Information Retrieval. Wesley Mathew

Transcription

1 Information Retrieval Wesley Mathew

2 Introduction and motivation Indexing methods B-Tree and the B+ Tree R-Tree IR- Tree Location-aware top-k text query 2

3 An increasing amount of trajectory data is being annotated with text descriptions to efficiently capture the semantics associated with locations; One fifth of web search queries are geographical; Find the top K results taking into account both location proximity and text relevancy for points of interest with associated text. 3

4 1. GPS-trajectory-sharing websites (e.g., Mountain Bike: GPS sharing: GPSies: and the Geolife dataset. 2. In location based social network services, each place is associated with tags and users can check in when located at such places (e.g., Four Square) 3. Trajectories with text descriptions can be extracted from travel itineraries, as well as Flickr photos 4

5 meadow waterfall, meadow, kiosk waterfall, cave meadow, kiosk waterfall, kiosk cave 5

6 B-tree is a tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time. The B Tree contains only data pages The B-tree is a generalization of a binary search tree, in which a node can have more than two children 6

7 B+ Tree combines features of ISAM and B Trees. (ISAM - Indexed Sequential Access Method) B+ tree represents sorted data in a way that allows for efficient insertion, retrieval and removal of records, each of which is identified by a key B+ tree contains index pages and data pages. The index pages in a B+ tree are constructed through the process of inserting and deleting records. 7

8 The data pages always appear as leaf nodes in the tree. The root node and intermediate nodes are always index pages These features are similar to ISAM. 8

9 The B -Tree provides the foundations for the R Tree R -Tree is a depth-balanced tree A spatial database consists of a collection of tuples representing spatial objects Every leaf node contains between m and M index records, unless it is the root node M is the maximum number of entries in a node m= {0, M/2} 9

10 Leaf nodes have index record entries like (I, tuple-identifier) Tuple-identifier refers to tuple in database, I refers to n-dimensional rectangle which is the bounding box of the spatial object index. Every non-leaf node has between m and M children unless it is the root The Non leaf nodes have entries like (I, child-pointer) child pointer is the address of a lower node in the R tree The I rectangle covers all rectangles in the lower nodes entries 10

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12 Traverse the R-Tree top to down, starting from the root, At each level - If there is a node whose directory rectangle contains the mbb to be inserted, then search the sub tree. - Else choose the node such that the enlargement of the directory rectangle is minimal, then search the subtree - If more than one node satisfy this, choose the one with smallest area. Repeat until a leaf node is reached 12

13 If a leaf node is not full, an entry [mbb, oid] is inserted into the tree Else if the leaf node is full - Split the leaf node and inserted into the correct one - Update the directory rectangles of the ancestor nodes if necessary 13

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16 Suppose a Leaf node has M entries If a new entry is to be inserted, then M+1 mbbs will be partitioned in to two nodes, such that The total area of the two nodes is minimized The overlapping of the two nodes is minimized Sometimes the two goals are conflicting Use the 1 st as the primary goal 16

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18 The IR tree is essentially an R tree Each node of which is enriched with reference to an inverted file for the objects contained in the sub-tree rooted at the node. A leaf node contains entries like (O, rectangle, O.di) O is an object in database D, rectangle is the bounding rectangle of object O O.di is the identifier of the document of object O. 18

19 A leaf node also contains a pointer to an inverted file for the textual contents of the object being indexed 1) vocabulary for all distinct terms in a collection of documents 2) A set of posting lists, each of which relates to a term t. Each posting list is a sequence of pairs <d, w d,t > d is the document contain term t w d,t is the weight of term t in document d. 19

20 A non-leaf node has the form (cp, rectangle, cp.di) cp is the address of a child node rectangle is the MBR of all rectangle in entries of the child node cp.di is the identifier of a pseudo document. The pseudo document represents all documents in the entries of the child node. The pseudo document enable us to estimate a bound of the text relevancy to a query of all the documents contain the subtree rooted at cp 20

21 N<- ChooseLeaf(MBR) Add MBR to node N, add document to the inverted file of N If N needs to be split then {O,P}<-N.split() If N is root node then initialize a new node M, Add O and P to node M, and update the inverted file of O, P, M Set M to the root node Else Ascending from N to the root, adjusting covering rectangles, updating the inverted file and propagating node splits as necessary; Else Update the covering rectangles and inverted files of the ancestor nodes of N 21

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24 O1.doc O2.doc O3.doc O4.doc O5.doc O6.doc O7.doc O8.doc Chinese Spanish Restaur ant Food

25 Vocabulary Inv File4 Posting list Inv File5 Posting list Inv File6 Posting list Inv File7 Posting list Chinese <O1.doc, 5 > <O3.doc, 7 > <O5.doc, 4 > <O7.doc, 1> Spanish <O2.doc, 5 > <O8.doc, 3 > <O6.doc, 4> <O7.doc, 1 > Restaurant <O1.doc, 5 > <O2.doc, 5 > <O4.doc, 7>, <O5.doc, 4>, <O8.doc, 3> <O6.doc, 3 >, <O7.doc, 4 > food <O3.doc, 1>, <O4.doc, 1 > <O7.doc, 1 > Vocabulary Inv File 2 Posting list Inv File3 Posting list Inv File1 Posting list Chinese <R1.doc, 5 >, <R2.doc, 7 > <R3.doc, 4 >, <R4.doc, 1 > <R5.doc, 7 >, <R6.doc, 4 > Spanish <R1.doc, 5 >, <R2.doc, 3 > <R4.doc, 4 > <R5.doc, 5 >, <R6.doc, 4 > Restaurant <R1.doc, 5 >, <R2.doc, 7 > <R3.doc, 4 >, <R4.doc, 4 > <R5.doc, 7 >, <R6.doc, 4 > food <R2.doc, 1 > <R3.doc, 1> <R5.doc, 1 >, <R6.doc, 1 > 25

26 D is the spatial database, Object O is the pair (O.loc, O.doc) O.loc is the location description, O.doc is a document The value of a term in the document vector as follows tf(t,o.doc) is the number of occurrence t in the document O.doc, tf(t, Coll) is the count of term t in the document collection Coll of D. tf(t,o.doc)/ O.doc is the maximum likelihood estimate of term t in the document O.doc ft(t,coll)/ Coll is the maximum likelihood estimate of term t in the collection Coll. is the smoothing parameters 26

27 LkT query retrieves k objects in the database D locations are the closest to the location specified in query their textual descriptions are the most relevant to the keywords in query. The objects returned are ranked according to a ranking function f(d Ԑ, P(Q.keywords/O.doc)) D Ԑ is the Euclidian distance between Q and O P(Q:keywords/O.doc) is the probability of generating query Q:keywords from the language models of the documents Ranking function for query likelihood language model: 27

28 Derive a ranking function as a linear interpolation of normalized factors for ranking as a object O with regard to a query Q. α (0,1) is a parameter used to balance the location proximity and text relevancy Euclidian distance between Q and O is normalized by maxd maxp is used to normalized the probability score into the range from Spatial Keyword Search in Trajectory Database 28

29 Minimal spatial textual distance (MIND ST )offers a lower bound on the actual spatial-textual distance between query Q and objects enclosed in the rectangle of node N MIND Ԑ (Q.loc, N.rectangle) is the minimum Euclidian distance between Q.loc and N.rectangle 29

30 For retrieving the top-k objects, the best-first traversal algorithm is used. A priority queue is used to keep track of the nodes and objects that have yet to be visited. The values of D ST and MIND ST are used as the keys of objects and nodes, respectively. The algorithm picks the node N with smallest MIND ST (Q,N) value among the unvisited nodes, when deciding which node is to be visited next. The algorithm terminates when the k nearest objects (ranked according to D ST ) have been found. 30

31 C. Gao and J. Christian S. and W. Dingming, Efficient retrieval of the top-k most relevant spatial web objects. Proceedings of. Very Large Database Endowment, C. Gao and L. Hua and O. B. Chin and Z. Dongxiang and Z. Meihui, Efficient Spatial Keyword Search in Trajectory Databases, Published in Computing Research Repository,

32 Thank you Questions? 32