved by the queries suggested by LKS decreases as bincreases. This is because a large b weighs the user locationlow; the textual relevance criterion dominates the spatialcloseness criterion, therefore fewer nearby documents arerelevant to the suggestions. Note that our experiments onAOL show similar results and are thus omitted.

Next, we evaluate how relevant the suggested keywordqueries are to the user’s information needs. To begin with,we first evaluate the textual relevance between the originalinput and the keyword queries suggested by INF or LKS,

following a similar approach used in [33], [34], [35]. Specifi-cally, we utilize the Open Directory Project database (ODP,a.k.a. DMOZ),9 which provides a comprehensive humanedited directory of the web. ODP can match a given queryto a hierarchy of categories. For example, the query “HardDisk” matches category “Computers: Hardware: Storage:Hard Disk” and the query “Memory” matches “Computers:Hardware: Components: Memory”. Hence, the relevancebetween two queries can be evaluated by the similaritybetween their corresponding categories C1 and C2 in thehierarchy. Similarity is measured by the length of the lon-gest common path prefix P ðC1; C2Þ normalized by thelength of the longer path in the hierarchy, i.e.,

simðC1; C2Þ ¼ jP ðC1;C2ÞjmaxfjC1j;jC2jg

. For example, the similarity betw-

een “Hard Disk” and “Memory” is 2=4 as the longest com-mon path “Computers: Hardware” has length 2. In ourexperiments, we evaluated the relevance between the origi-nal input and the top suggested keyword queries by INF orLKS, based on their most similar categories provided byODP. The results are presented in Fig. 12a. The first observa-tion is that the LKS-based suggestions are generally morepromising than INF based ones, unless b is close to 0 (spatialonly). This is because INF relies merely on co-occurrence tojudge textual relevance, which cannot capture many hiddensemantic relationships between keyword queries. LKS, onthe other hand, captures textual proximity based on thewhole structure of KD-graph and thus retrieves more reli-able suggestions. In addition, we also observe that LKSachieves best ODP similarity when b is selected between0:25 and 0:75.

After the direct evaluation of suggested query keywordsin the previous experiment, we now evaluate the nearbydocuments retrieved by them. Let fdoig be the set of top-10documents retrieved by the original query and fdsig be theset of top-10 documents retrieved by a suggested querywithin a spatial range (r ¼ 0:1), where i indicates the rank-ing position of a document. We compute the cosine similar-ity cos ðdoi ; dsi Þ between the documents with the sameranking position from the two sets fdoig and fdsig. We adoptthe nDCGmeasure of [36] to aggregate these cosine similari-ties so that the document similarity is reduced logarithmi-cally, proportionally to its ranking position

COS ¼ cos ðdo1; ds1Þ þP10

i¼2 cos ðdoi ; dsi Þ=logðiÞ1þ

P10i¼2 1=logðiÞ

:

Fig. 11. Number of retrieved nearby documents.

Fig. 12. Textual relevance evaluation.

8. We tested various r values from 0:1 to 0:0001 and observed thatwith decreasing r, more nearby documents are retrieved, but thesemantic relevance of the suggested keywords declines. We presentonly the results with r ¼ 0:001, which retains the best balance betweenthe two factors. 9. http://www.dmoz.org


The higher the value of COS is, the closer the nearby docu-ments are to user’s information needs. Besides, we also com-pare the textual relevance (i.e., tf % idf) of documents fdsigand fdoigw.r.t. the original query. Let soi and ssi be the textualscore of document doi and dsi w.r.t. the original query, respec-tively. We take the ratio of ssi to soi for the same ranking posi-tion. Similar to COS, these ratios are aggregated as TS.Fig. 12b shows the average COS and TS over the workloadof TWEET when varying b. The results are mostly consistentwith Fig. 12a. LKS again has better textual quality than INFunless b is very small (< 0:25). In the meantime, LKSachieves best effectiveness at non-extreme b values, where ittakes advantage of both the textual relationships from theoriginal KD-graph, and the local intent of the input query.

Considering the above factors, we conclude that an aver-age value of b (e.g., 0:25 < b < 0:75) should be used inorder for the keyword query suggestions to have a sufficientnumber of documents near the user location as results,which also meet the information needs of the user. In sum-mary, our LKS framework, which balances between rele-vant and nearby search results, is very effective, based onour experimental analysis.

4.3 EfficiencyIn this section, we evaluate the performance of BA andPA on the two datasets under various settings and reporttheir average runtime over the workload of 100 queries.10

4.3.1 Varying "

Both BA and PA follow the general idea of BCA [25], andtheir runtime depends on parameter ". The smaller " is, thesmaller the error incurred by BCA (and BA/PA) on comput-ing the PageRank scores on Gq. We find that when " + 10'8,the top query suggestions become stable. Thus, we considerthe top suggestions calculated using " ¼ 10'8 as the base forcomputing the approximation error of the top suggestionscalculated using " > 10'8. Following [28], the error is com-puted as 1'AP where AP is the average precision of theretrieved results compared to the true ones. An appropriate" value should be selected so that (1) the computation canbe finished in real time and (2) the error rate is reasonablylow. Fig. 13 shows that the response time of BA drops dra-matically as " increases, since a large " significantly reducesthe number of iterations in BA and saves many computa-tions. However, the approximation error is high for largevalues of ". On the other hand, PA runs fast even for small

values of ", for which the approximation error is low. PAoutperforms BA by 1-2 orders of magnitude when " issmaller than 10'6. Therefore, under the same time con-straint (e.g., < 1 s), PA can support smaller " values, andcan thus guarantee a lower error rate.

Because of ", BA and PA may produce different sugges-tions, but the differences are mainly in the low-ranked sug-gestions. In practice, users only consider the highly rankedsuggestions. In our experiments, the top-5 suggestionsoffered by BA and PA are identical in 98 and 99 percent ofthe times on AOL and TWEET, respectively.

4.3.2 Varying a

Parameter a in Eq. (3) indicates the random walk restartprobability that corresponds to the proportion of inkretained on a query node. As shown in Fig. 14 the responsetimes of both BA and PA decrease as a increases. This isbecause for larger a, more amount of ink is retained at thekeyword query nodes; thus, the amount of active inkdrops quickly and the termination condition is satisfiedearly. We observe that PA is more robust to a and outper-forms BA significantly when a is small. In the special case,when a ¼ 1, all the ink will be retained on the query nodein the beginning, thus both algorithms terminate immedi-ately returning no results. In the other extreme case, whena ¼ 0, no ink is retained in any node at each step, thereforethe ink keeps being redistributed until the random walkprocess converges to a stable state. In this case, the finalscores of the nodes only depend on the structure of thegraph, and not on the starting node (query node); no mat-ter what query is given, the suggestions are always thesame (i.e., similar to global PageRank scores). Therefore,both extreme cases (a ¼ 1 or 0) cannot give useful resultsand are not considered.

4.3.3 Varying b

Parameter b in Fig. 15 shows the response time whenvarying b. Both BA and PA are bell-shaped. When bapproaches 0 or 1, only the documents that are eitherclose to the query location or have high textual relevanceto the user supplied keywords are involved in the com-putation. However, when b is close to 0.5, the responsetime increases slightly, since more documents are consid-ered, i.e., the ones that are a bit far from the query loca-tion but with high textual relevance and the ones that areclose to the query location but with slightly low textualrelevance. Algorithm PA outperforms BA for all valuesof b by a wide margin.

Fig. 13. Response time when varying " ð%10'5Þ. Fig. 14. Response time when varying a.

10. Experiments with larger workloads gave us similar results.


4.3.4 Varying Partitioning Methods and Number ofPartitions

We evaluate the four partitioning methods introduced inSection 3.2 using various number of partitions on the twodatasets. The results are shown in Figs. 16a and 16b. Theperformance of PA seems to be insensitive to which parti-tioning approach is used. This can be attributed to the factthat the KD-graph and its corresponding matrices are verysparse. Therefore, the difference between the clustersformed by these approaches is not significant enough toinfluence the performance of PA. To verify this assertion,we conducted experiments using two denser versions ofour datasets; the dense AOL_D is built by selecting the top-50 percent documents with the most connecting edges fromAOL, and the dense TWEET_D is built by selecting the top-30 percent documents from TWEET. To make the graphseven denser, we employ item-based collaborative filtering(IBCF) [37] to estimate additional edge weights from queriesto documents (queries correspond to “users” and docu-ments correspond to “items”). We first calculate the similar-ity among nearby documents (within 1 percent distancethreshold), based on their co-connected queries andweights. Afterwards, for each non-existent keyword to doc-ument edge ðk; dÞ, we estimate its weight by consideringdocuments Ds that are similar to d and the weights of edgesconnecting k toDs. Formally,

veðk; dÞ ¼P

d02Dssimðd; d0Þ % vðk; d0Þ

Pd02Ds

simðd; d0Þ: (4)

If the estimated weight veðk; dÞ is again zero, we keep thepair ðk; dÞ unconnected. After the above procedure, we haveAOL_D containing over 26 M edges among 328 K queriesand 325 K documents, and TWEET_D containing over 38 Medges among 302 K queries and 477 K documents. Com-pared to our original datasets, AOL_D is 27 times denserthan AOL and TWEET_D is 17 times denser than TWEET.The experimental results of Figs. 16c and 16d confirm thatwith denser matrices, the partitioning methods do have aneffect on performance. Specifically, the hybrid method out-performs all other approaches because it takes advantage ofboth the spatial and textual factors during the ink propaga-tion procedure, and thus predicts better how the ink maytend to flow and cluster, achieving better partitioning.

Note that the number of partitions N , directly affects theperformance PA performs best when the number of parti-tions is 64. When N is small, the lazy distribution mecha-nism has little effect, since the size of each partition is large

and there is little chance that the ink is being accumulated.Thus, the cost saved by the ink accumulation is limited. Onthe other hand, when N is too large, the lazy distributionmechanism is applied for too many partitions and thebookkeeping overhead at each node for the accumulatedink per partition is high, negatively affecting the perfor-mance of PA and counterbalancing the savings due to thelazy distribution.

4.3.5 Varying Data Scale

To test the effect of data size, we constructed a largeTWEETUS dataset from about 10M tweets published in gen-eral US. area, in similar way to the TWEET dataset. We usesubsets of TWEETUS with various numbers of documents /keywords. Fig. 17 reports the response time of BA and PAwhen jDj varies from 0.5 to 2.5 M. Note that with differentjDj, the corresponding keyword node set size jKj alsochanges, as shown on the top of Fig. 17. Based on the experi-ments, PA constantly outperforms BA by three-four timeswith various jDj or jKj settings.

5 RELATED WORK

Related work on query suggestion is discussed inSection 5.1. Techniques for RWR computation are reviewedin Section 5.2.

Fig. 15. Response time when varying b.

Fig. 16. Varying partitioning methods andN.

Fig. 17. Varying number of documents and keywords.


5.1 Keyword Query SuggestionKeyword query suggestion approaches can be classified intothreemain categories: randomwalk based approaches, learn-ing to rank approaches, and clustering based approaches. Wealso briefly review alternative methods that do not belong toany of these categories. To the best of our knowledge, no pre-viouswork considers user location in query suggestion.

5.1.1 Random Walk Based Approaches

The methods in this category use a graph structure to modelthe information provided by query logs, and then apply arandom walk process on the graph to compute the sugges-tions. Craswell and Szummer [4] apply such an approachon the query-click graph and suggest queries based on per-sonalized PageRank scores. Mei et al. [5] rank queries basedon hitting time, which reflects the probability that a randomwalker arrives a node within certain steps. Song and He [6]combine both the clicked and skipped URLs from users inthe query-URL bipartite graphs in order to also considerrare query suggestions (using clicked URLs only favorspopular queries). This work was extended in [38] to achievediversification for the recommended queries; the suggestedqueries are re-ranked in a way that maximizes the diversifi-cation function. Zhu et al. [39] generate query recommenda-tions by considering diversity and relevance in a unifiedway during RWR search. Miyanishi and Sakai [7] introduceTime-aware Structured Query Suggestion (TaSQS), an algo-rithm for presenting query suggestions along a timeline.Our proposed LKS framework is orthogonal to and can beeasily integrated in all the suggestion methods that use thequery-URL bipartite graph.

Boldi et al. [9] proposed an approach that applies RWRfrom the original query or from a small set of queries repre-senting the recent querying history of the current user on aquery-flow graph. Deng et al. [35] investigate and develop anentropy-biased framework for modeling click graphs, inwhich common clicks on frequent and general pages aregiven less weight than those on less frequent but more spe-cific ones. Anagnostopoulos et al. [8] formulate the query-recommendation problem as a decision problem on how toperturb the transition probabilities between queries in thequery-flow graph so as to maximize the expected utility of arandom walk. Song et al. [10] mine a term-transition graphfrom search engine logs and apply a topic-based unsuper-vised Pagerank model that suggests queries based on thetopic distribution and term-transition probability withineach topic. The idea of our LKS framework can be appliedto methods that use a query-flow graph, since the query his-tory may also have location information. This is an interest-ing subject for our future work.

5.1.2 Learning to Rank Approaches

Some query suggestion approaches [40] are based on learn-ing models trained from co-occurrences of queries in searchlogs. Another learning-to-rank approach [41] is trainedbased on several types of query features, including queryperformance prediction. Li et al. [11] train a hidden topicmodel. For each candidate query, its posterior distributionover the hidden topic space is determined. Given a userquery q, a list of suggestions is produced based on their

similarity to q in the topic distribution space. Our work isnot based on learning models; in the future, it would beinteresting to study how these models can be extended toconsider location information.

5.1.3 Clustering Based Approaches

Beeferman and Berger [2] view the query log as a query-URL bipartite graph. By applying an agglomerative cluster-ing algorithm on the vertices in the graph, query clusterscan be identified. Then, given a user-supplied query q, thequeries that belong to the same cluster as q does arereturned to the user as suggestions. Wen et al. [42] furtherextended the approach to also take into account the similar-ity between the query content during clustering. In [1], asimilar approach is proposed: the queries are modeled asterm-weighted vectors and then clustered. The vector of aquery q includes the clicked URLs by the users who posed qas terms and the weights are calculated based on term fre-quency and the click popularity of the URL in the answersof q. Cao et al. [3] take into account the immediately preced-ing queries as context in query suggestion. They summarizequeries in search logs into concepts by clustering a query-URL bipartite graph. User session data are converted to con-cept sequences and indexed by a suffix tree. The querysequence submitted by the user is mapped to a sequence ofconcepts; the suffix tree is then searched to find query sug-gestions. Finally, Li et al. [43] cluster queries from searchlogs to extract query concepts, based on which recom-mended queries are selected and employ a probabilisticmodel and a greedy heuristic algorithm to achieve recom-mendation diversification. Location information could alsobe considered in all these clustering models. Such anapproach is out of the scope of our current work, but we areinterested in investigating its effectiveness in the future.

5.1.4 Miscellaneous Approaches

Zhang and Nasraoui [44] create a graph with edges betweenconsecutive queries in each session, weighted by the textualsimilarity between these queries. A candidate suggestionfor a given query is given a score based on the length of thepath between the two queries, aggregated across all sessionsin a query log where the query and the suggestion co-occurred. Cucerzan and White [45] generate query sugges-tions based on user landing pages (that is, the webpages thatusers end a query with, through post-query browsing).Given a user query, they utilize its recorded landing pagesand suggest other queries that have these landing pages intheir top ranked results. A probabilistic mechanism [31]generates query suggestions from the corpus without usingquery logs.

5.1.5 Location-Aware Type-Ahead Search (LTAS)

References [17] and [18] both study the problem of location-aware type-ahead search, also known as instant search.LTAS finds documents near a user location, as the usertypes in a keyword query character by character. This prob-lem is more related to keyword query completion than tothe query suggestion problem that we study in this paper,since the recommended keywords must have the user’s


input as prefix. On the other hand, the query suggestionproblem that we study in this paper takes a completedquery and recommends other queries that are semanticallyrelevant without the constraint that the suggestions shouldhave the original user query as prefix. Therefore, our LKSframework is more flexible and can help users to expressvarious aspects of a topic. The suggested keywords can bedifferent than the user-supplied keywords, but they shouldbe textually relevant. In addition, the methods for LTAS arevery different to our LKS algorithms, as they take advantageof the prefix requirement to reduce the search space (withthe help of trie data structures).

5.1.6 Location-Aware Suggestions Based onUser History

Google [46] provides location-based query suggestions bysimply selecting the user’s past search queries that haveresults close to the user’s current location. These sugges-tions may be insufficient if the user did not perform any his-torical searches near her current location. In addition, querysuggestion based on location only may not match the user’ssearch intent. On the other hand, our framework aims atsuggesting keyword queries that satisfy the user’s informa-tion needs and have nearby results, irrespectively to theuser’s search history.

5.1.7 Query Relaxation

A relevant problem to query suggestion in relational data-bases is called query relaxation. The objective is to generalizean SQL query in case of too few or no results [47]. Queryrelaxation approaches cannot be applied for keyword querysuggestion, because they require the relaxed query to con-tain the results of the original query, which is not essentialin our case.

5.1.8 Heterogeneous Graphs

The basic structure of the KD-graph used in our model andother existing suggestion model is one type of heteroge-neous graph that consists of multiple types of nodes andedges. There exist some research focus on the similaritysearch in heterogeneous graphs. PathRank [48] extends thePersonalized PageRank algorithm on heterogeneous graphsby discriminating different paths during the random walkprocess guided by predefined meta-paths. Sharing the simi-lar idea, the construction of the KD-graph widely used inthe query suggestion is actually guided by so-call meta-pathKEYWORD-DOCUMENT-KEYWORD. However, the Path-Rank does not provide a specific edge-weighing methodsuitable for our problem. PathSim [49] and PCRW [50] mea-sure the proximity between nodes in heterogeneous graphsby only exploiting the given meta-path without consideringthe overall structure of given heterogeneous graph, which isinferior to PathRank. In addition, this line of research paymore attention to the graph models and apply existing algo-rithms for computing the most similar nodes, while algo-rithm PA proposed in this paper is also applicable toclusterable heterogeneous graphs for the purpose of compu-tation acceleration.

5.2 RandomWalk ComputationRandom walk with restart, also known as Personalized Pag-eRank, has been widely used for node similarity measuresin graph data, especially since its successful application bythe Google search engine [51].

5.2.1 Pre-Computation Based Approaches

Matrix-based methods [20], [21] solve PPR by pre-computing the inversion matrix. Tong et al. [20] propose amatrix-based approach B_LIN that reduces the pre-compu-tation cost of the full matrix inversion by partitioning thegraph. Fujiwara et al. [21] propose a K-dash method thatfinds the top-k nodes with the highest PPR scores, based ona LU decomposition of the transition matrix. Alternative tomatrix-based approaches, Monte Carlo (MC) methods [22],[23], [24] can simulate the RWR process. Fogaras et al. [22]propose to approximate PPR by pre-computing and approx-imating for each node u a set of ending vertices for randomwalks starting from u. If u later becomes a query node, itsPPR is approximated according to the distribution of thesevertices. Similarly, Bahmani et al. [23] approximate PPR bycounting the number of times a node is visited by pre-com-puted random walks. All above methods require the aprioriknowledge of the complete graph; however, in our problem,the edge weights are dynamically adjusted according to theuser location, thus these approaches are inapplicable.

5.2.2 Online Approaches

MC can also be applied online, without relying on pre-com-putations; a number of random walks are tried from thequery node and the PPR score of other nodes are estimatedfrom these samples [24]. However, as shown later in [28], alarge number of (expensive) random walks are required inorder to achieve acceptable precision. Fujiwara et al. [28]propose a method for efficient ad-hoc top-k PPR searchwith exact node ranking. They compute the random walk(without restart) probabilities of the nodes, and employ theprobabilities to estimate upper/lower bounds of the candi-date nodes. This approach is applicable when the completetransition matrix is available beforehand, however, obtain-ing the complete transition matrix in our problem involvesthe multiplication of two matrices and it is very expensive.Berkhin [25] proposes the Bookmark Coloring Algorithm toderive an approximation of the PPR vector. Gupta et al. [27]extend BCA and employ early termination heuristics for thetop-k PPR calculation. We extend BCA [25] as our baselinealgorithm for location-aware suggestions.

6 CONCLUSION

In this paper, we proposed an LKS framework providingkeyword suggestions that are relevant to the user informa-tion needs and at the same time can retrieve relevant docu-ments near the user location. A baseline algorithm extendedfrom algorithm BCA [25] is introduced to solve the problem.Then, we proposed a partition-based algorithm which com-putes the scores of the candidate keyword queries at thepartition level and utilizes a lazy mechanism to greatlyreduce the computational cost. Empirical studies are con-ducted to study the effectiveness of our LKS framework


and the performance of the proposed algorithms. The resultshows that the framework can offer useful suggestions andthat PA outperforms the baseline algorithm significantly. Inthe future, we plan to further study the effectiveness of theLKS framework by collecting more data and designing abenchmark. In addition, subject to the availability of data,we will adapt and test LKS for the case where the locationsof the query issuers are available in the query log. Finally,we believe that PA can also be applied to accelerate RWRon general graphs with dynamic edge weights; we willinvestigate this potential in the future.

ACKNOWLEDGMENTS

This work was funded by EC grant 657347/H2020-MSCA-IF-2014 and by GRF grant 17205015 from Hong Kong RGC.Dingming Wu is the corresponding author.

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Shuyao Qi received the bachelor’s degree ofengineering from the Department of ComputerScience and Technology, Zhejiang University, in2012. He is working toward the PhD degree atthe Department of Computer Science, Universityof Hong Kong. His research focuses on queryprocessing on spatial and textual data.

Dingming Wu received the bachelor’s and themaster’s degrees in computer science from theHuazhong University of Science and Technologyand Peking University in 2005 and 2008, respec-tively. She received the PhD degree in computerscience from Aalborg University in 2011. She is apostdoc fellow at the University of Hong Kong.She was a postdoc teaching fellow at Hong KongBaptist University from 2011 to 2013. Herresearch concerns spatial keyword search, geo-social networks, and recommendation systems.

Nikos Mamoulis received the diploma incomputer engineering and informatics from theUniversity of Patras, Greece, and the PhD degreein computer science from the Hong Kong Univer-sity of Science and Technology. Since 2001, hehas been a faculty member in the Department ofComputer Science, University of Hong Kong.Since 2014, he moved to the Department of Com-puter Science and Engineering, University ofIoannina. His research focuses on managingcomplex data types, privacy and security in

databases, and uncertain data management.

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