Indexing LBSC 796/CMSC 828o Session 9, March 29, 2004 Doug Oard.

Indexing

LBSC 796/CMSC 828oSession 9, March 29, 2004

Doug Oard

Agenda

• Questions

• Finish up evaluation from last time

• Computational complexity

• Inverted indexes

• Project planning

User Studies

• Goal is to account for interface issues– By studying the interface component– By studying the complete system

• Formative evaluation– Provide a basis for system development

• Summative evaluation– Designed to assess performance

Quantitative User Studies• Select independent variable(s)

– e.g., what info to display in selection interface• Select dependent variable(s)

– e.g., time to find a known relevant document• Run subjects in different orders

– Average out learning and fatigue effects• Compute statistical significance

– Null hypothesis: independent variable has no effect– Rejected if p<0.05

Variation in Automatic Measures

• System– What we seek to measure

• Topic– Sample topic space, compute expected value

• Topic+System– Pair by topic and compute statistical significance

• Collection– Repeat the experiment using several collections

Additional Effects in User Studies

• Learning– Vary topic presentation order

• Fatigue– Vary system presentation order

• Topic+User (Expertise)– Ask about prior knowledge of each topic

Presentation Order

Document Selection Experiments

InteractiveSelection

F0.8

StandardRanked List

Topic Description

Measures of Effectiveness• Query Formulation: Uninterpolated Average Precision

– Expected value of precision [over relevant document positions]

– Interpreted based on query content at each iteration

• Document Selection: Unbalanced F-Measure:– P = precision– R = recall = 0.8 favors precision

• Models expensive human translation

RP

F 1

1

])(

[jrjEAP j

End-to-End Experiments

QueryFormulation

AutomaticRetrieval

InteractiveSelection

AveragePrecision

F0.8

Topic Description

End-to-End Experiment ResultsF α

=0.8

English queries, German documents4 searchers, 20 minutes per topic

Summary

• Qualitative user studies suggest what to build

• Design decomposes task into components

• Automated evaluation helps to refine components

• Quantitative user studies show how well it works

Supporting the Search Process

SourceSelection

Search

Query

Selection

Ranked List

Examination

Document

Delivery

Document

QueryFormulation

IR System

Indexing Index

Acquisition Collection

Some Questions for Today• How long will it take to find a document?

– Is there any work we can do in advance?• If so, how long will that take?

• How big a computer will I need?– How much disk space? How much RAM?

• What if more documents arrive?– How much of the advance work must be repeated?– Will searching become slower?– How much more disk space will be needed?

A Cautionary Tale• Searching is easy - just ask Microsoft!

– “Find” can search my hard drive in a few minutes• If it only looks at the file names...

• How long would it would take for the Web?– A 100 GB disk?– For the World Wide Web?

• Computers are getting faster, but…– How does Google give answers in 3 seconds?

Find “complex” in the dictionary

marsupial

belligerentcomplex

marsupial

belligerentcomplex

arcadeastronomical

mastiffrelativelyrelaxationresplendent

Computational Complexity• Time complexity: how long will it take?• Space complexity: how much memory is needed?

• Things you need to know to assess complexity:– What is the “size” of the input? (“n”)

• What aspects of the input are we paying attention to?– How is the input represented?– How is the output represented?– What are the internal data structures?– What is the algorithm?

Worst Case Complexity

0

500

1000

1500

2000

2500

3000

3500

4000

4500

10 20 30 40

10nn^2100n

0

20000

40000

60000

80000

100000

120000

140000

50 200 350

10nn^2100n100n+25263

10n: O(n)100n: O(n)100n+25263: O(n)

n2: O(n2)n2+45662: O(n2)

“Asymptotic” Complexity• Constant, i.e. O(1)

n doesn’t matter • Sublinear, e.g. O(log n)

n = 65536 log n = 16• Linear, i.e. O(n)

n = 65536 n = 65536• Polynomial, e.g. O(n3)

n = 65536 n3 = 281,474,976,710,656• Exponential, e.g. O(2n)

n = 65536 beyond astronomical

The “Inverted File” Trick

• Organize the bag of words matrix by terms– You know the terms that you are looking for

• Look up terms like you search dictionaries– For each letter, jump directly to the right spot

• For terms of reasonable length, this is very fast

– For each term, store the document identifiers• For every document that contains that term

• At query time, use the document identifiers– Consult a “postings file”

An Example

quick

brown

fox

over

lazy

dog

back

now

time

all

good

men

come

jump

aid

their

party

00110000010010110

01001001001100001

Term Doc

1D

oc 2

00110110110010100

11001001001000001

Doc

3D

oc 4

00010110010010010

01001001000101001

Doc

5D

oc 6

00110010010010010

10001001001111000

Doc

7D

oc 8

A

B

C

FD

GJLMNOPQ

T

AIALBABR

THTI

4, 82, 4, 61, 3, 7

1, 3, 5, 72, 4, 6, 8

3, 53, 5, 7

2, 4, 6, 83

1, 3, 5, 72, 4, 82, 6, 8

1, 3, 5, 7, 86, 81, 3

1, 5, 72, 4, 6

PostingsInverted File

The Finished Product

quick

brown

fox

over

lazy

dog

back

now

time

all

good

men

come

jump

aid

their

party

Term

A

B

C

FD

GJLMNOPQ

T

AIALBABR

THTI

4, 82, 4, 61, 3, 7

1, 3, 5, 72, 4, 6, 8

3, 53, 5, 7

2, 4, 6, 83

1, 3, 5, 72, 4, 82, 6, 8

1, 3, 5, 7, 86, 81, 3

1, 5, 72, 4, 6

PostingsInverted File

What Goes in a Postings File?

• Boolean retrieval– Just the document number

• Ranked Retrieval– Document number and term weight (TF*IDF, ...)

• Proximity operators– Word offsets for each occurrence of the term

• Example: Doc 3 (t17, t36), Doc 13 (t3, t45)

How Big Is the Postings File?

• Very compact for Boolean retrieval– About 10% of the size of the documents

• If an aggressive stopword list is used!

• Not much larger for ranked retrieval– Perhaps 20%

• Enormous for proximity operators– Sometimes larger than the documents!

Building an Inverted Index• Simplest solution is a single sorted array

– Fast lookup using binary search– But sorting large files on disk is very slow– And adding one document means starting over

• Tree structures allow easy insertion– But the worst case lookup time is linear

• Balanced trees provide the best of both– Fast lookup and easy insertion– But they require 45% more disk space

Starting a B+ Tree Inverted File

now timegoodall

aaaaa now

Now is the time for all good …

Adding a New Term

now timegoodall

aaaaa now

Now is the time for all good men …

aaaaa men

men

How Big is the Inverted Index?

• Typically smaller than the postings file– Depends on number of terms, not documents

• Eventually, most terms will already be indexed– But the postings file will continue to grow

• Postings dominate asymptotic space complexity– Linear in the number of documents

Index Compression• CPU’s are much faster than disks

– A disk can transfer 1,000 bytes in ~20 ms– The CPU can do ~10 million instructions in that time

• Compressing the postings file is a big win– Trade decompression time for fewer disk reads

• Key idea: reduce redundancy– Trick 1: store relative offsets (some will be the same)– Trick 2: use an optimal coding scheme

Compression Example

• Postings (one byte each = 7 bytes = 56 bits)– 37, 42, 43, 48, 97, 98, 243

• Difference– 37, 5, 1, 5, 49, 1, 145

• Optimal Huffman Code– 0:1, 10:5, 110:37, 1110:49, 1111: 145

• Compressed (17 bits)– 11010010111001111

Indexing and Searching

• Indexing– Walk the inverted file, splitting if needed– Insert into the postings file in sorted order– Hours or days for large collections

• Query processing– Walk the inverted file– Read the postings file– Manipulate postings based on query– Seconds, even for enormous collections

Summary• Slow indexing yields fast query processing

– Key fact: most terms don’t appear in most documents

• We use extra disk space to save query time– Index space is in addition to document space– Time and space complexity must be balanced

• Disk block reads are the critical resource– This makes index compression a big win

Project Options

• LBSC 796 MLS/MIM– Option 1: TREC-like IR evaluation (team of 2)– Option 2: Design and run a user study (team of 3)

• LBSC 796 Ph.D.– Research paper

• LBSC 828o– Program a new capability

One Minute Paper

What was the muddiest point in today’s lecture?