Automated Ranking Of Database Query Results

Sanjay Agarwal - Microsoft Research Surajit Chaudhuri - Microsoft Research Gautam Das - Microsoft Research Aristides Gionis - 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

IntroductionAutomated 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)

IntroductionHow 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 values2. 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 similarityQFIDF SimilarityIndex 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”

AttributesNumerical Attribute

CategoricalAttribute

SNO MFR PRICE COLOR MODEL TYPE1 AUDI 2000.00 RED Q5 SUV

2 BMW 3000.50 RED Z4

3 TOYOTA 3000.00 BLUE CAMRY SEDAN

4 HONDA 2000.00 GREEN ACCORD SEDAN

5 NISSAN 4000.00 WHITE 350Z CONVERTIBLE

Tuples

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=tT=<t1,……tm> Q=<q1,…...qm> Condition is of the form “WHERE A1=q1 AND A2=q2 ,….., AND

Am=qm “

Sk (u,v) = IDFk(u) if u=vOtherwise,Sk (u,v)=0

),(),(1

qtS kk

m

kk

QTSIM

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 RWHERE PRICE=300K AND BEDROOM = 10;

S(u,v) will incorrectly evaluate to zero.Since 315K and 305K are close to 300K (resp. 9 & 10) but not

equal.

ID PRICE BEDROOM

CITY

1 315K 9 DALLAS2 300K 10 FTW3 305K 10 ARLINGTO

N

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 02. 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) 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 else 0

Similarity between different attributes

If we use IDF or QF Similarity to measure any of the following we get 0 as the answerS(Toyota, Honda)=0S(Accord, Camry)=0

1.But we know that Honda and Toyota makecars 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)=0.8S(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 “Fort-Worth” 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 SimilarityOutput: 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 required1. Sorted Access2. Random Accessuse 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.

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:

a: 0.9b: 0.8c: 0.72

.

.

.

.

L1L2

d: 0.9a: 0.85b: 0.7

c: 0.2

.

.

.

.f: 0.65

d: 0.6

f: 0.6

Seen

Possibly unseen

Threshold value

Threshold Algorithm

T = min(0.72, 0.7) = 0.7

ID A1 A2 Min(A1,A2)

Step 1: - parallel sorted access to each list

(a, 0.9)

(b, 0.8)

(c, 0.72)

(d, 0.6)

.

.

.

.

L1 L2

(d, 0.9)

(a, 0.85)

(b, 0.7)

(c, 0.2)

.

.

.

.

a

d

0.9

0.9

0.85 0.85

0.6 0.6

For each object seen: - get all grades by random access - determine Min(A1,A2) - amongst 2 highest seen ? keep in

buffer

Example – Threshold Algorithm

ID A1 A2 Min(A1,A2)a: 0.9

b: 0.8

c: 0.72

d: 0.6

.

.

.

.

L1 L2

d: 0.9

a: 0.85

b: 0.7

c: 0.2

.

.

.

.

Step 2: - Determine threshold value based on objects currently seen under sorted access. T = min(L1, L2)

a

d

0.9

0.9

0.85 0.85

0.6 0.6

T = min(0.9, 0.9) = 0.9

- 2 objects with overall grade ≥ threshold value ? stop else go to next entry position in sorted list and repeat step 1

Example – Threshold Algorithm

ID A1 A2 Min(A1,A2)

Step 1 (Again): - parallel sorted access to each list

(a, 0.9)

(b, 0.8)

(c, 0.72)

(d, 0.6)

.

.

.

.

L1 L2

(d, 0.9)

(a, 0.85)

(b, 0.7)

(c, 0.2)

.

.

.

.

a

d

0.9

0.9

0.85 0.85

0.6 0.6

For each object seen: - get all grades by random access - determine Min(A1,A2) - amongst 2 highest seen ? keep in buffer

b 0.8 0.7 0.7

Example – Threshold Algorithm

ID A1 A2 Min(A1,A2)a: 0.9

b: 0.8

c: 0.72

d: 0.6

.

.

.

.

L1 L2

d: 0.9

a: 0.85

b: 0.7

c: 0.2

.

.

.

.

Step 2 (Again): - Determine threshold value based on objects currently seen. T = min(L1, L2)

a

b

0.9

0.7

0.85 0.85

0.8 0.7

T = min(0.8, 0.85) = 0.8

- 2 objects with overall grade ≥ threshold value ? stop else go to next entry position in sorted list and repeat step 1

Example – Threshold Algorithm

ID A1 A2 Min(A1,A2)a: 0.9

b: 0.8

c: 0.72

d: 0.6

.

.

.

.

L1 L2

d: 0.9

a: 0.85

b: 0.7

c: 0.2

.

.

.

.

Situation at stopping condition

a

b

0.9

0.7

0.85 0.85

0.8 0.7

T = min(0.72, 0.7) = 0.7

Example – Threshold Algorithm

Algorithm

Experiment Results

Quality resultsFor 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?articleid=1563479

Ppt Slides by Ramya Soumri(Fall 09)[14] R. Fagin. Fuzzy Queries in Multimedia

Database Systems. PODS 1998.

Thank You