Document retrieval Similarity –Vector space model –Multi dimension Search –Range query –KNN query Query processing example

Range Query x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7

Information retrieval in Structured P2P overlay High dimension -> Low dimension –Dimension reduction! Support range query and KNN query Guarantee precision and recall

pSearch: Information Retrieval in Structured Overlays

Peer-to-Peer VSM (pVSM) VSM : vector space model Basic ideas –The m most heavily-weighted terms t i, i=1,…,m are identified –The corresponding (h(t i ), index) pairs are stored in DHT Index : pointer to the actual document.

Example

Peer-to-Peer LSI (pLSI) LSI : Latent semantic indexing –Use SVD to transform and truncate a matrix of a terms vectors computed from VSM to discover the semantics of terms and documents Basic idea –l: dimensionality of LSI semantic space –k: dimensionality of Can cartesian space –Make l=k

pLSI (cont.) Challenges for pLSI –Sphere distribution of semantic vectors –Solution Transforming the sphere space

Latent Semantic Indexing vector space model SVD project new vectors compute similarity 12 TSVD

M-Chord: A Scalable Distributed Similarity Search Structure

iDistance – Indexing the Distance Space partitioning into n clusters –Reference points p i Each cluster mapped to an interval Each object x mapped to 1-d iDist(x)=i*c+dist(p i,x) Values indexed in a B+-Tree

Query R(q,r) –If a query intersects with a cluster dist(p i,q)-r ≦ r i –Scan the interval [i*c+dist(p i,q)-r,i*c+dist(p i,q)+r]

M-Chord Basic principles –Choose a set of n pivots p 0,…,p n-1 from a priori given sample dataset –Divide the set of indexed objects I into clusters C 0,…, C n-1 : –Every object x may be excluded without evaluating d(q,x) if

M-chord Pivot selection –Influence the performance of the search algorithm Publish –Use iDistance to map the dataset into a one- dimensional domain and join this domain with the Chord protocol –Using order preserving function h to a [0,2 m ) interval

M-Chord Data structure –Chord routing information –B+-tree storage for the (K i-1, K i ] (mod 2 m ) interval

M-Chord Range search –for each cluster C i, determine interval I i of keys to be scanned: –send an INTERVALSEARCH(I i, q, r) request to node N Ii responsible for the midpoint of interval –wait for all responses and create the final answer set.

M-Chord INTERVALSEARCH(I i, q, r)

M-Chord KNN search –The iDistance approach to KNN query processing a sequence of range queries with growing radius is not suitable for distributed environment multiple range iterations would result in an unpleasant number of successive message transmissions increasing the overall response time –Solution Employ a low-cost heuristic to find k objects that are near q Run the Range(q, Qk) query and return the nearest objects from the query result