Transcript ppt slides

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Sanjay Agarwal
Surajit Chaudhuri
Gautam Das
Aristides Gionis
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Microsoft Research
Microsoft Research
Microsoft Research
Computer Science Dept
Stanford University
Presented at the first Conference on Innovative Data Systems Research (CIDR) in
the year 2003
Ramya Somuri
Nov ‘10 2009
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Introduction
Problem Formulation
Similarity Functions
Implementation
Experiments
Conclusion
Boolean Semantics of SQL: Success
and Barrier?
Example:
Problems:
Select *
From Realtor R
Where 400K<Price<600K AND #Bedrooms= 4
Query Semantics:
•True/False { BOOLEAN MODEL}
Similarity,
Relevance,
Preference
What do we want?
Query Results Representation:
• Empty Answers
• Many Answers
A Ranked
List
What do we want?
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In this case it would be desirable to return a
ranked list of ‘approximately’ matching
tuples without burdening the user to specify
any additional conditions.
In other words, an automated approach for
ranking and returning approximately
matching tuples.
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As the name suggests ‘Ranking’ is the
process of ordering a set of values (or data
items) based on some parameter that is of
high relevance to the user of ranking process.
Ranking and returning the most relevant
results of user’s query is a popular paradigm
in information retrieval.
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Automated ranking of query results is the
process of taking a user query and mapping
it to a Top-K query with a ranking function
that depends on conditions specified in the
user query.
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Develop a method for automatically ranking
database records by relevance to a given query
Derive a Similarity Function
Apply Similarity Function between Query &
Records in database
Rank the Result-Set and return Top-K records
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IDF Similarity
- Mimics the TF-IDF concept for
Heterogeneous data.
QF Similarity
- Utilizes workload information.
QFIDF Similarity
- Combination of QF and IDF.
Numerical
Attribute
T
u
p
l
e
s
Categorical
Attribute
Attributes
SNO
MFR
PRICE
1
AUDI
2000.00
2
BMW
3
COLOR
MODEL
TYPE
RED
Q5
SUV
3000.50
RED
Z4
TOYOTA
3000.00
BLUE
CAMRY
SEDAN
4
HONDA
2000.00
GREEN
ACCORD
SEDAN
5
NISSAN
4000.00
WHITE
350Z
CONVE
RTIBLE
Vk
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R
- Relation
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{Al,…,Am}
- Set of Attributes
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Vk
– Set of valid attribute values for
an attribute Ak
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{tl,……,tm}
- Tuples/records
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A tuple t is expressed as t = <tl,……tm> for a
tuple with values tk ε Vk for each k
Q
- <Tl,…..Tm>
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Where clause of Query Q is of the form
“WHERE Cl AND …….AND Ck”
Each Ci is of the form
Ai IN {valuel,………..,valuek} / Ai IN [lb,ub]
Similarity coefficient Sk(u,v) can be defined as
“similarity” for the attribute values [u,v]
Sk(u,v) =1 if u=v
=0 if u,v are dissimilar
Wk – “importance” of attribute/Attribute weight
0<wk<1; Σwk=1
IR technique
w
d
Q = set of key words
IDF(w) = log(N/F(w))
N
- No of documents
F(w) - No of occurrences of
documents in which w
appears
TF(w,d)=Frequency of
occurrence of w in d
Database(only categorical attribute)
T=<t1,……tm>
<attribute,value>
tuple
Q=<q1,…...qm> Condition is “WHERE is A1=q1”
IDFk(t)=log(n/Fk(t))
n-number of tuples in database
Fk(t) -Frequency of tuples in database where Ak=t
Similarity between T and Q is
m
SIM (T , Q)   S k (t k , q )
k
Cosine similarity between query
k 1
and document is normalized dot Sum of corresponding similarity coefficients over all
product of the two corresponding attributes
vector
• Dot product is un-normalized
Similarity function known as
cosine similarity with TF-IDF
weightings
• TF is irrelevant
Similarity function known as IDF similarity
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Select model from automobile_database
Where TYPE=“convertible” and MFR=“Nissan”;
System generates tuples in the following order
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Nissan Convertibles
Convertibles by other manufacturer
Other cars/types by Nissan
“Convertible” is rare and has higher IDF than
“Nissan” which is a common car manufacturer
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No
Example
Select *
From automobile_database
Where price=3000
Sk(u,v) = 1 if (u=v) otherwise 0 is a bad
definition since two numerical values might
be close but not equal.
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Sk(u,v) = 1-d/ | uk-lk | where d=|v-u| is the
distance between the value & [lk,uk] is the
domain of Ak
 Example:
Select * from Realtor R where #rooms=4
Bedrooms
d=|v-u|
Sk(u,v)
|uk-lk|
4
0
1
3
3
1
0.66
3
1
3
0
3
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For numeric data
 Inappropriate to use previous similarity coefficients/functions.
 frequency of numeric value depends on nearby values.
 Discretizing numeric to categorical attribute is problematic.
 Solution:
 {t1,t2…..tn} be the values of attribute A. For every value t,
sum of ”contributions” of t from
every other point it contributions
modeled as Gaussian distribution
 Similarity function is
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Problem:
In a realtor database, more homes are built in
recent years such as 2007 and 2008 as compared
to 1980 and1981. Thus recent years have small
IDF.Yet newer homes have higher demand.
Solution:
QF Similarity.
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Importance of attribute values is directly related to
the frequency of their occurrence in workload.
In the previous example, it is reasonable to assume
that more queries are requesting for newer homes
than for older homes. Thus the frequency of the year
2008 appearing in the workload will be more than
that of year 1981.
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Query frequency QF(q) = RQF(q)/ RQFMax
RQF(q)
- raw frequency of occurrence of value q of attribute A
in query strings of workload
RQFMax
- raw frequency of most frequently occurring value in
workload
S(t,q)= QF(q), if q=t
0 , otherwise
Consider a workload W = { Q1,Q2,Q3,Q4}
Q1Q2Q3Q4-
Select
Select
Select
Select
*
*
*
*
from
from
from
from
Realtor
Realtor
Realtor
Realtor
R
R
R
R
where year=“2009”
Where year=“2009”
Where year=“2008”
Where year=“2007”
Attribute Year= { 1981,……., 2009}
QF (2008) = RQF(2008)/RQFMax = 1/2 .
If a query requests for an attribute value not in the
workload, then QF=0. Ex- QF(1981)=0
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Problem/Example:
SMFR(Toyota,Honda) =0
SMODEL (Camry, Accord) =0
Solution:
Similarity Coefficients that are non-zero even
when the pair of categorical attributes is
different
Eg:SMFR(Toyota,Honda) =0.9
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Similarity between pairs of different categorical
attribute values can also be derived from workload
The similarity coefficient between tuple and query
in this case is defined by jaccard coefficient scaled
by QF factor as shown below.
S(t,q)=J(W(t),W(q))QF(q)
 Analyzing IN clauses of queries:
If certain pair of values often occur together in
the workload ,they are similar .e.g. queries with C
as “MFR IN {TOYOTA,HONDA,NISSAN}”
 Several recent queries in workload by a specific
user repeatedly requesting for TOYOTA and
HONDA.
 Numerical values that occur in the workload can
also benefit from query frequency analysis.
Why QFIDF?
 QF is purely workload-based.
 Doesn't use data at all.
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Fails in case of insufficient & unreliable workloads.
What is QFIDF?
 QFIDF is a hybrid ranking function obtained by combing IDF,
QF weights by multiplying them
 For QFIDF Similarity
 S(t,q)=QF(q) *IDF(q) ,when t=q
0, otherwise
where QF(q)=(RQF(q)+1)/(RQFMax+1).
 Thus we get small non zero QF even if value is never referenced in
workload model.
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In case of many answers problem, the
recently discussed ranking functions might
fail to perform.
This is because many tuples may tie for the
same similarity score. Such a scenario could
arise for empty answer problem also.
To break this tie, requires looking beyond the
attributes specified in the query, i.e., missing
attributes.
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Solution: Determine the weights of missing attribute values
that reflect their “global importance” for ranking purposes by
using workload information.
 Extend QF similarity ,use quantity Σlog(QFk(tk)) to break
ties.
Consider a query requesting for 4 bedroom houses .
- Result set= many # of homes
- Examine the other attributes other than # of bed
rooms(missing attributes). Ex- Location
- Dallas is more important than Arlington .
- Rank the 4 bed room homes in Dallas higher than that of
Arlington
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Rank the tuples with large IDF for missing attributes higher
Arlington homes are given more preference than Dallas
homes since Arlington has a higher IDF, but this scenario is
not true in real practice.
Rank the tuples with small IDF for missing attributes higher
Consider homes with decks , but since we are considering
smaller IDF preference will be given to homes without decks
since they have a smaller IDF which is not true in real
practice.
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Pre-processing component
Query–processing component
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Compute and store a representation of similarity
function in auxiliary database tables.
 For categorical data:
Compute IDF(t) (resp QF(t)) ,to compute frequency
of occurrences of values in database and store
the results in auxiliary database tables.
 For numeric data:
An approximate representation of smooth
function IDF() (resp(QF()) is stored, so that
function value of q is retrieved at runtime.
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Main task: Given a query Q and an integer K,
retrieve Top-K tuples from the database using one
of the ranking functions.
 Ranking function is extracted in pre-processing
phase.
 SQL-DBMS functionality used for solving top-K
problem.
Handling simpler query processing problem
 Input: table R with M categorical columns, Key
column TID, C is conjunction of form Ak=qk.....
and integer K.
 Output: top-K tuples of R similar to Q.
 Similarity function: Overlap Similarity.
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Traditional approach ?
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Indexed based approach
 overlap similarity function satisfies the following monotonic property.
 If T and U are two tuples such that for all K, S k(tk,qk)< Sk(uk,qk)
then SIM(T,Q) < SIM(U,Q)
 To adapt TA implement Sorted and Random access methods.
 Performs sorted access for each attribute, retrieve complete tuples with
corresponding TID by random access and maintains buffer of Top-K tuples seen so
far.
Threshold Algorithm (TA)
Read all grades of an object once seen from a sorted access
• No need to wait until the lists give k common objects
Do sorted access (and corresponding random accesses) until
you have seen the top k answers.
• How do we know that grades of seen objects are higher
than the grades of unseen objects ?
• Predict maximum possible grade unseen objects:
L2
L
1
Seen
Possibly unseen
a: 0.9
d: 0.9
b: 0.8
a: 0.85
c: 0.72
.
.
.
f: 0.65
.
d: 0.6
b: 0.7
.
f: 0.6
.
.
.
c: 0.2
T = min(0.72, 0.7) = 0.7
Threshold
value
Example – Threshold Algorithm
Step 1: - parallel sorted access to each list
For each object seen:
- get all grades by random access
- determine Min(A1,A2)
- amongst 2 highest seen ? keep in buffer
L1
L2
(a, 0.9)
(d, 0.9)
(b, 0.8)
(a, 0.85)
(c, 0.72)
(b, 0.7)
.
.
.
.
.
.
.
.
(d, 0.6)
(c, 0.2)
ID
A1
A2
Min(A1,A2)
a
0.9
0.85
0.85
d
0.6
0.9
0.6
Example – Threshold Algorithm
Step 2: - Determine threshold value based on objects currently
seen under sorted access. T = min(L1, L2)
- 2 objects with overall grade ≥ threshold value ? stop
else go to next entry position in sorted list and repeat step 1
L1
L2
a: 0.9
d: 0.9
b: 0.8
a: 0.85
c: 0.72
b: 0.7
.
.
.
.
.
.
.
.
d: 0.6
c: 0.2
ID
A1
A2
a
0.9
0.85
d
0.6
0.9
Min(A1,A2)
T = min(0.9, 0.9) = 0.9
0.85
0.6
Example – Threshold Algorithm
Step 1 (Again): - parallel sorted access to each list
For each object seen:
- get all grades by random access
- determine Min(A1,A2)
- amongst 2 highest seen ? keep in buffer
L2
L1
(a, 0.9)
(d, 0.9)
(b, 0.8)
(a, 0.85)
(c, 0.72)
(b, 0.7)
.
.
.
.
.
.
.
.
(d, 0.6)
(c, 0.2)
ID
A1
A2
Min(A1,A2)
a
0.9
0.85
0.85
d
0.6
0.9
0.6
b
0.8
0.7
0.7
Example – Threshold Algorithm
Step 2 (Again): - Determine threshold value based on objects currently
seen. T = min(L1, L2)
- 2 objects with overall grade ≥ threshold value ? stop
else go to next entry position in sorted list and repeat step 1
L1
L2
a: 0.9
d: 0.9
b: 0.8
a: 0.85
c: 0.72
b: 0.7
.
.
.
.
.
.
.
.
d: 0.6
c: 0.2
ID
A1
A2
a
0.9
0.85
b
0.8
Min(A1,A2)
0.7
T = min(0.8, 0.85) = 0.8
0.85
0.7
Example – Threshold Algorithm
Situation at stopping condition
L1
L2
a: 0.9
d: 0.9
b: 0.8
a: 0.85
c: 0.72
b: 0.7
.
.
.
.
.
.
.
.
d: 0.6
c: 0.2
ID
A1
A2
Min(A1,A2)
a
0.9
0.85
0.85
b
0.8
0.7
0.7
T = min(0.72, 0.7) = 0.7
Sorted access
Random
access
Stopping Condition
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Hypothetical tuple – current value a1,…, ap for
A1,… Ap, corresponding to index seeks on L1,…, Lp
and qp+1,….. qm for remaining columns from the
query directly.
Termination – Similarity of hypothetical tuple to the
query< tuple in Top-k buffer with least similarity.
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Automated Ranking Infrastructure for SQL
databases.
Extended TF-IDF based techniques from
Information retrieval to numeric and mixed data.
Implementation of Ranking function that exploited
indexed access (Fagin’s TA)