Associative Peer to Peer Networks: Harnessing Latent Semantics

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Associative Peer to Peer Networks Harnessing
Latent Semantics

• Edith Cohen
• ATT Labs-research

Amos Fiat Haim Kaplan Tel-Aviv University
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Traditional Client-server Web
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Peer-to-peer Networks
Distributed network for sharing content (music,
video, software, etc.), where each host acts as
both a server and a client

• Harness vast resources
• Scalability/Robustness to failures/shutdowns

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P2P Search

Overall performance of a P2P network highly
depends on the efficiency and versatility of
search
What features are important ?

• Scope ability to locate rare items
  Find the 10th episode of Star Trek Voyager
• Partial-match/complex queries
  Find an Indiana Jones movie
• Or Indiana Joens movie..

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(search in) Basic P2P Architectures
Partial-Matches
Scope
Centralized (Napster) central index service.

• Decentralized peers are connected by low-degree
  overlay network.

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Associative P2P networks

• Retain Gnutellas desirable properties
• Distributed overlay network
• Peers store only what they need (common good at
  par with own welfare)
• No tight control of topology/content
• Support partial-match queries
• AND
• Have search scope (orders of magnitude
  improvement over Gnutella)

• Make implicit use of latent semantics
• Provably good on a reasonable model
• Very good on simulations

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P2P search framework

• Search queries are propagated on the overlay
  (from peer to a neighbor peer).
• When a peer receives a query, it checks if it can
  satisfy it decreases hop count and forwards it
  to a subset of its neighbors.
• Each search includes query and a propagation
  rule, which determines which neighbors the
  search is propagated to.

DHTs propagation rule hash of
query Gnutella propagation rule independent
of query Associative propagation rules are
predicates (guide rules)
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Overview

• What do we mean by latent semantics ?
• Challenges in using latent semantics in P2P
  setting
• Our proposal search propagation via Possession
  rules
• Possession rules overlays
• Search strategies
• Possession rules search strategies Rapier, GAS
• Models for blind search strategies (gnutella)
• Analysis in the Itemsets model
• Experimental evaluation
• More on GAS search strategy

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View of P2P file sharing network
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What is latent semantics?

• Selections people make are dependent
• If you buy baby formula, you are more likely to
  buy diapers.
• If two people loved a show, they are more likely
  to agree on other shows.

• Peer/Item matrix is Market Basket dataset.
  Similar to buyers/items, Document/terms,
  Web-pages/hyperlinks, movies/viewers.
• Applications for extracting patterns from market
  basket data Information Retrieval, Collaborative
  Filtering, Web search, Marketing, Recommendation
  Systems,. (clustering, search, association
  rules)

?? P2P search direct queries to peers with
interests that match yours
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Challenges

• Overlay topology (networking aspects) must be
  coupled with search strategy (Information
  Retrieval/Data-Mining)
• Traditional IR and data-mining tools are not
  adapted to the highly distributed P2P setting.
• Similarity metrics/clustering/ranking involve
  matrix operations on the market basket data
  principal component analysis (LSI), eigenvalue
  computations, association rules

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Possession Rules

• Rule(O) do you possess item O ?
• Peer maintains a possession rule for each item in
  its index (subset if index is large)
• Search strategy a sequence of possession rules
  (with hop counts/search size limit)

Making this work
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Possession-rules overlays
Peer26
Index of P26 Rules/Items Rule(A) Rule(B) Rule(C
) Rule(D)
item Rule(item) neighbors
A P11,p7,p3
B P2,p6,p9
C P13,p15,p1
D P4,p5,p10
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Rules/Items Rule(A) Rule(B) Rule(C ) Rule(D)
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Possession-rule overlay
Network is gnutella-like, within each rule

• Coverage The induced overlay on peers that
  satisfy each rule constitutes of large connected
  components.
• Small degree Each peer participates in a limited
  number of rules. (yet, overall there is a large
  number rules), for each rule it participates
  in, the peer maintains several participating
  neighbors.
• Overlay and search boost each other (easy to find
  appropriate neighbors for each rule)

• When you find O, you often discover multiple
  peers that have O when you give O, the searcher
  informs you of other peers with O.
• Peers that have O can find other peers that have O

( can use super-peer overlay within each rule
!!)
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Search strategies

• To beat blind search, associative search should
  probe peers that are more likely to answer than
  random peers
• Associative search
• RAPIER Random Possession Rule crudest
  strategy
• GAS Greedy Selection refined strategy

• Blind search
• Urand (gnutella) all peers have same
  likelihood of being probed in each query
• Prand (gnutella modified) peers are probed
  proportionally to their index size (RAPIER has
  same bias)

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RAPIER Random Possession Rulesimplest
possession-rule based strategy

• RAPIER Search strategy
• Repeat until found
• Pick a random item O from your index
• Search peers that have this item (using rule(O))

Straightforward to implement on top of a
possession-rule overlay network
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Analysis Itemsets Model

• Items belong to topics. There are very many
  topics but each peer can only select items from
  a fixed set of topics. Topic popularities can
  highly vary but each peer has equal interest in
  each of its topics.
• We show that
• RAPIER is at least as good as Prand
• RAPIER is better than Prand when peers have fewer
  topics
• Simple model that hints on what is going on

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Experiments

• Data used Client/Hostname matrix from proxy
  logs as peer/item matrix. Each entry, in turn,
  is treated as a search item.
• Similarly-structured market basket data
• Has rare items (which current P2P networks dont
  support)
• No universal model for market basket data
• Cant get a full index for many peers from
  current P2P networks and these networks dont
  reflect well on rare items.
• Metric ESS (Expected Search Size number of
  peers probed till search is resolved). CDF of
  fraction of searches that have ESS below x.

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ESS Expected Search Size

• ESS 1/(success probability in each probe) (when
  probes are independent not true for GAS)
• Probe success probability
• Urand fraction of peers that have the item in
  their index
• Prand weight of each peer is its index size
  divided by sum of index sizes of all peers.
• Success prob (weight of peers with item) /
  (weight of peers without item)
• RAPIER the average, over possession rules peer
  participates in, of fraction of peers in rule
  that have the item.

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Peer-Item Matrix - Experiment
Items
0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 1 0 0 1 1
1 1 0 0 0 0 1 0 0 0
0 0 1 0 1 0 0 0 1 0
0 0 0 0 0 0 1 1 1 0
1 1 0 0 0 0 0 0 1 0
0 0 0 1 1 0 0 1 1 1
0 0 1 1 0 0 0 0 1 0
1 1 0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 0
?
?
?
?
?
?
Peers
?
?
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Urand and Prand
Items
0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 1 0 0 1 1
1 1 0 0 0 0 1 0 0 0
0 0 1 0 1 0 0 0 1 0
0 0 0 0 0 0 1 1 1 0
1 1 0 0 0 0 0 0 1 0
0 0 0 1 1 0 0 1 1 1
0 0 1 1 0 0 0 0 1 0
1 1 0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 0
Peers
?
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RAPIER (Random Possession Rule)
Items
0 0 1 1 1 0 0 0 0 0
0 0 0 0 0 1 0 0 1 1
1 1 0 0 0 0 1 0 0 0
0 0 1 0 1 0 0 0 1 0
0 0 0 0 0 0 1 1 1 0
1 1 0 0 0 0 0 0 1 0
0 0 0 1 1 0 0 1 1 1
0 0 1 1 0 0 0 0 1 0
1 1 0 0 0 1 0 0 0 0
0 1 0 0 1 0 0 0 1 0
Peers
?
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Caveat comparing apples and oranges

• When searching by possession rules we have bias
  towards peers that participate in more rules/
  have more items.
• But, with this bias, a strategy has better chance
  of finding what it is looking for! So
• We show that the likelihood of being probed is
  proportional to number of rules you participate
  in.
• Prand blind search strategy has same bias.
• Thus, it is fair to compare Prand search with
  possession-rule based RAPIER

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GAS Refining RAPIER

• Ideas
• Some rules are better than others (e.g.,
  possession of a very popular item carries weaker
  information)
• Unsuccessful search carries information suppose
  you lost something, you think you lost it at
  home. You search home going through various
  closets and drawers and dont find it, then you
  may decide to go search the office, even if you
  have not completed an exhaustive search at home.
  What happened? The posterior distribution on the
  items location had changed as a result of the
  search.

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All Items

• Urand Blind search (Gnutella),
• Prand Gnutella modified,
• Rapier, GAS our algorithms

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Rare Items present in 1 of peers
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Rarer items 0.1 of peers
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Even Rarer Item 0.01 of peers
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GAS Greedy Strategy

• Idea use the search strategy that would have
  optimized your search on previous queries.
• Caveat this is NP-Complete
• Can do greedy approximation strategy GAS

• GAS
• initialize the query vector to a uniform
  distribution on previous selections.
• Iterate the following
• Apply the possession rule that maximizes success
  probability with respect to the query posterior
• update the query posterior.

Theorem GAS is a constant factor approximation
of the optimal strategy
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Building GAS strategies

• GAS
• Take a sample of items currently in your index
  D,E,F,G.
• search for these items in each possession rule
  you participate A,B,C
• obtain a matrix fraction of peers with item x in
  rule(y)

Item Rule() D E F G
rule(A) 0.03 0.2
rule(B) 0.04 0.1
rule(C) 0.1 0.2 0.03
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GAS strategy (example)
Item Rule() D E F G
rule(A) 0.03 0.2
rule(B) 0.04 0.1
rule(C) 0.1 0.2 0.03
C,C,C,A,C,C,A,C,A,C,B,B,A,C,B,B,C,A,B,B,C
GAS search of size 21 10 probes in rule(C)
6 probes in rule(B) 5 probes in rule(A)

RAPIER search of size 21 7 probes in
rule(C) 7 probes in rule(B) 7 probes in
rule(A)
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Summary

• We proposed a general framework for associative
  P2P search exploit patterns inherent in human
  selections to boost search. Adapted to the P2P
  setting.
• Search strategies and the overlay structure are
  symbiotic and guided/boosted by previous
  selections/queries.
• Common good in par with own welfare All data
  maintained by each peer has direct personal
  benefit (like gnutella). Helping others helps
  you
• Possession rules
• Strategies are approximations to standard
  similarity metrics that work!!.
• Easy to find other sources of desired item (for
  alternative/parallel downloads)

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Related work

• IR-DM association rules/collaborative
  filtering/Web search
• P2P networks unstructured networks DHTs
• DHTs have symbiotic overlay/search strategy
• Caching at peers (Freenet) adapt overlay
  according to search
• Intersection
• Crespo/Garcia-Molina 02 routing indexes
• System isolates topicsmap queries/items to
  topics.
• Peer knows summary of what can be reached thru
  it/each neighbor
• Query keywords are used to select a neighbor who
  is a best match
• Differences from our approach
• No connection between search and overlay topology
  
• Uses only text/keywords. We use co-location
  associations between items.
• CG02 tradeoff between topic divergence (all
  nodes ending up with similar index summary) or
  restricted coverage (number of peers included in
  each peer summary)
• neurogrid.net (Sam Joseph, U. Tokyo) agent
  text-based approach
• Peers learn and remember content of other peers

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Future

• Integrate text matching (of query keywords) in
  search strategy (use rule(O) if query keywords
  match Os metadata)
• Select which possession rules to participate in
  (e.g., using item popularity heuristic or
  GAS-like selection)
• Search strategy gives more weight to more recent
  selections (are more indicative of next query)
• Explore other types of propagation rules
• P2P communities ?
• Integrate Recommendation Systems in P2P ?
• Implementation

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Thank You!
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Some Extra Comments

• Issues with straightforward importing of IR
  techniques
• Vector space approach
• Similarity metrics
• Why we need to use several propagation rules in a
  search? (when searching according to examples
  in the index)

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Straight IR vector-space approach

• Peers are mapped to vectors, according to their
  index content. Queries are mapped to the vectors
  in the same space.
• Overlay topology is correlated with distances in
  this vector space (bias towards closer peers)
• Search propagation targets regions of the space
  that are closest to the query.

• neighborsO(dimension) - want small dimension
• Yet, Matrix operations, e.g principal component
  analysis (LSI), are hard in our distributed
  setting
• Yet, each peer should be able to compute the
  mapping for its queries and/or index
• Proximity metric alone is insufficient (Need
  different propagation rules)

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Why we need several propagation rules for the
same query decision-tree like search

• propagation rule approx interest area
• Each peer covers several interest areas, peers
  have different sets of interest areas.
• Peer Query 80 basketball 20polo
• World Index 5 basketball 0.1 polo
• All basketball lovers would be close matches
  but need to direct search to more polo lovers
• multi-rule search strategy basketball 200
  peers polo 200 peers