Information Retrieval(2)

Prof. Dragomir R. Radev

radev@umich.edu

IR WINTER 2010

…3. Document preprocessing. Tokenization. Stemming. The Porter algorithm. Storing, indexing and searching text.

Inverted indexes.…

Document preprocessing

• Dealing with formatting and encoding issues

• Hyphenation, accents, stemming, capitalization

• Tokenization:– Paul’s, Willow Dr., Dr. Willow, 555-1212, New

York, ad hoc, can’t– Example: “The New York-Los Angeles flight”

Non-English languages

– Arabic:

– Japanese:

– German: Lebensversicherungsgesellschaftsangesteller

كتاب

この本は重い。

Document preprocessing

• Normalization:– Casing (cat vs. CAT)– Stemming (computer, computation)– Soundex– Labeled/labelled, extraterrestrial/extra-terrestrial/extra

terrestrial, Qaddafi/Kadhafi/Ghadaffi

• Index reduction– Dropping stop words (“and”, “of”, “to”)– Problematic for “to be or not to be”

Porter’s algorithm

Example: the word “duplicatable”

duplicat rule 4duplicate rule 1b1duplic rule 3

The application of another rule in step 4, removing “ic,” cannotbe applied since one rule from each step is allowed to be applied.

Porter’s algorithm

Computable Comput

Intervention Intervent

Retrieval Retriev

Document Docum

Representing Repres

Representative Repres

Links

• http://maya.cs.depaul.edu/~classes/ds575/porter.html

• http://www.tartarus.org/~martin/PorterStemmer/def.txt

Approximate string matching

• The Soundex algorithm (Odell and Russell)

• Uses:– spelling correction– hash function– non-recoverable

The Soundex algorithm

1. Retain the first letter of the name, and drop all occurrences of a,e,h,I,o,u,w,y in other positions

2. Assign the following numbers to the remaining letters after the first:b,f,p,v : 1

c,g,j,k,q,s,x,z : 2

d,t : 3

l : 4

m n : 5

r : 6

The Soundex algorithm

3. if two or more letters with the same code were adjacent in the original name, omit all but the first

4. Convert to the form “LDDD” by adding terminal zeros or by dropping rightmost digits

Examples:

Euler: E460, Gauss: G200, H416: Hilbert, K530: Knuth, Lloyd: L300

same as Ellery, Ghosh, Heilbronn, Kant, and Ladd

Some problems: Rogers and Rodgers, Sinclair and StClair

IR WINTER 2010

…4. Word distributions.

The Zipf distribution.The Benford distribution.Heap‘s law.TF*IDF

…

Word distributions

• Words are not distributed evenly!• Same goes for letters of the alphabet

(ETAOIN SHRDLU), city sizes, wealth, etc.

• Usually, the 80/20 rule applies (80% of the wealth goes to 20% of the people or it takes 80% of the effort to build the easier 20% of the system), more examples coming up…

Shakespeare

• Romeo and Juliet:• And, 667; The, 661; I, 570; To, 515; A, 447; Of, 382; My, 356; Is, 343; That, 343; In, 314; You, 289; Thou, 277;

Me, 262; Not, 257; With, 234; It, 224; For, 223; This, 215; Be, 207; But, 181; Thy, 167; What, 163; O, 160; As, 156; Her, 150; Will, 147; So, 145; Thee, 139; Love, 135; His, 128; Have, 127; He, 120; Romeo, 115; By, 114; She, 114; Shall, 107; Your, 103; No, 102; Come, 96; Him, 96; All, 92; Do, 89; From, 86; Then, 83; Good, 82; Now, 82; Here, 80; If, 80; An, 78; Go, 76; On, 76; I'll, 71; Death, 69; Night, 68; Are, 67; More, 67; We, 66; At, 65; Man, 65; Or, 65; There, 64; Hath, 63; Which, 60;

• …• A-bed, 1; A-bleeding, 1; A-weary, 1; Abate, 1; Abbey, 1; Abhorred, 1; Abhors, 1; Aboard, 1; Abound'st, 1;

Abroach, 1; Absolved, 1; Abuse, 1; Abused, 1; Abuses, 1; Accents, 1; Access, 1; Accident, 1; Accidents, 1; According, 1; Accursed, 1; Accustom'd, 1; Ache, 1; Aches, 1; Aching, 1; Acknowledge, 1; Acquaint, 1; Acquaintance, 1; Acted, 1; Acting, 1; Action, 1; Acts, 1; Adam, 1; Add, 1; Added, 1; Adding, 1; Addle, 1; Adjacent, 1; Admired, 1; Ado, 1; Advance, 1; Adversary, 1; Adversity's, 1; Advise, 1; Afeard, 1; Affecting, 1; Afflicted, 1; Affliction, 1; Affords, 1; Affray, 1; Affright, 1; Afire, 1; Agate-stone, 1; Agile, 1; Agree, 1; Agrees, 1; Aim'd, 1; Alderman, 1; All-cheering, 1; All-seeing, 1; Alla, 1; Alliance, 1; Alligator, 1; Allow, 1; Ally, 1; Although, 1;

http://www.mta75.org/curriculum/english/Shakes/indexx.html(visited in Dec. 2006)

The BNC (Adam Kilgarriff)• 1 6187267 the det• 2 4239632 be v• 3 3093444 of prep• 4 2687863 and conj• 5 2186369 a det• 6 1924315 in prep• 7 1620850 to infinitive-marker• 8 1375636 have v• 9 1090186 it pron• 10 1039323 to prep• 11 887877 for prep• 12 884599 i pron• 13 760399 that conj• 14 695498 you pron• 15 681255 he pron• 16 680739 on prep• 17 675027 with prep• 18 559596 do v• 19 534162 at prep• 20 517171 by prep

Kilgarriff, A. Putting Frequencies in the Dictionary.International Journal of Lexicography10 (2) 1997. Pp 135--155

Stop words

• 250-300 most common words in English account for 50% or more of a given text.

• Example: “the” and “of” represent 10% of tokens. “and”, “to”, “a”, and “in” - another 10%. Next 12 words - another 10%.

• Moby Dick Ch.1: 859 unique words (types), 2256 word occurrences (tokens). Top 65 types cover 1132 tokens (> 50%).

• Token/type ratio: 2256/859 = 2.63

Zipf’s law

Rank x Frequency Constant

Rank Term Freq. Z Rank Term Freq. Z

1 the 69,971 0.070 6 in 21,341 0.128

2 of 36,411 0.073 7 that 10,595 0.074

3 and 28,852 0.086 8 is 10,099 0.081

4 to 26.149 0.104 9 was 9,816 0.088

5 a 23,237 0.116 10 he 9,543 0.095

Zipf's law is fairly general!

• Frequency of accesses to web pages • in particular the access counts on the Wikipedia page,with s approximately equal to 0.3 • page access counts on Polish Wikipedia (data for late July 2003) approximately obey Zipf's law with s about 0.5

• Words in the English language • for instance, in Shakespeare’s play Hamlet with s approximately 0.5

• Sizes of settlements• Income distributions amongst individuals • Size of earthquakes• Notes in musical performances

http://en.wikipedia.org/wiki/Zipf's_lawhttp://www.nslij-genetics.org/wli/zipf/http://www.cut-the-knot.org/do_you_know/zipfLaw.shtml

Zipf’s law (cont’d)

• Limitations:– Low and high frequencies– Lack of convergence

• Power law with coefficient c = -1– Y=kxc

• Li (1992) – typing words one letter at a time, including spaces

Heap’s law

• Size of vocabulary: V(n) = Kn

• In English, K is between 10 and 100, β is between 0.4 and 0.6.

n

V(n)

http://en.wikipedia.org/wiki/Heaps%27_law

Heaps law (cont’d)

• Related to Zipf’s law: generative models

• Zipf’s and Heap’s law coefficients change with language

Alexander Gelbukh, Grigori Sidorov. Zipf and Heaps Laws’ Coefficients Depend on Language. Proc.CICLing-2001, Conference on Intelligent Text Processing and Computational Linguistics, February 18–24, 2001, Mexico City. Lecture Notes in Computer Science N 2004, ISSN 0302-9743, ISBN 3-540-41687-0, Springer-Verlag, pp. 332–335.

The Benford law

• the first digit of a random number is d with the probability log10 (1+1/d).

• Number ones are much more frequent that number nines.

• Useful in forensic accounting, political science:– Mebane, Walter R., Jr. 2006. Detecting

Attempted Election Theft: Vote Counts, Voting Machines and Benford's Law

IDF: Inverse document frequency

N: number of documentsdk: number of documents containing term kfik: absolute frequency of term k in document iwik: weight of term k in document i

idfk = log2(N/dk) + 1 = log2N - log2dk + 1

TF * IDF is used for automated indexing and for topicdiscrimination:

Vector-based matching

• The cosine measure

sim (D,C) =

(dk . ck . idf(k))

(dk)2 . (ck)2

k

k

k

Asian and European news

622.941 deng306.835 china196.725 beijing153.608 chinese152.113 xiaoping124.591 jiang108.777 communist102.894 body 85.173 party 71.898 died 68.820 leader 43.402 state 38.166 people

97.487 nato92.151 albright74.652 belgrade46.657 enlargement34.778 alliance34.778 french33.803 opposition32.571 russia14.095 government 9.389 told 9.154 would 8.459 their 6.059 which

Other topics

120.385 shuttle 99.487 space 90.128 telescope 70.224 hubble 59.992 rocket 50.160 astronauts 49.722 discovery 47.782 canaveral 47.782 cape 40.889 mission 35.778 florida 27.063 center

74.652 compuserve65.321 massey55.989 salizzoni29.996 bob27.994 online27.198 executive15.890 interim15.271 chief11.647 service11.174 second 6.781 world 6.315 president

Readings

• 2: MRS9

• 3: MRS13, MRS14