P2P Information Retrieval Using Semantic Overlay Networks

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P2P Information RetrievalUsing Semantic Overlay
Networks

• Authors Tang(Univ Rochester), Zu(HP Labs),
  Dwarkadas(Univ Rochester)

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Problems with Current P2P

• Can only be searched by keyword.
• Documents not semantically organized
• Ways to Search
• Centralized Search
• Decentralized Search floods nodes.

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How to Solve?

• pSearch
• Decentralized, non-flooding algorithm
• VSM (Vector Space Model)
• LSI (Latent Semantic Indexing)
• CAN Network

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Vector Space Modeling

• Represents documents and search terms as vectors.
• When searching documents are ranked by according
  to similarity of document vector and the query
  vector.
• Given Vectors X and Y
• cos(X,Y) SUM(Xi Yi) i 0 k
• k X Y

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VSM Cont.

• Represents a Corpus as a t x d Matrix A
• t is the number of search terms in the corpus
• d is the number of documents in the corpus
• arj is the importance of term r in document j

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Latent Semantic Indexing

• Uses statistically derived conceptual indices
• Singular Value Decomposition
• Transform High-Dimensional Vector from VSM into a
  Lower-Dimensional semantic vector

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What SVD does

• Takes the matrix A from the VSM and decomposes it
  into the product of 3 matrices
• A UED
• U u1 ur a t x r matrix
• E diag(e1 er) a r x r diagonal matrix
• ejs are As singular values
• V v1 vr a d x r matrix

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LSI Cont

• What LSI does with SVD
• Approximates matrix A of rank r by a matrix Al of
  lower rank
• Al UlElVl
• Omits all but largest l singular values
• Rows of ElVl the semantic vectors for documents
• Given UlElVl semantic vectors of queries,
  documents, or terms that were not originally in
  the space can be folded into the space

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LSI Cont

• By choosing appropriate l noise from smaller
  singular values is eliminated
• Studies suggest l 50350 is best

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Content Addressable Networks

• Values of CAN
• Fault-tolerant distributed hash table
• Partitions a d-dimensional Cartesian space into
  zones and assigns each zone to a node
• Locating a document is reduced to routing to the
  node that contains that document

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Finding something in a CAN

• D joins and takes over part of Cs zone
• D is looking for a document with key 0.4,0.1
• Routed to E then to A

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pSearch

• pLSI modified LSI for pSearch
• Large number of machines are organized into a
  semantic overlay.
• This forms the pSearch Engine
• Engine is subset of nodes with good connectivity

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pLSI Algorithm

• Sets the dimensionality of the CAN to be the
  dimensionality of the semantic space
• Index for a document is stored in the CAN using
  the semantic vector as the index.
• How it works
• Engine node receives Document A and creates the
  Semantic vector Va via LSI and is used as the key
• Receiving a query the Engine nodes transforms the
  query into a vector Vq and routes it to the
  correct node
• When node is reached query is flooded to nodes in
  radius r
• All receiving nodes do query via LSI

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pLSI Cont

• Relies on inverse document frequency and basis of
  semantic space
• Allows nodes to compute semantic vectors of
  queries and documents independently
• Challenges
• Dimensionality mismatch
• There are not enough nodes to partition the can
  when it has the dimensionality set by the LSI,
  50350

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pLSI Cont

• Uneven Distribution of Indices
• Vectors are normalized and reside on the surface
  of the unit sphere S in the semantic space
• cos ? (similarity) is proportional to the
  distance between A and B to their distance p on
  the circle since on a unit sphere cos ? cos p
• Large Search Space
• Limiting the search space in a high-dimensionality
  is difficult

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Solving Dimensionality

• For a l-dimensional CAN network with n nodes each
  node should maintain 2l neighbors only if l lt
  log2(n)
• Since 2x zones will be produced by partitioning
  along x dimensions
• This results in more zones than nodes
• If l gt log2(n) and zones partitioned evenly then
  only log2(n) neighbors are required

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Solving Dimensionality Cont

• This results in only the low dimensionality
  semantic vectors being partitioned
• Example
• Supposed we have Va (-0.1,0.55,0.57,-0.6) and
  Vq (0.55,-0.1,0.6,-0.57)
• They have similarity of .574 with a majority
  contributed by the last two parts of the vector.
  If we have only four nodes the 4-Dimensional CAN
  may only be split on first two parts of the
  vector.

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Solving Dimensionality Cont

• Solving only low dimensionality partitioning
• Rolling Semantic Indexes
• Given V(v0,,vl) we rotate m dimensions each
  time to produce a new vector.
• Support Vector
• Vi(vi-m,,vi-m-1) m2.3ln(n)
• Given a document A with vector Va we store its
  index on p places in the CAN Vai where i 0
  p-1
• The pLSI algorithm uses different Vqi query
  vectors to search and return relative documents.

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Rolling Index Example

• m 2

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Balancing Indexes

• Content Aware Boot Strapping
• Forces the distribution of nodes to follow the
  distributions of indices
• At partitioning the node randomly picks a
  document and computes the semantic vector and
  rotates it by i (0 lt i lt p) the space is then
  partitioned a across the lowest un-partitioned
  dimension and then hands over half that zone

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Balancing Indexes Cont

• Advantages Provided
• More balanced index
• Larger num of nodes used in semantic space with
  greater num of documents
• Index Locality
• Assuming the documents published by a node have
  similar semantics, on space i, indices of a
  nodes documents are likely to be published on
  itself or its neighbors.
• Query Locality
• Assuming documents published by a node are good
  indications of user queries, more nodes near the
  user are likely to have relevant documents to the
  query.

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Reducing Search Space

• Content Directed Search
• Search Algorithm

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Content Directed Search

• Use indices and last queries on nodes to guide
  search
• Example

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1-25 are the node ids, q is the query, and a-f
are document vectors. N13 N8,12,14,18 14
is searched next because its samples are most
relevant N8,12,18,9,15,19 9 searched
next N8,12,18,15,19,4,10 4 searched next
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Algorithm Description

• XZ XZ,Y mean X is a parameter of Z with Y as
  an additional attribute
• DZ is set of Semantic Vector indices stored at
  node Z
• QZ is the set of semantic vectors of queries
  recently processed at Z
• UiZ summarizes the indices stored on Z and the
  queries recently processed by Z
• UiZ H/H H sum(d) d ? DiZ sum(q) q ?
  QiZ
• Z requests each of its neighbors P to send kc
  document vectors similar to UiZ and kr random
  samples

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Algorithm Cont

• When Z is under search for query q then Z uses
  the following to estimate Vqi
• eiP,Vqi max(cos(d,Vqi)) d ? SiZ,P
• Directs search on each rotated space
• Visits nodes with high value first and stops when
  T nodes have yielded no result.

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Experiment

• Used Text Retrieval Conference corpus

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Varying System Size
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Varying System and Corpus
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Content vs Query
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With Replication