context-sensitive ranking
DESCRIPTION
Context-sensitive ranking. Rakesh AgrawalMicrosoft Search Labs Ralf RantzauIBM Silicon Valley Lab Evimaria TerziUniversity of Helsinki & Microsoft Search Labs. Work done largely while the authors were in IBM Almaden. The curse of abundance: Too many data and too many answers. - PowerPoint PPT PresentationTRANSCRIPT
SIGMOD 2006
Context-sensitive ranking
Rakesh Agrawal Microsoft Search Labs
Ralf Rantzau IBM Silicon Valley Lab
Evimaria Terzi University of Helsinki &Microsoft Search Labs
Work done largely while the authors were in IBM Almaden
SIGMOD 2006
The curse of abundance:Too many data and too many answers
• Query shopping.com for a digital camera:
• Query Froogle for a tennis racquet:
SIGMOD 2006
Ranking query results
• Algorithms for ranking web pages have been quite successful ([BP’98,Kleinberg98])
– Key idea: Exploit the graph of hyperlinks between web pages
• Can we take similar approach for ranking database query results?
– Need for a graph structure that accurately describes the relationships between tuples in the database
- Past attempts: schema and key constraints or queries [BHP’04, BHNCS’02, GMT’04]
But are these graphs natural or do they reflect design optimization decisions?
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Using preferences to induce a graph of tuples
Genre (G)
Actor (A) Title (T) Language
t1 Drama Kidman Birth English
t2 Drama Cruz Vanilla Sky English
t3 Sci-Fi Reeves Matrix English
t4 Comedy Cruz Sin noticias de Dios
Spanish
t5 Comedy Aniston Rumor has it… English
• Drama > Sci-Fi• Kidman > Reeves • Matrix > Birth
t1>t3 and t2>t3
t1>t3
t3>t1
t1 t2
t3
[ Preferences are predicates of the form “X=x1 > X=x2” ]
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Augment preferences with context
Genre (G) Actor (A) Title (T) Language (L)
t1 Drama Kidman Birth English
t2 Drama Cruz Vanilla Sky English
t3 Sci-Fi Reeves Matrix English
t4 Comedy Cruz Sin noticias de Dios Spanish
t5 Comedy Aniston Rumor has it English
– in general (*)• English > Spanish | *
– but in the context of Comedies• Spanish > English| Comedies
[ Contexts are predicates of the form “Y=a” ]
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Preferences in the past
• Preferences expressed via a numeric score [AW’00,KI’04,KI’05]– Nicole Kidman : 0.9– Penelope Cruz : 0.4– Dramas : 0.8– Comedies : 0.3
• Pairwise preferences in ML literature [CSS’97]• Preferences as partial orders [Kieβling’02]• Preferences as first-order formulas [Chomiki’03]
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Contextual preferences
Genre (G)
Actor (A)
Title (T) Language (L)
t1 Drama Kidman Birth English
t2 Drama Cruz Vanilla Sky English
t3 Sci-Fi Reeves Matrix English
t4 Comedy Cruz Sin noticias de Dios
Spanish
t5 Comedy Aniston Rumor has it… English
• P1={G=Drama > G=Sci-Fi | L=English}
• P2={A=Kidman > A=Reeves | L = English}
• P3={T=matrix > T=Birth | L=English }
t1>t3|En and t2>t3|En
t1>t3|En
t3>t1|En
Genre (G)
Actor (A)
Title (T) Language (L)
t1 Drama Kidman Birth English
t2 Drama Cruz Vanilla Sky English
t3 Sci-Fi Reeves Matrix English
t4 Comedy Cruz Sin noticias de Dios
Spanish
t5 Comedy Aniston Rumor has it… English
t1 t2
t3
2/3
1/3
1
1/2
1/2t1 t2
t3
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Obtaining preferences
• Users provide preferences voluntarily – in the same way users rate products and services
• Preferences can be automatically collected via browser plug-ins or taskbars (with user permission)
• Preferences can be learned from past data
• Preferences can also be learned from the data (e.g., using association-rule mining)
Preferences are obtained from various sources and can contain cycles and contradictions, which are resolved
democratically
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Overview
Question:How to incorporate users preferences when ranking query results?
Approach:• Accumulate contextual preferences of the form i1>i2|X
• Order the answer tuples such that the preferences are maximally respected, giving higher weight to those preferences whose contexts have closer match to the query
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Issues
• How to define similarity between a query and a context ? – See paper for the distance function.
• Can we create orders in an offline step and use their information at query time ?
• Should we save all orders?
• How to combine the saved orders while answering queries ?
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Problem decomposition
[Problem 1]: For every context X build an order τX (Ordering)
[Problem 2]: Given a set of orders Tm = {τ1,…, τm} find ℓ representative orders Tℓ (ClusterOrders)
• Assign each of the input orders to one of the representatives (the closest)
• Associate with each representative σ a set of contexts Yσ
[Problem 3]: Provide top-k results for the query Q– respecting the representative orders and– weight respect according to the similarity between
query and contexts (Querying)
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Problem 1: The Ordering problem
For a given context X and a set of preferences PX over the tuples D={t1,…,tn} find an ordering τ of D such that
)Agree(maxarg ' Xτ',P
t1 t2
t3
1/2
1/2
2/3
1/3
1
t1 t2
t3
t2
t1
t3
Agree = 1 +1/2 = 2/3 = 13/6
SIGMOD 2006
Problem 2: The ClusterOrders problem
Given m orders Tm={τ1,…,τm} , each corresponding to a single concept Xi, find ℓ representative orders Tℓ such that cost(Tℓ) is minimized where
and
We use the standard Spearman footrule and Kendall tau distances for comparing orderings
mT
TdT
),()(Cost
),(min),( dTdmT
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The ClusterOrders problem: Example
a
b
c
d
e
f
a
b
c
d
e
f
a
b
c
d
e
f
f
e
d
c
b
a
f
e
d
c
b
a
a
b
c
d
e
f
f
e
d
c
b
a
Cost(τ1) = 2
0 1 1 0 1
Cost(τ2) = 1
Cost(τ1, τ2) = 2+1=3
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Problem 3: The Querying problem
Provide top-k results for query Q respecting the representative orders and weighting respect using the corresponding set of contexts
SIGMOD 2006
Problem decomposition
[Problem 1]: For every context X build an order τX (Ordering)
[Problem 2]: Given a set of orders Tm = {τ1,…, τm} find ℓ representative orders Tℓ (ClusterOrders)
• Assign each of the input orders to one of the representatives (the closest)
• Associate with each representative σ a set of contexts Yσ
[Problem 3]: Provide top-k results for the query Q– respecting the representative orders and– weight respect according to the similarity between
query and contexts (Querying)
SIGMOD 2006
Constructing orders from preferences [Problem1]
• Problem is NP-hard; need for heuristics • PickPerm algorithm : pick a random permutation, inverse it
and pick the best of the two
t1 t2
t3
1/2
1/2
2/3
1/3
1
t1 t2
t3
t2
t3
t1
A = 11/6
t1
t3
t2
A = 5/6
t2
t3
t1
[ Inspired by the 2-approximation algorithm for finding the maximum acyclic subgraph of a given graph ]
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Greedy algorithm [CSS’97]
• At the i-th iteration pick the i-th element of the output permutation
• At each iteration pick the tuple t with the highest s_val(t) = OutDegree(t)-InDegree(t)
in the remaining preference graph
t1 t2
t3
1/2
1/2
2/3
1/3
1
t1 t2
t3
1/3
2/3
1/3
t1
t3
1
-4/3
t2
1/3
-1/3
t2
t1
t2
t1
t3
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MC-algorithm
• Reverse the directions of the edges on the preference graph
• Run a random walk (with random restarts) on the reversed graph
• Rank according to the stationary distribution
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Performance
• Data generation– Fix an order on the tuples– Generate preferences that
respect this order– Pc: the probability that a
preference is generated between a pair of tuples
• Observations– For small pc values more
orders are compatible, all algorithms are good
– For large pc values MC and Greedy find the optimal order
SIGMOD 2006
Problem decomposition
[Problem 1]: For every context X build an order τX (Ordering)
[Problem 2]: Given a set of orders Tm = {τ1,…, τm} find ℓ representative orders Tℓ (ClusterOrders)
• Assign each of the input orders to one of the representatives (the closest)
• Associate with each representative σ a set of contexts Yσ
[Problem 3]: Provide top-k results for the query Q– respecting the representative orders and– weight respect according to the similarity between
query and contexts (Querying)
SIGMOD 2006
Reducing the number of orders [Problem 2]
• Finding ℓ representative orders is NP-hard
• Finding ℓ orders from the input ones (good approximation, but still hard)
• Need for heuristics
• Greedy algorithm– Always pick the order (from the input) that introduces the
minimum cost
• Furthest algorithm– Start by picking a random order τ and add it in the output set
of orders Tℓ
– For ℓ-1 iterations pick the order that is furthest away from the orders already in Tℓ
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Refine the representative orders
• Given the set of representative orders Tℓ, assign each input order τЄTm to its closest representative in Tℓ. (partition Tm into ℓ partitions)*
– Discrete refinement: For each partition pick the best representative of the partition
– Continuous refinement: ([DKNS’01]) For each partition find the best representative of the partition
*Notice the resemblance between this problem and Catalog Segmentation problem by [KPR’04]
SIGMOD 2006
Performance
• Data generation– Fix ℓ underlying orders T– Generate other orders
from T by picking an order in T and adding noise (swaps)
– Compute the cost of the solution wrt to the ground truth• Observations
– Without refinements: Greedy performs steadily better than Furthest
– With refinements: Both algorithms are equally good
– The groupings are equivalent
SIGMOD 2006
Problem decomposition
[Problem 1]: For every context X build an order τX (Ordering)
[Problem 2]: Given a set of orders Tm = {τ1,…, τm} find ℓ representative orders Tℓ (ClusterOrders)
• Assign each of the input orders to one of the representatives (the closest)
• Associate with each representative σ a set of contexts Yσ
[Problem 3]: Provide top-k results for the query Q– respecting the representative orders and– weight respect according to the similarity between
query and contexts (Querying)
SIGMOD 2006
Problem 3: The Querying problem
• Use variation of the TA algorithms [FLN’02, FKS’03]– Assume k = 2 and query Q such that:
• sim(Q,Y1) = 0.5, sim(Q,Y2) = 0.3, sim(Q,Y3)=0.1
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
0.5 0.3 0.1
SIGMOD 2006
Problem 3: The Querying problem
1. At each sequential accessa. Set the threshold TH to be the aggregate of the
scores seen in this access
TH =0.5*5+0.3*5+0.1*5=4.5
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
0.5 0.3 0.1
SIGMOD 2006
Problem 3: The Querying problem
1. At each sequential accessb. Do random accesses and compute the score of the
objects seen
TH =0.5*5+0.3*5+0.1*5=4.5
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
t1 3.7
t2 3.6
t4 2.1
0.5 0.3 0.1
SIGMOD 2006
Problem 3: The Querying problem
1. At each sequential accessb. Do random accesses and compute the score of the
objects seen
TH =0.5*5+0.3*5+0.1*5=4.5
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
t1 3.7
t2 3.6
0.5 0.3 0.1
SIGMOD 2006
Problem 3: The Querying problem
1. At each sequential accessc. Maintain a list of the top-k objects seen so far
TH =0.5*5+0.3*5+0.1*5=4.5
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
t1 3.7
t2 3.6
0.5 0.3 0.1
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Problem 3: The Querying problem
1. At each sequential accessd. When the scores of the top-k are greater or equal
to the threshold, stop
TH =0.5*4+0.3*4+0.1*4=3.6
Y1,T1
t1 5
t2 4
t3 3
t4 2
T5 1
Y2,T2
t2 5
t3 4
t1 3
t4 2
t5 1
Y3,T3
t4 5
t3 4
t1 3
t5 2
t2 1
t1 3.7
t2 3.6
0.5 0.3 0.1
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Accuracy of top-k results
• IMDB dataset– Automatically generate
preferences via association-rule mining:‘A1=a’ > ‘A1=b’ |X if conf(Xa)>conf(Xb)
– Solk: top-k results obtained after clustering
– Gk: top-k results without clustering
|Sol|
|Sol|),,Accuracy(
kk
kk
G
GkGSol
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Accuracy of top-k results
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Recap
• Notion of contextual preferences
• Use of contextual preferences to order database results
• Use of association rules to obtain contextual preferences
• Experimental validation of the effectiveness of the proposed techniques using both synthetic and real data
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Conclusions and future work
• The framework of contextual preferences is both intuitive and practical
• The framework is easily extended to accommodate for top-k lists and bucket orders
• Scalability of the algorithms needs further investigation
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Questions?