Automated Ranking Of Database Query Results
 Sanjay Agarwal
 Surajit Chaudhuri
 Gautam Das
 Aristides Gionis
- Microsoft Research
- Microsoft Research
- Microsoft Research
- Computer Science Dept
Stanford University
 Presented by: Suvigya Jaiswal (Fall 10)
Ranking
 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.
Database Ranking Example
Introduction
 Automated Ranking is used in Information
Retrieval(IR).
 Database Systems do not support Automated
Ranking but support only Boolean Query model.
Following scenarios not handled well by SQL
Systems
1. Empty Answers(Query too specific)
2. Many Answers(Query not specific)
Introduction
 How to adapt ranking functions from IR to
handle Database ranking problem?
1.When each of the attribute in the relation is a
categorical attribute , mimic the IR solution by
applying the TD-IDF idea of frequency of values
2. When attributes are also numerical ,extend the
TD-IDF concepts to numerical domains.
 In some cases the TF-IDF idea does not produce
results with desired accuracy, in these cases we
use workload information to arrive at better
results.
Contributions of Paper
 IDF Similarity
 QF similarity
 QFIDF Similarity
 Index Based Threshold Algorithm:
IDF Similarity: Intro
 Given:
A Table R
Attributes {A1,….,Am)
Tuples {T1,….,Tn}
Valuek
Query’s WHERE clause is of the form:
“Where C1 AND C2 AND ….. AND Cm”
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
Cosine Similarity
 Cosine Similarity from IR can be applied when the
database has only categorical attributes.
Tuple and Query are considered a small document.
A documents is an m-dimensional vector with m words
ith element in the vector represents the TF of the word.
Cosine Similarity:
Cosine Similarity
 IDF used to further refine Cosine Similarity
IDF(w)= log(N/F(w))
N is number of documents
F(w) is the number of documents in which w appears.
 Idea behind using IDF?
More often occurring words convey
information than rarely occurring words.
IDF Similarity
For every value t in the domain of Ak , IDFk(t) is defined as
IDFk(t)=log(n/Fk(t))
n=# of tuples , Fk(t)) is the frequency of tuples Ak=t
T=<t1,……tm>
Q=<q1,…...qm>
Condition is of the form “WHERE A1=q1 AND A2=q2
Sk (u,v) = IDFk(u) if u=v
Otherwise,
Sk (u,v)=0
m
SIM (T , Q)   S k (t k , q )
k 1
k
,…..,
AND Am=qm “
Uses
 As an Example say we want to find all convertibles
made by Nissan.
The System will return the following:
1. All Convertibles made by Nissan.
2. All the Convertibles made by other
manufacturers.
3. All Nissan Cars which may not be convertibles.
Why so?
Convertible is a rarer car type than other Nissan
cars.
IDF Similarity for Numerical Data
 Why the IDF Similarity for categorical data cannot
be used for numeric data?
SELECT *
FROM R
WHERE PRICE=300K AND BEDROOM = 10;
ID
PRICE
BEDROOM
CITY
1
315K
9
DALLAS
2
300K
10
FTW
3
305K
10
ARLINGTON
S(u,v) will incorrectly evaluate to zero.
Since 315K and 305K are close to 300K (resp. 9 & 10) but not equal.
IDF Similarity for Numerical Data
Solution:
{t1,t2…..tn} be the values of attribute A. For every value t
The denominator represents the sum of contributions to t from every other ti
Further t is from ti , lesser is the contribution from ti
IDF Similarity for Numerical Data
Similarity is defined as
density at ‘t’ of a Gaussian
Distribution centered at q.
Suppose there are n1 tuples that have the same value and the remaining
n-n1 tuples have a value far from t.
1. If q belongs to n-n1 then S(t,q) almost 0
2. If q belongs to n1 then S(t,q) = log (n/nt)
QF Similarity
Why is IDF Similarity not sufficient ?
Examples:
1. In a database , more homes are built in recent years
than in the pervious years (1980’s). But IDF of the
homes built in recent years will be less. Yet the
demand for newer homes is more.
2. In a bookstore DB, the demand of a particular
author’s work might be more even if he has written
many books. But the IDF of that author will be low.
QF Similarity
 The Idea behind QF Similarity is that the importance
of attribute values is related to the frequency of their
occurrence in the query string in the workload
 In previous example it is reasonable to assume that
the queries for newer homes appears more often
than queries for older homes
 Also the query for a particular author might appear
more often than the other authors if his books are
more popular in spite of him having many books
QF Similarity
We define query frequency QF as
QF(q) = RQF(q)/ RQFMax
RQF(q)
RQFMax
raw frequency of occurrence of value q of attribute A
in query strings of workload
raw frequency of most frequently occurring
value in workload
S(t,q)=QF(q) if q=t else 0
Similarity between different attributes
If we use IDF or QF Similarity to measure any of
the following we get 0 as the answer
S(Toyota, Honda)=0
S(Accord, Camry)=0
1.But we know that Honda and Toyota make
cars that are directed toward the same market
segment.
2.Accord and Camry are the same type of Cars of
comparable quality
Similarity between different attributes
 To solve this problem we apply the intuition that if certain pair of
values(t<>u) often occur together in the work load then they are
similar.
 For example if we receive many queries which has C-Conditions of the
form
“MFR IN {Toyota, Honda, Nissan}”
It suggest that Toyota, Honda and Nissan are more similar to each other
than they are to Ferrari or Mercedes
Hence we can say that by using this metric,
S(Toyota, Honda)=0.8
S(Ferrari, Toyota)=o.1
Similarity between different attributes
Let W(t) be the subset of Queries in workload W in
which the categorical value t appears(in our example
say Toyota) in an IN clause.
Jaccard Coefficient measures similarity b/w W(t) and W(q)
Similarity coefficient is then defined as:
QFIDF Similarity
 QF Similarity can be unreliable in certain situations.
 This happens because QF Similarity is purely workload
based. It doesn’t take data values into account.
 To tackle this we define QFIDF Similarity:
S(t,q)=QF(q) *IDF(q) when t=q
0, otherwise
where QF(q)=(RQF(q)+1)/(RQFMax+1).
1 is added to the numerator and denominator so that QF is
never zero.
Many Answer Problem.
 IDF Similarity and QF Similarity may sometimes run into
problem: many tuples may tie for the same similarity score and
thus get ordered arbitrarily.
 Approach is to determine weights of missing attribute values that
reflect their “global importance” for ranking purposes
 IF we seek homes with four bedrooms in DB, we can examine
attributes other than number of bedrooms to rank the result set.
If we knew that “Dallas” is a more important location than “FortWorth” in a global sense, we would rank four bedroom homes in
Dallas higher than four bedroom homes in Fort-Worth.
 We use workload information to determine global
importance of missing attribute values.
 We define the global importance of missing attribute
value tk as log(QFk(tk))
 Extend QF Similarity to use the quantity
Sum(log(QFk(tk))) to break ties in each equivalence class
(larger this quantity1, higher the rank of the tuple) where
the summation is over missing attributes.
 An alternative strategy is to rank tied tuples higher if
their missing attribute values have small IDF, i.e. occur
more frequently in the database.
Implementation
 Two Phases:
Pre-processing component
Query processing component
Pre-processing component
 Compute IDF(t) (resp. QF(t)) for all categorical
values t involves scanning the database (resp.
scanning/parsing the workload) to compute
frequency of occurrences of values in the database
(resp. workload), and store the results in auxiliary
tables.
 We cannot pre-compute IDF(q) (resp. QF(q)) for
numerical attributes; thus we have to store an
approximate representation of the smooth function
IDF( ) (resp. QF( )) so that the function value at any
q can be retrieved at runtime.
Query processing component
 main task of the query processing component is,
given a query Q and an integer K, to efficiently
retrieve the Top-K tuples from the database using
one of the ranking functions.
A simpler query processing problem
 Inputs:
(a) a database table R with m categorical columns, clustered on key column TID,
where standard database indexes exist on a subset of columns,
(b) A query expressed as a conjunction of m single-valued conditions of the form
Ak = qk., and
(c) an integer K.
Similarity function: Overlap Similarity
Output: The Top-K tuples of R most similar to Q.
An index-based Top-K implementation:
 monotonic property: if T and U are two tuples such
that for all k, Sk(tk,qk)< Sk(uk,qk) then
SIM(T,Q) <=SIM(U, Q).
 adapt Fagin’s Threshold Algorithm (TA)
 Two types of access methods required
1. Sorted Access
2. Random Access
 use of an early stopping condition, by which the
algorithm can detect that the final Top-K tuples have
been retrieved before all tuples have been processed.
Threshold Algorithm
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:
L1
Seen
Possibly unseen
L2
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
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)
For each object seen:
- get all grades by random access
- determine Min(A1,A2)
- amongst 2 highest seen ? keep in buffer
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
T = min(0.9, 0.9) = 0.9
Min(A1,A2)
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
d
0.6
0.9
0.6
b
0.8
0.7
0.7
0.85
Example – Threshold Algorithm
Step 2 (Again): - Determine threshold value based on
objects currently seen. T = min(L1, L2)
L1
L2
a: 0.9
d: 0.9
b: 0.8
c: 0.72
a: 0.85
b: 0.7
.
.
.
.
.
.
.
.
d: 0.6
c: 0.2
- 2 objects with overall grade ≥ threshold value ? stop
else go to next entry position in sorted list and repeat step 1
ID
A1
A2
a
0.9
0.85
b
0.8
0.7
T = min(0.8, 0.85) = 0.8
Min(A1,A2)
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
a
0.9
0.85
b
0.8
Min(A1,A2)
0.85
0.7
T = min(0.72, 0.7) = 0.7
0.7
Algorithm
Experiment Results
 Quality results
 For queries with empty answers, QFIDF produced the best






rankings, followed by QF, then IDF, and finally Overlap.
For queries with empty answers, the ranking quality of QF
improves with increasing workload size.
For queries with numerous answers, QF produced better
rankings than IDF.
Performance results
The preprocessing time and space requirements of all
techniques scale linearly with data size.
When all indexes are present, ITA is more efficient than SQL
Server Top-K for all similarity functions.
Even when a subset of indexes is present, ITA can perform
well
References
 http://www.emeraldinsight.com/journals.htm?articl
eid=1563479
 Ppt Slides by Ramya Soumri(Fall 09)
 [14] R. Fagin. Fuzzy Queries in Multimedia Database
Systems. PODS 1998.
Thank You