Explaining and Reformulating Authority Flow Queries

Transcription

1 Explaining and Reormulating Authority Flow ueries Ramarishna Varadaraan Florida International Uniersity Vagelis Hristidis Florida International Uniersity Louiqa Raschid Uniersity o Maryland louiqa@umiacs.umd.edu Abstract Authority low is an eectie raning mechanism or answering queries on a broad class o data. Systems hae been deeloped to apply this principle on the Web (PageRan and topic sensitie PageRan, bibliographic databases (ObectRan, and biological databases (Hubs o Knowledge proect. Howeer, these systems hae the ollowing drawbacs: (a There is no way to explain to the user why a particular result receied its current score; (b The authority low rates, which hae been shown to dramatically aect the results quality in ObectRan, hae to be set manually by a domain expert; (c There is no query reormulation methodology to reine the query results according to the user s preerences. In this wor, we address these shortcomings by introducing a ramewor and algorithms to explain query results and reormulate authority low queries based on the user s eedbac. The query reormulation process can be used to learn the user s preerences and automatically adust the authority low rates to acilitate personalized authority low searching. We experimentally ealuate our algorithms in terms o perormance and quality.. Introduction Authority low is an eectie raning mechanism or answering queries on a broad class o data. In the context o the Web, PageRan [BP98] is used to compute a global raning o the pages based on the hyperlin structure. ObectRan [BHP4] applies the idea o authority low on a data graph, where nodes represent entities lie tuples, and edges represent associations lie primary-to-oreign eys. In contrast to PageRan, ObectRan proides queryspeciic raning by using the query-speciic nodes as the authority source (called base set. Another ey eature o ObectRan, as explained below, is that dierent edge types carry dierent amounts o authority. Another appropriate domain or authority low raning is that o biological data. The Hubs o Knowledge proect [SIY6] applies the PageRan algorithm on a query-dependent subgraph o the original biological graph. Raschid et al. [RWL+6] apply PageRan and ObectRan to answer naigational queries on biological data. We note that not all databases are appropriate or authority low query answering. Our wor is applicable to the ones that do hae the notion o authority low along their associated edges as the ones described aboe. Web search is out o the scope o this wor, since we ocus on typed domain-speciic data graphs. ObectRan: We build our wor on ObectRan, since it is the most general o the aailable authority low raning approaches. We use a modiication o ObectRan, which we reer to as ObectRan2, where the nodes in the base set are weighted according to Inormation Retrieal (IR techniques. Consider the example o Figure, which illustrates a small subset o the DBLP database in the orm o a labeled graph (some author, conerence and year nodes are omitted to simpliy the igure. Schema graphs, such as the one o Figure 2, describe the structure o database graphs. ien a eyword query, e.g. the single-eyword query OLAP, ObectRan sorts the database obects by their releance with respect to the user-proided eywords. ien the subgraph o Figure, the Data Cube paper is raned on the top, een though it does not contain the eyword OLAP. This is a ey adantage o ObectRan compared to traditional IR approaches. Conceptually, the raning is produced in the ollowing way: Myriads o random surers are initially ound at the obects containing the eyword OLAP, which we call the base set, and then they traerse the database graph. In particular, at any time step, a random surer is ound at a node and either (i maes a moe to an adacent node by traersing an edge, or (ii umps randomly to an OLAP node without ollowing any o the lins. The probability that a particular traersal happens depends on multiple actors, including the type o the edge. These actors are depicted in an authority transer schema graph. Figure 3 illustrates the authority transer schema graph used by the ObectRan proect [BHP4]. Assuming the probability that the surer moes bac to an OLAP node is 5% (damping actor random ump probability [BP98], the collectie probability to moe to a reerenced paper is up to 85% 7% (7% is the authority transer rate o the citation edge as we explain below, and so on. As is the case with the PageRan algorithm as well, as time goes on, the expected percentage o surers at each node conerges to a limit r(. Intuitiely, this limit is the ObectRan o the node. Limitations o ObectRan: Raning the obects o a data graph using ObectRan has the ollowing limitations: (a There is no way to explain to the user why a particular result receied its current score; e.g., the user may want to

2 see proo to beliee that the Data Cube paper is important or OLAP. This is een more critical in complex biological databases where obects (e.g., proteins with no obious connection to the query (e.g., gene TNF are returned. Figure 4 shows a subgraph o the biological schema graph we are using in our experiments. We reormulate the query based both on the content, in the spirit o traditional IR query expansion, as well as the lin-structure, by adusting the authority low rates. The explaining subgraphs o the selected results are used to capture the user s preerence and build the reormulated query. (b The authority low rates, which hae been shown to dramatically aect the results quality o ObectRan [BHP4,HVP6], hae to be set manually by a domain expert. For instance, what is the ratio o authority lowing rom a gene to a PubMed publication oer that lowing to a protein at Entrez Protein? (c There is no query reormulation methodology to reine the query results according to the user s preerences. uery reormulation based on user releance eedbac is a mature and well-studied process in traditional document IR [SB9, RL3, Har88]. Howeer, there is no wor on handling user eedbac or authority low raning systems. As we discuss below, our reormulation strategy exploits the user eedbac in terms o content (in the spirit o traditional query expansion [BSA+95, MSB98, SVR83, Eth93] as well as lin structure. Figure 4: Subgraph o biological schema graph. 3. Eicient algorithms are presented and ealuated to explain a result, and create and ealuate the reormulated query. 4. An ObectRan2 query and reormulation system has been built and deployed on bibliographic and biological datasets, aailable on the Web at 5. User sureys were conducted, which proe the utility o the system in explaining and reormulating queries, as well as in automatically training the authority low rates, which was done manually beore [BHP4].. Figure : A subset o the DBLP graph. Figure 2: The DBLP schema graph. Figure 3: The DBLP authority transer schema graph. Contributions: This paper has the ollowing contributions:. We present a methodology to explain a result o an authority low query. For that we generate and display an explaining subgraph. 2. A process is presented to automatically reormulate a query based on a selection o good results by the user. The rest o the paper is organized as ollows. Section 2 presents the ramewor. Section 3 deines a query and presents ObectRan2. Section 4 presents the result explanation technique while Section 5 presents the query reormulation techniques. Section 6 present the quality and perormance experiments. Section 7 describes the related wor. Finally Section 8 discusses our conclusions. 2. Framewor In this section we present the ramewor and essential deinitions, which are later used to describe our result explanation and query reormulation techniques. Note that we ollow the terminology o [BHP4]. We iew a database as a labeled graph, which is a model that captures both relational and XML databases. The data graph D(V D,E D is a labeled directed graph where eery node has a label λ( and a set o eywords. For example, the node ICDE 997 o Figure has label Year and the set o eywords { ICDE, 997, Birmingham }. Each node represents an obect o the database and may hae a sub-structure. Without loss o generality, ObectRan assumes that each node has a tuple o attribute name/attribute alue pairs. For example, the Year nodes o Figure hae name, year and location attributes. Notice that the eywords appearing in the attribute alues comprise

3 the set o eywords associated with the node. One may assume richer semantics by including the metadata o a node in the set o eywords. For example, the metadata Forum, Year, Location could be included in the eywords o a node. Each node has a role λ(. For instance, the ICDE conerence node in Figure has role conerence. Each edge e rom u to is labeled with its role λ(e (we oerload λ and represents a relationship between u and. For example, eery paper to paper edge o Figure has the label cites. When the role is eident and uniquely deined rom the labels o u and, we omit the edge label. For simplicity we will assume that there are no parallel edges and we will oten denote an edge e rom u to as u. The data graph can represent relational [ACD2, HP2] and XML [HPB3, SB + 3] databases, as well as the Web [BP98], although we repeat that the Web is out o the scope o this wor. The schema graph (V,E (Figures 2, 4 is a directed graph that describes the structure o D. Eery node has an associated label. Each edge is labeled with a role, which may be omitted, as discussed aboe or data graph edge labels. For instance, the Entrez ene to PubMed edge in Figure 4 has role genepubmedassociates. We say that a data graph D(V D,E D conorms to a schema graph (V,E i there is a unique assignment µ o data-graph nodes to schema-graph nodes and a consistent assignment o edges such that:. or eery node V D there is a node µ( V such that λ( = λ(µ(; 2. or eery edge e E D rom node u to node there is an edge µ(e E that goes rom µ(u to µ( and λ(e = λ(µ(e. Authority Transer Schema raph. From the schema graph (V,E, we create the authority transer schema graph A (V,E A to relect the authority low through the edges o the graph. In particular, or each edge e = (u o E, two authority transer edges, e = (u and b e = ( u are created. The two edges carry the label o the schema graph edge and, in addition, each one is annotated with a (potentially dierent authority transer rate - α ( e and b α ( e respectiely. We say that a data graph conorms to an authority transer schema graph i it conorms to the corresponding schema graph. (Notice that the authority transer schema graph has all the inormation o the original schema graph. In Balmin at el. [BHP4] the authority transer rates or each edge type was assigned manually by a domain expert on a trial and error basis. In contrast, our techniques allow this tas to be done automatically based on the user s eedbac as we explain in Section 5. Figure 3 shows the authority transer schema graph that corresponds to the schema graph o Figure 2 (the edge labels are omitted. The motiation or deining two edges or each edge o the schema graph is that authority potentially lows in both directions and not only in the direction that appears in the schema. For example, a paper passes its authority to its authors and ice ersa. Notice howeer, that the authority low in each direction (deined by the authority transer rate may not be the same. For example, a paper that is cited by important papers is clearly important but citing important papers does not mae a paper important. Figure 5: The DBLP Authority transer data graph. Authority Transer Data raph. ien a data graph D(V D,E D that conorms to an authority transer schema graph A (V,E A, we can derie an authority transer data graph D A (V D, A E D as ollows. For eery edge e = (u E D the authority transer data graph has two edges e = (u and b e = ( u. The edges e and e b are annotated with authority transer rates a(e and a(e b. Assuming that e is o type e, then α ( e α(, ioutdeg e = OutDeg ( u, e, ioutdeg ( u, e = e ( u, e > where OutDeg ( u, is the number o outgoing edges rom u, o type e. The authority transer rate a(e b is deined similarly. Figure 5 illustrates the authority transer data graph that corresponds to the data graph o Figure and the authority transer schema graph o Figure 3. Each edge is annotated with its authority transer rate. Notice that the sum o authority transer rates o the outgoing edges o a node u o type µ(u in the authority transer data graph may be less than the sum o authority transer rates o the outgoing edges o µ(u in the authority transer schema graph, i u does not hae all types o outgoing edges. 3. uery Deinition and ObectRan2 In this section we deine a query and describe a slightly modiied ersion o ObectRan originally presented in [BHP4], called ObectRan2. The modiication to the original deinition is that the nodes o the base set are (

4 weighted. The weights are computed using IR techniques or the original query and using query expansion techniques or subsequent queries as we describe in Section 5. Keyword uery. A eyword query is deined as a tuple o eywords =[t,,t m ]. To incorporate weighing in the base set, we deine the query ector as ollows: uery Vector. For each query =[t,,t m ] we deine a query ector =[w,.., w m ] where w i is the weight o the query eyword t i. The initial query ector or a query is [,,], since we assume that the query term weights are all. These weights change during the query expansion stage described in Section 5. The answer to is a list o obects with descending ObectRan2 scores with respect to. ObectRan2 is computed as ollows. Let (V,E be a graph, with a set o nodes V = {,..., n } and a set o edges E. A surer starts rom a node (database obect i o the base set o V and at each step, he/she ollows an edge with probability d or gets bored and umps to a node in the base set with probability d. The ObectRan2 alue o i is the probability that at a gien point in time, the surer is at i. ien a query, we irst ind the query base set S(, (rom now on reerred to simply as base set when the eyword is implied which is the set o nodes/obects that contain at least one eyword in. In contrast to the original ObectRan [BHP4], the random surer umps to dierent nodes o the base set with dierent probabilities. This probability or a node is proportional to the IR score IRScore(, o the node (a node is also iewed as a document we oerload symbol in this case gien the query ector. IRScore(, = (2 where denotes the dot product operator, =[W(,t,,W(,t m ] is the document ector or, and W(,t is the IR weight o term t or document. W(,t is deined using a traditional IR weighing ormulas lie BM25 [RW94] or Oapi [Sin]. The latter is deined below: n d +.5 ( + t ( 3 + qt ln.. (3 d +.5 dl + qt ( ( b + b + t adl t, 3 where, or a term t, t is the requency o t in the document, d is the number o documents in the database containing term t, dl is the size o in characters, adl is the aerage document size, n is the total number o documents in the database, and (between. 2., b (usually.75, and 3 (between are constants. We use a tuple and not a set as in [BHP4], because the order o the eywords becomes important when we introduce the notion o the weighted base set. We normalize the IR scores o the nodes in the base set to sum to one, since they represent probabilities. The ObectRan2 scores ector r = [r (,,r ( n ] T gien query ector, where n= V D, is deined as ollows: r dar ( d + s S ( = (4 where A is a n n matrix with A i = α(e i there is an edge e( i in A E D and otherwise, d is the damping actor which controls the base set importance, and s = [s,..s i., s n ] T is the base set ector, where s i = IRScore( i, i i S( and s i = otherwise. Note that the only dierence to ObectRan is the deinition o the s i s which were or in [BHP4]. 4. Explaining uery Results In this section we tacle the problem o explaining a query result. For instance, as discussed in Section, the Data Cube paper in Figure (see Figure 5 or corresponding authority transer data graph is raned high or the query OLAP. What is the best way to explain to the user why this paper, reerred to as the target obect, receied a high ran? This problem is een more critical in complex biological databases as the one o Figure 4. Figure 6: The DBLP Authority transer data graph annotated with authority lows or query OLAP. Intuitiely, we want to show to the user the paths in the authority transer data graph D A that authority traersed to reach the target obect, starting rom the nodes in the base set S(. For that, we create an explaining subgraph o D A that contains all edges that transer authority to gien, and eery edge in is annotated with the amount o authority that lows on this edge and eentually reaches. We create in two stages: (i Construction stage: contains all nodes and edges o D A that are part o a directed path going rom the base set S( to. That is, contains all edges that can potentially carry authority low to.

5 (ii Flow adustment stage: We compute the explaining authority lows on the edges o. The explaining authority low Flow(e o an edge e is the amount o authority low that is transerred through e and eentually reaches, on D A or. Figure 7: Intuition behind low adustment. The construction stage is straightorward and is achieed as ollows: We irst construct the temporary subgraph D, starting rom the target node and traersing edges o D A ollowing the edges in the opposite direction in a breadth irst manner (depth irst would also wor until no more edges can be traersed. Then, we start rom the authority sources (base set nodes o D and traerse the edges o D in the orward direction until no more edges can be traersed. All nodes and edges traersed in the orward stage are added to the explaining sub graph. The low adustment stage is more challenging because we hae to adust the original edge authority lows or to subtract the authority low not reaching to. For instance, in Figure 7 we must subtract rom the edge lows the amount that will eentually lea out o through 2 4. By original lows we reer to the authority lows at conergence state in D A or ObectRan2 execution or query. The original low or edge i is: Flow ( = d α ( r ( (5 i i i where a( i is the authority transer rate o edge e = ( i in D A according to Equation. Figure 6 illustrates the original authority lows or d =.85 and query =[ OLAP ], on the authority transer data graph o Figure 5. The computed ObectRan2 scores ector r = [.76,.2,.9,.76,.7,.25,.83] T, ater 5 iterations. It is more intuitie to iew the problem as adusting the edge lows instead o adusting the node scores, although the adusted node scores can be easily computed gien the edge lows in the end. One could thin o simply reducing the low on an incoming edge i o proportionally to the ratio o.2 the outgoing low o going outside. Howeer, this approach will ail i there are cycles in, since adusting the low o an edge can hae a ripple eect. Hence, an iteratie method is used, in the spirit o the PageRan/ObectRan computation. In particular, or eery 4 node u, with the exception o the target node, we iteratiely reduce its incoming lows proportionally to the low going rom u towards nodes outside o. We do not adust the incoming lows o the target node, as the purpose o the explaining subgraph is to explain to the user the total authority that receies rom other nodes in D A. We assume all edges are bidirectional (arbitrarily small low rates can be assigned to direction o small importance to guarantee conergence as proed by Theorem. For instance, or the explaining subgraph in Figure 7 with target node, where we assume d= (i.e., nodes pass all their authority to their neighbors and all edges are o the same type, we adust the original edge lows o 2 and 3 2 as ollows: Hal o the low going through these edges goes through 2 and hal through 2 4. Since 2 4 is outside, we cut the lows o 2 and 3 2 to hal, i.e., to.5 and.5 respectiely. This process is repeated iteratiely or all edges in until the computation conerges. Note that the low on edges i, i.e., edges that end at, are not adusted. Details o adustment stage: The details o the adusting algorithm are as ollows: For each node in, let O( be the summation o all outgoing lows o in and I( be the summation o all incoming lows o in (we consider all incoming edges in and not D A Obseration below shows that both are equal. It is (, since Ι( = Flow( (6a O ( = Flow ( (6b (, Obseration : There is no incoming edge i with nonzero authority low, where is in but i is outside. I such en edge existed, it would hae been included to during the construction stage. As mentioned beore, our goal is to compute the actor h( by which the incoming low I( o each node must be reduced to be consistent with the reduced outgoing low O( o in. It is: Flow, = h( Flow (, (7 ( Intuitiely, this actor h( is computed by the ratio o r ( and r ( which are the ObectRan score o in (the original score and D A respectiely. Hence, or a node : O( r '( = (8 d

6 Explain-ObectRan(Target Obect, raph D A, Base Set S(={s,,s n},threshold T { /*Construction Stage */ Create a temporary subgraph D by executing breadth-irst search on D A with as the root node, traersing edges in opposite direction; 2Create explaining subgraph, by executing breadth-irst search on D with the nodes in base set S( as root nodes, traersing edges in right direction; /*Flow Adustment Stage */ 3For each edge i-> in,compute Flow ( i-> using Equation 5; 4For each node in set h( =; 5While not conerged do For each node in except do Compute h( using Equation ; 6Update the Flow o each edge in using Equation 7; 7Return ; Figure 8: Algorithm to Compute Flows in Explaining Subgraph. r '( h( = (9 r ( Combining Equations 6b, 7, 8 and 9, we get the ollowing ixpoint equation or the computation o h(. h( = ( h( Flow(, (, d r ( We rewrite this equation using Equation 5: h( = ( h( d α (. r ( (, which then becomes h( and inally, = d r ( d * r ( ( h( α ( (, d r ( ( h ( ( h( = α ( (, Obseration 2: The original ObectRan2 scores are not used in computing the reduction actor h(. Implementation note: While executing the iteratie algorithm deined by Equation, we need to store the current h( actor or each node. The current alues o the incoming lows do not need to be stored since they can be on-the-ly computed rom the original alues using Equation 7. Theorem : Iteratiely computing Equation on the explaining subgraph conerges. Proo: The ixpoint computation o Equation is equialent to the PageRan computation, i we replace incoming by outgoing edges and remoe the damping actor. The PageRan computation has been shown to conerge i the graph is aperiodic and irreducible [MR95]. The ormer is generally satisied, whereas the latter is satisied or connected graphs. The explaining subgraph is connected due to its construction method all nodes are connected to the target node. To guarantee conergence, we always consider a non-zero reerse direction edge type or eery edge type. Furthermore, there are no low sins [BP98] since there is a path rom eery node to the target node. When it conerges, we update all edge lows using Equation 7. Figure 8 shows the steps o the algorithm to create the explaining subgraph. Figure 9: Explaining Subgraph or Range ueries in OLAP paper in Figure 6. Example. Figure 9 shows the explaining subgraph or =[ OLAP ] and target obect 4 ater 5 iterations o Equation. Note that the Data Cube paper (see Figure 6 is not in, since there is no path rom that paper to 4. Notice that the incoming lows o the target obect 4 are the same as the original ones o Figure 6. The computed reduction actors ater 5 iterations are as ollows: h(=.59e-4, h(2=4.77e-4, h(3=., h(4=., h(5=.6 and h(6=.67. Note that h(4 is as 4 is the target obect which implies that its incoming low rom 5 is not adusted as shown in Figure 9. Also notice that the incoming low reduction actor o is small because its incoming low needs to be reduced proportionally to eliminate the large low rom to 7 (see Figure 6, which is going outside o. This in turn creates a ripple eect reducing the incoming lows o nodes 3 and 2, according to their reduction actors. The explaining subgraph can be ery large which would mae its generation slow and its display to the user, impossible. Hence, in practice we limit the radius o to L (longer paths are generally unintuitie [C69] and carry

7 less authority and only eep the paths with high authority low. We apply these techniques in our online demo. We hae ound that a relatiely small L (e.g., L=3 alue is adequate to eectiely explain a result and produce useul reormulations (see Section uery Reormulation uery reormulation using releance eedbac has been well studied in traditional IR [SB9, RL3, Eth93, BSA+95, Har88], where query expansion has been the dominant strategy. That is, eywords are added to the original query according to the user s eedbac. Such techniques are not adequate or ObectRan2, since they ignore the lin-structure o the graph which plays a ey role in the raning. In this section we tacle or the irst time the problem o reormulating authority low queries. We propose an automatic query reormulation technique gien the results selected by the user. For instance, i the user selects the Range ueries in OLAP paper in Figure 5 as a releant obect, what is the best way to reormulate the query using this paper (reerred as eedbac obect? The explaining subgraph described in Section 4 is a ey structure or query reormulation since a ote o the user or eedbac obect can be iewed as ote o the user or the explaining subgraph o. Oeriew o process: First, the system computes the top- obects with the highest ObectRan2 alues. The user mars a result obect (or multiple obects as releant user s clic-through could be used to implicitly derie such marings. Then the explaining subgraph o is computed. Based on the content and lin-structure o we reormulate the initial query. In particular, the Contentbased component (Section 5. o the reormulation is inspired by traditional query expansion ideas and leads to a query expansion; whereas the Structure-based component (Section 5.2 adusts the authority transer rates o the authority transer schema graph based on the edge types in. The two reormulation components can be combined. 5. Content-based Reormulation According to traditional reormulation techniques, the terms in the eedbac obect (iewed as a document should be added, appropriately weighted, to the original query. Howeer, due to the nature o authority low raning, we extend this idea to also include terms in the obects that transer high authority to. These obects are the nodes o the explaining graph. The weight o an expansion term t is proportional to the low that the nodes that contain t pass to, that is, the outgoing low o these nodes in. We consider a single eedbac obect we extend to multiple eedbac obects in Section 5.3. A term t is weighted according to its distance rom and the amount o authority it transers to, as shown in Equation. The authority low a node transers to is its outgoing low in the explaining graph Section 4. w as explained in D (, ( t = ( C d Flow ( ( t (, where C d is the decay actor (in the spirit o XRANK [SB + 3] which is typically set to.5, and D(, is the distance (length in number o edges o rom. Note that i is, then we use d Flow( instead o Flow(, (, (, since the outgoing low o is not speciied in. We select the top-s terms Z with highest weight (ignoring stop words and add them, ater normalizing them as explained below, to the original query ector. The reormulated query ector i at iteration i is deined as i + C e > = w ( t t, i (2 i t Z, i = where t is the ector o term t (as in the ector space model [Sin], and C e is the expansion actor, typically.5, used to scale the weights o new terms (as well as new weights o old terms with respect to the terms present in current query ector. Normalization o term weights: The computed term weights using Equation must be normalized with respect to the weights in the current query ector. This done as ollows: Compute the aerage a o the term weights o the current query ector i, 2 Let x = max w ( t be the maximum weight o any t S term in Z. Let t s be the term that has this weight. 3 We normalize the term weight o terms in Z such that w (t s becomes a. That is, we multiply all term weights in Z a with. x Example 2. Consider the authority transer data graph o Figure 5, query =[ OLAP ], and eedbac obect, is the Range ueries in OLAP paper. The explaining subgraph (Figure 9 is created. Using Equation, and assuming C d and C e are.5, the top-5 new terms are olap(., cubes(.99, range(.99, multidimensional(.5 and modeling(.5. Note that the terms in the eedbac obect (target obect o generally get a higher weight due to the decay actor C d. The reormulated query ector computed by Equation is [olap, cubes, range,

8 multidimensional, modeling] = [2.,.99,.99,.5,.5]. 5.2 Structure-based Reormulation The structure-based reormulation adusts the authority transer rates based on the explaining subgraph. We consider a single eedbac obect we later extend to multiple eedbac obects in Section 5.3. Intuitiely, i edges o an edge type e carry large authority in then the user probably beliees e is an important edge type or the query. We boost the authority transer rate o each edge type present in according to the authority it transers (to the eedbac obect. The reormulated authority transer rate a (e o edge type e is computed by α'( e = + C Flow( α( e (3 (, (, has type e where C is the authority transer rate adustment actor, typically set to.5, used to scale the authority transer rates with respect to their preious alues, α e ( is the preious authority low rate o edge type e. The actor F ( e = Flow ( in (, (, has Equation 3 is normalized beore used, as explained below. Normalization: In order to hae a controlled modiication o authority transer rates we do the normalization as ollows: For each edge type e we normalize the actor F(e by setting its maximum alue M or an edge type to. Then diide others by M. 2 Compute a (e or each edge type e using Equation 3 and the normalized alues rom Step. 3 Normalize a (e as in Step, such that α '( e. 4 Finally we once again adust a (e o each edge type such that the sum o authority transer rates o the outgoing edges o eery schema node in the authority transer schema graph is less than or equal to, which is required or the conergence o ObectRan2. Example 2 (cont d. The authority transer rates o the original query are [PP,PP,PA,AP,CY,YC,YP,PY] = [.7,.,.2,.2,.3,.3,.3,.]. Using Equation 3 and the normalization process, the reormulated authority transer rates are [.67,.,.24,.6,.24,.24,.24,.8]. Notice that the transer rates o PA and AP edge types are increased and decreased respectiely as they carry greater and lesser authority to the eedbac obect respectiely. 5.3 Multiple Feedbac Obects When the user selects multiple eedbac obects U, we combine the expansion term weights (in Content-based reormulation and the low weights (in Structure-based reormulation across the explaining subgraphs o dierent type e eedbac obects using a monotone aggregation unction. Typical choices are sum, min, max and aerage. We use summation in our user sureys and experiments. That is, or content-based reormulation we add the expansion term weights. w ( t = w ( t (4 i U i where w i (t is the weight or term t or eedbac obect i, computed by Equation. For Structure-based reormulation, similarly we add the F(e actors or each edge types. F ( e = F ( e (5 i U i where F i (e is the sum o lows or edges o type e or eedbac obect i, computed by Equation 3. We ollow the same normalization process ater aggregating the weights to yield the necessary query reormulation. 6. Experiments We experimentally ealuate our algorithms in terms o quality and perormance. We conducted user sureys to ealuate the quality o our query reormulation techniques. We also ealuate the perormance o our algorithms and show that explaining query results and reormulating authority low queries are easible oer large graphs. This section is organized as ollows: First we briely describe the datasets used or ealuation and then Sections 7. and 7.2 present the user sureys and the perormance experiments respectiely. Datasets: We use our real datasets (Table. DBLPcomplete and DBLPtop are the complete DBLP dataset and a databases-related subset respectiely. We shredded the downloaded DBLP ile into the relational schema o Figure 2. DS7, whose schema is shown in Figure 4, is a collection o biological sources downloaded rom PubMed. DS7cancer is a subset o DS7 consisting o PubMed publications related to cancer and all biological entities related to these publications. Name #nodes #edges Size (MB DBLPcomplete 876, 46,662,6 395 DBLPtop 22,653 66,96 36 DS7 699,99 353,375,6 289 DS7cancer 37,796 38,46 Table : Real and Synthetic Datasets. 6. User Sureys We used DBLPtop or our user sureys and not DBLPcomplete since on-the-ly ObectRan2 executions on the latter are slow and surey subects would be irritated.

9 The irst phase (Section 6.. was conducted at Florida International Uniersity (FIU inoling ie proessors and PhD students rom the database lab, who were not inoled with the proect. The goal o this surey was to compare content-based, structure-based, and content & structurebased reormulations. The result was that structure-based reormulation is superior. The second phase (Section 6..2 ocused on structure-based reormulation and inoled FIU and outside (including IBM TJ Watson and Almaden database researchers, not inoled in the proect. In both phases we also measure the capability o our system to discoer the authority transer rates set by a domain expert Internal Surey. First we measure the precision/recall o our releance eedbac algorithms using the standard releance eedbac ealuation method o residual collection [RL3, SB9]. Then we show how our structure-based reormulation component can be used to automatically train the authority transer rates o the DBLP authority transer schema graph (Figure 3. We measure the quality o this training assuming the ground truth rates or this dataset are the ones ound at [BHP4]. The residual collection method [RL3, SB9] can be summarized as ollows: All obects seen by the user or mared as releant are remoed rom the collection and both the initial and all reormulated queries are ealuated using the residual collection. We use the aerage precision as the ealuation measure. Note that the recall is the same as the precision in our case since we limit the output results to. We report the surey results or 4 releance eedbac iterations and or the ollowing 3 settings: i Content-Only reormulation (C =&C e =.2, ii Content & Structurebased reormulation (C =.5& C e =.2 and iii Structure- Only reormulation (C =.5& C e =. (We hae ound that these alues o C and C e are appropriate or this dataset. The decay actor C d is set to.5.we use L=3 to limit the size o the explaining subgraph as explained in Section 4, We initialize the authority transer rates o each edge type to.3. Figure shows the surey results. We see that the structure-only reormulation perorms the best. Contentbased reormulation is not eectie in our setting because the users are domain experts and hence now the right eywords, i.e., traditional query expansion is not eectie. Note that in a dierent domain the results could ary. Next we ealuate the eectieness o structure-based reormulation to automatically train the authority transer rates o the DBLP authority transer schema graph and compare the learned weights to the ones o [BHP4], which we iew as ground truth. The rates there were assigned manually by domain experts in a trial and error manner. We start by setting the transer rates o all edge types to.3. We again limit the length o paths o the explaining graph with L=3. Let UserVector[PP,PP,PA,AP,CY,YC,YP,PY] be the authority rates ector. It is initialized to [.3,.3,.3,.3,.3,.3,.3,.3]. The ground truth ObVector is [.7,.,.2,.2,.3,.3,.3,.]. At each iteration we compute the current UserVector produced by the reormulation and compute the cosine similarity cos(obvector,uservector. Aerage Precision 5.% 4.% 3.% 2.%.% Initial Reormulated ueries uery Content & Structure-based Structure-Only Content-Only Figure : Aerage Precision or dierent calibration parameters. Figure shows the cosine similarity training cures or 4 users aeraged oer 5 queries each or a dierent alue o C (C e is always. We see that the cosine similarity initially increases with the number o iterations and then decreases due to oeritting. Larger C alues lead to aster pea, since the adustment o the rates is less smooth (see Equation 3. Cosine Iterations C=. C=.3 C=.5 C=.7 C=.9 Figure : Training o the Authority Transer Rates. ObectRan2 s. ObectRan: Finally, we also conducted a surey comparing the quality o ObectRan2 with ObectRan [BHP4]. Users were presented with 7 queries (single as well as multi-eyword queries with Top- results obtained using ObectRan2 and a modiied ersion o ObectRan as explained below. Table 2 shows the precision o Top- results using ObectRan2 and ObectRan techniques. ObectRan2 is slightly better than ObectRan or the DBLP dataset, but we expect that it will be considerably better or datasets with longer text descriptions (DBLP titles are too short or IR unctions to show a great beneit. We used a slightly modiied ersion o ObectRan in order to mae the

10 Precision or each query DBLP eyword ueries ObectRan2 ObectRan [olap], [query, optimization] 9 [xml], [mining], [proximity, search] [xml, indexing] 9 8 [raned, search] 9 Aerage precision Table 2: ObectRan2 s. ObectRan. comparison air, with our weighted base set approach. A drawbac o ObectRan [BHP4] is that it aors the more popular eywords in a query. The ObectRan alues o obects tend to be sewed towards popular eywords in a query. The modiied ormula is gien below: t,..., t 2 i i r ( = ( r ( (6 i=,..., m t g( t where g t is a normalizing exponent, set to t ( i / log( S ( t i External Surey. g = We conducted an external surey operating on DBLPtop using only structure-based reormulation as it was ound to be the best, in the internal surey. Figure 2 shows the aerage precision cure or 5 iterations aeraged oer 2 queries by users (2 queries per user. Figure 3 shows the authority transer rate training cures or the external surey which are similar to those in the internal surey. Aerage Precision 4.% 35.% 3.% 25.% Initial uery Reormulated ueries Structure-Only Iterations Figure 2: Aerage Precision using structure-only reormulation with C = Perormance Experiments To ealuate the perormance o our algorithms, we conducted experiments on all the our datasets. We used a linux machine with Power 4+.7Hz processor and 2B o RAM. The total execution time is measured or arious stages: (a computing the top- obects or the initial or reormulated query, (b creating the explaining subgraph, (c executing the explaining ObectRan2 on the explaining subgraph, and (d creating the reormulated query. ( i Cosine Iterations C=.5 Figure 3: Training o the Authority Transer Rates. Manipulating Initial ObectRan alues: As in [BHP4], or the initial user query, we initialize eery node in D A with their global ObectRan alues, to achiee aster conergence. Then, or the irst reormulated query we use the ObectRan alues o the initial query and so on. The intuition is that the ObectRan alues o the newly reormulated query are expected to be close to the ones obtained by the preious query. Figures 4(a and 5(a show the query and reormulation times oer DBLPcomplete and DBLPtop respectiely. They show the execution times or the arious components o the process: execute the query (irst bar, and create the reormulated query (last three bars at each user eedbac and reormulation iteration. We use L=3 as the radius o the explaining subgraph, and conergence threshold.. Figures 4(b and 5(b show the number o ObectRan2 iterations or the initial and the reormulated queries oer the whole graph. Clearly, using the preious scores as initial alues accelerates the conergence o ObectRan2. Time(secs ~ ~28.5 ~28.76 ~28.88 ~ `.5 Initial uery Reormulated ueries ObectRan2 Execution Explaining ObectRan2 Execution Explaining Subgraph Creation uery Reormulation (a: uery and Reormulation Times. The query reormulation step, where the reormulated query is generated gien the conerged Explaining ObectRan2 alues, is ast, as the complexity o that step is O( V (in case o content-only reormulation and O( E (or structure-only reormulation and O( V + E or both content and structure-based reormulations, where V and E are the ertex and edge sets o the explaining subgraph respectiely.

11 ObectRan2 Iterations Initial uery Reormulated ueries (b: ObectRan2 iterations. Figure 4: DBLPcomplete Execution. The ObectRan2 execution times or DBLPcomplete and DS7 are clearly too long or exploratory searching. This can be addressed in one o the ollowing ways: use aster hardware, precompute ObectRan2 alues as in [BHP4], or deine ocused subsets lie DBLPtop and DS7cancer. The ObectRan2 execution times or these datasets are 2 seconds or the initial query and less than sec or the subsequent reormulated queries [VHR7]. Table 3 shows the number o Explaining ObectRan2 (not to be conused with ObectRan2 iterations oer arious datasets and or arious iterations. Dataset Iterations DBLPcomplete DBLPtop DS DS7cancer Table 3: Aerage Explaining ObectRan2 Iterations. A similar set o results are obtained or the biological datasets, DS7 and DS7Cancer as shown in Figures 6 and Related Wor We irst present how state-o-the-art wors ran the results o a eyword query, using traditional IR techniques and exploiting the lin structure o the data graph. Then we discuss about related wor on the releance eedbac and query reormulation. Traditional IR raning. For an oeriew o modern IR techniques we reer to [Sin]. Any state-o-the-art IR raning unction is based on the t-id principle [Sin]. The shortcoming o these semantics is that they miss obects that are much related to the eywords, although they do not contain them. The most popular speciicity metric in Inormation Retrieal is the document length (dl. The releance inormation is hidden in the lin structure o the data graph which is largely ignored by the traditional IR techniques. Lin-based semantics. Saoy [Sa92] was the irst to use the lin-structure o the Web to discoer releant pages. This idea became more popular with PageRan [BP98], where a global score is assigned to each Web page. HITS [Kle99] employ mutually dependant computation o two alues or each web page: hub alue and authority. Balmin et al. [BHP4] introduce the ObectRan metric. In contrast to PageRan, it is able to ind releant pages that do not contain the eyword, i they are directly pointed by pages that do. Haeliwala [Ha2] proposes a topic-sensitie PageRan, where the topic-speciic PageRans or each page are precomputed and the PageRan alue o the most releant topic is used or each query. Both wors apply to the Web and do not address the unique characteristics o structured databases, as we discuss in Section. Furthermore, they oer no adusting parameters to calibrate the system according to the speciics o an application. Recently, the idea o PageRan has been applied to structured databases [SB + 3, HXY3]. XRANK [SB + 3] proposes a way to ran XML elements using the lin structure o the database. Furthermore, they introduce a notion similar to ObectRan transer edge bounds, to distinguish between containment and IDREF edges. Huang et al. [HXY3] propose a way to ran the tuples o a relational database using PageRan, where connections are determined dynamically by the 33 query worload and not statically by the schema. Howeer, none o these wors exploits the lin structure to proide eyword-speciic raning. Furthermore, they ignore the schema semantics when computing the scores. Releance Feedbac & uery Expansion. Salton and Bucley [SB9] introduced the idea o using releance eedbac or improing search perormance. Releance eedbac coers a range o techniques intended to improe a user s query and acilitate retrieal o inormation releant to a user s inormation need. In [BSA94, BSA + 95], they showed that query expansion and query term reweighting are essential to Releance Feedbac. For a detailed surey o releance eedbac methods we reer to [RL3, Har92]. The basic approach o term selection, term reweighing and query expansion [Eth93, Har88, MSB98, SVR83, SB95, KF6, XC96, LJ, HC93] using terms drawn rom the releant documents wors well or traditional IR which is content-based. For lin-based metrics lie ObectRan [BHP4] this yields poor results as shown in Section 6... Hence, we need lin-based

12 .7 ~2.7 ~.76 ~.47 ~.47 ~ Initial uery Reormulated ueries ObectRan2 Execution Explaining subgraph creation Explaining ObectRan2 Execution uery Reormulation Initial uery Reormulated ueries Time(secs (a: uery and Reormulation Times. (b: ObectRan2 iterations. Figure 5: DBLPtop Execution. ObectRan2 Iterations Time(secs ~99.54 ~37.9 ~3.9 ~32.2 ~3.59 ~ Initial uery Reormulated ueries ObectRan2 Execution Explaining ObectRan2 Execution Explaining Subgraph Creation uery Reormulation ObectRan2 Iterations Initial uery Reormulated ueries (a: uery and Reormulation Times. Figure 6: DS7 Execution. (b: ObectRan2 iterations..25 ~2.27 ~.92 ~.72 ~.93 ~.7 ~.6 5 Time(secs Initial uery Reormulated ueries ObectRan2 Execution Explaining Subgraph Creation Explaining ObectRan2 Execution uery Reormulation ObectRan2 Iterations Initial uery Reormulated ueries (a: uery and Reormulation Times. (structure-based releance eedbac methods as described in Section 5. A recent wor [VB6] on releance eedbac is based on web-graph distance metrics. The basic idea, which is similar to our content-based reormulation technique, is that releant pages tend to point to other releance pages, while irreleant pages are pointed to by other irreleant pages. Another recent study on releance propagation oer the web [LZ + 5] propose site-based propagation models that out-perorm hyperlin-based models. Another recent wor [SZ5] describes actie Figure 7: DS7cancer Execution. (b: ObectRan2 iterations. eedbac algorithms that help to choose documents or releance eedbac so that the system can learn most rom the eedbac. 8. CONCLUSIONS In this wor we presented a technique to explain the results o authority low queries and also reormulate them. We discussed reormulations based on content and structure o the underlying graph. We also showed how to automatically train the authority transer rates o the schema graph based on user preerences. We presented eicient algorithms to

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