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Text Processing, Tokenization,�& Characteristics

By Elmurod Kuriyozov

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Previously

  • Documents
    • Corpus
    • Tokens (terms)
  • Evaluation
    • Relevance
    • Precision/recall
    • F measure
    • Competitions
  • Web crawlers
    • Crawler policy / breath vs depth first search
    • Robots.txt
    • Scrapy

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Text

  • Text parsing
    • Tokenization, terms
    • A bit of linguistics
  • Text characteristics
    • Zipf’s law
    • Heap’s law

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Why the focus on text?

  • Language is the most powerful query model
  • Language can be treated as text
  • Others?

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Text Documents

A text digital document consists of a sequence of words and other symbols, e.g., punctuation.

The individual words and other symbols are known as tokens or terms.

A textual document can be:

Free text, also known as unstructured text, which is a

continuous sequence of tokens.

Fielded text, also known as structured text, in which the text

is broken into sections that are distinguished by tags or other

markup.

Examples?

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Text Based Information Retrieval

Most matching methods are based on Boolean operators.

Most ranking methods are based on the vector space model.

Web search methods combine vector space model with ranking based on importance of documents.

Many practical systems combine features of several approaches.

In the basic form, all approaches treat words as separate tokens with minimal attempt to interpret them linguistically.

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Interface

Query Engine

Indexer

Index

Crawler

Users

Web

A Typical Web Search Engine

Text processing

(preprocessing)

Pre-indexing

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Focus on documents

Decide what is an individual document

Can vary depending on problem

  • Documents are basic units consisting of a sequence of tokens or terms and are to be indexed.
  • Terms (derived from tokens) are words or roots of words, semantic units or phrases which are the atoms of indexing
  • Repositories (databases) and corpora are collections of documents.
  • Query is a request for documents on a query-related topic.

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Building an index

  • Collect documents to be indexed
    • Create your corpora
  • Tokenize the text
  • Linguistic processing
  • Build the inverted index from terms

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What is a Document?

  • A document is a digital object with an operational definition
    • Indexable (usually digital)
    • Can be queried and retrieved.
  • Many types of documents
    • Text or part of text
    • Web page
    • Image
    • Audio
    • Video
    • Data
    • Email
    • Etc.

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What is Text?

  • Text is so common that we often ignore its importance
  • What is text?
    • Strings of characters (alphabets, ideograms, ascii, unicode, etc.)
      • Words
      • . , : ; - ( ) _
      • Σψμβολσ
      • 1 2 3, 3.1415, 1010
      • f = ma, H20
      • Tables
      • Figures

    • Anything that is not an image, etc.
    • Why is text important?
      • Text is language capture
        • an instantiation of language, culture, science, etc.

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Collection of text

  • Corpora: collection of texts
    • especially if complete and self contained; the corpus of Anglo-Saxon verse
    • Special collection
  • In linguistics and lexicography, a body of texts, utterances or other specimens considered more or less representative of a language and usually stored as an electronic database (The Oxford Companion to the English Language 1992)
  • A collection of naturally occurring language text chosen to characterize a state or variety of a language (John Sinclair Corpus Concordance Collocation OUP 1991)

  • Types:
    • Written vs Spoken
    • General vs Specialized
    • Monolingual vs Multilingual
      • e.g. Parallel, Comparable
    • Synchronic (at a particular pt in time) vs Diachronic (over time)
    • Annotated vs Unannotated
    • Indexed vs unindexed
    • Static vs dynamic

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Written corpora

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Text Processing – Lexical Analysis

  • Standard Steps:
    • Recognize language class [english] (very easy)
    • Recognize document structure
      • titles, sections, paragraphs, etc.
    • Break into tokens – type of markup
      • Tokens are delimited text
        • Hello, how are you.
        • _hello_,_how_are_you_._
      • usually space and punctuation delineated
      • special issues with Asian languages
    • Lemmatization, stemming/morphological analysis
    • What is left are terms
    • Store in inverted index
  • Lexical analysis is the process of converting a sequence of characters into a sequence of tokens.
    • A program or function which performs lexical analysis is called a lexical analyzer, lexer or scanner.

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Basic indexing pipeline

Tokenizer

Token stream.

Friends

Romans

Countrymen

Linguistic modules

Modified tokens (terms).

friend

roman

countryman

Indexer

Inverted index.

friend

roman

countryman

2

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Documents to

be indexed.

Friends, Romans, countrymen.

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Parsing a document�(lexical analysis)

  • What format is it in?
    • pdf/word/excel/html?
  • What language is it in?
  • What character set is in use?

Each of these is a classification problem which can be solved using heuristics or machine learning methods.

But there are complications …

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Format/language stripping

  • Documents being indexed can include docs from many different languages
    • A single index may have to contain terms of several languages.
  • Sometimes a document or its components can contain multiple languages/formats
    • French email with a Portuguese pdf attachment.
  • What is a unit document?
    • An email?
    • With attachments?
    • An email with a zip containing documents?

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Tokenization is the basic part of document preprocessing

  • Convert byte sequences into a linear sequence of characters
  • Trivial with ascii, but not so with Unicode or others
    • Use ML classifiers or heuristics.

  • Crucial problem for commercial systems!

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Tokenization

  • Fundamental to Natural Language Processing (NLP), IR, deep Learning and AI
  • Parsing (chopping up) the document into basic units that are candidates for later indexing
    • What parts of text to use and what not
  • Issues with
    • Punctuation
    • Numbers
    • Special characters
    • Equations
    • Formula
    • Languages
    • Normalization (often by stemming)

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Tokenization

  • Not the tokenization of how to make data secure

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Tokenization

  • Not the tokenization of how to make data secure

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Sometimes called ”parsers”

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What tokenization did you use?

  • For real problems always ask this!
  • A fundamental question for all text processing
    • Natural language processing
    • Text mining
    • Machine learning and AI
    • Information retrieval and search

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Natural Language Toolkit (NLTK)

  • A suite of Python libraries for symbolic and statistical natural language programming
    • Developed at the University of Pennsylvania
    • Has its own tokenization
  • Developed to be a teaching tool and a platform for research NLP prototypes
    • Data types are packaged as classes
    • Goal of code is to be clear, rather than fastest performance
  • Online book: http://www.nltk.org/book/
    • Authors: Edward Loper, Ewan Kline and Steven Bird

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Lots of tokenizers out there

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Tokenization example

  • Input: “Friends, Romans and Countrymen
  • Output: Tokens
    • friends
    • romans
    • countrymen
  • Each such token is now a candidate for an index entry, after further processing
    • Described below
  • But what are valid tokens to emit?

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Tokenization

  • Issues in tokenization:
    • Finland’s capital →

Finland? Finlands? Finland’s?

    • Hewlett-Packard
      • Hewlett and Packard as two tokens?
      • State-of-the-art: break up hyphenated sequence.
      • co-education ?
      • the hold-him-back-and-drag-him-away-maneuver ?
    • San Francisco: one token or two? How do you decide it is one token?

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Numbers

  • 3/12/91
  • Mar. 12, 1991
  • 55 B.C.
  • B-52
  • My PGP key is 324a3df234cb23e
  • 100.2.86.144
    • Generally, don’t index as text.
    • Will often index “meta-data” separately
      • Creation date, format, etc.

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Tokenization: Language issues

  • L'ensemble → one token or two?
    • L ? L’ ? Le ?
    • Want ensemble to match with un ensemble

  • German noun compounds are not segmented
    • Lebensversicherungsgesellschaftsangestellter
    • ‘life insurance company employee’

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Tokenization: language issues

  • Chinese and Japanese have no spaces between words:
    • Not always guaranteed a unique tokenization
  • Further complicated in Japanese, with multiple alphabets intermingled
    • Dates/amounts in multiple formats

フォーチュン500社は情報不足のため時間あた$500K(約6,000万円)

Katakana

Hiragana

Kanji

“Romaji”

End-user can express query entirely in hiragana!

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Tokenization: language issues

  • Arabic (or Hebrew) is basically written right to left, but with certain items like numbers written left to right
  • Words are separated, but letter forms within a word form complex ligatures
  • استقلت الجزائر في سنة 1962 بعد 132 عاما من الاحتلال الفرنسي.
  • ← → ← → ← start
  • ‘Algeria achieved its independence in 1962 after 132 years of French occupation.’
  • With Unicode, the surface presentation is complex, but the stored form is straightforward

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Normalization

  • Need to “normalize” terms in indexed text as well as query terms into the same form
    • We want to match U.S.A. and USA
  • We most commonly implicitly define equivalence classes of terms
    • e.g., by deleting periods in a term
  • Alternative is to do limited expansion:
    • Enter: window Search: window, windows
    • Enter: windows Search: Windows, windows
    • Enter: Windows Search: Windows
  • Potentially more powerful, but less efficient

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Case folding

  • Reduce all letters to lower case
    • exception: upper case (in mid-sentence?)
      • e.g., General Motors
      • Fed vs. fed
      • SAIL vs. sail

    • Often best to lower case everything, since users will use lowercase regardless of ‘correct’ capitalization

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Normalizing Punctuation

  • Ne’er vs. never: use language-specific, handcrafted “locale” to normalize.
    • Which language?
    • Most common: detect/apply language at a pre-determined granularity: doc/paragraph.
  • U.S.A. vs. USA – remove all periods or use locale.
  • a.out

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Thesauri and soundex

  • Handle synonyms and homonyms
    • Hand-constructed equivalence classes
      • e.g., car = automobile
      • color = colour
  • Rewrite to form equivalence classes
  • Index such equivalences
    • When the document contains automobile, index it under car as well (usually, also vice-versa)
  • Or expand query?
    • When the query contains automobile, look under car as well

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  • Traditional class of heuristics to expand a query into phonetic equivalents
    • Language specific – mainly for names
    • E.g., chebyshevtchebycheff

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Stemming and Morphological Analysis

  • Goal: “normalize” similar words
  • Morphology (“form” of words)
    • Inflectional Morphology
      • E.g,. inflect verb endings and noun number
      • Never change grammatical class
        • dog, dogs
    • Derivational Morphology
      • Derive one word from another,
      • Often change grammatical class
        • build, building; health, healthy

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Lemmatization

  • Reduce inflectional/variant forms to base form
  • E.g.,
    • am, are, is be
    • car, cars, car's, cars'car
  • the boy's cars are different colorsthe boy car be different color
  • Lemmatization implies doing “proper” reduction to dictionary headword form

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Stemming

Morphological variants of a word (morphemes). Similar terms derived from a common stem:

engineer, engineered, engineering

use, user, users, used, using

Stemming in Information Retrieval. Grouping words with a common stem together.

For example, a search on reads, also finds read, reading, and readable

Stemming consists of removing suffixes and conflating the resulting morphemes. Occasionally, prefixes are also removed.

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Stemming

  • Reduce terms to their “roots” before indexing
  • “Stemming” suggest crude affix chopping
    • language dependent
    • e.g., automate(s), automatic, automation all reduced to automat.

for example compressed

and compression are both

accepted as equivalent to

compress.

for exampl compress and

compress ar both accept

as equival to compress

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Porter’s algorithm

  • Commonest algorithm for stemming English
    • Results suggest at least as good as other stemming options
  • Conventions + 5 phases of reductions
    • phases applied sequentially
    • each phase consists of a set of commands
    • sample convention: Of the rules in a compound command, select the one that applies to the longest suffix.

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Typical rules in Porter

  • ssesss
  • iesi
  • ationalate
  • tionaltion

  • Weight of word sensitive rules
  • (m>1) EMENT
      • replacement replac
      • cement cement

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Other stemmers

  • Other stemmers exist, e.g., Lovins stemmer http://www.comp.lancs.ac.uk/computing/research/stemming/general/lovins.htm
    • Single-pass, longest suffix removal (about 250 rules)
    • Motivated by Linguistics as well as IR

  • Full morphological analysis – at most modest benefits for retrieval

  • Do stemming and other normalizations help?
    • Often very mixed results: really help recall for some queries but harm precision on others

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Automated Methods are the norm

  • Powerful multilingual tools exist for morphological analysis
    • PCKimmo, Xerox Lexical technology
    • Require a grammar and dictionary
    • Use “two-level” automata
  • Stemmers:
    • Very dumb rules work well (for English)
    • Porter Stemmer: Iteratively remove suffixes
    • Improvement: pass results through a lexicon

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Porter’s algorithm

  • Commonest algorithm for stemming English
  • Conventions + 5 phases of reductions
    • phases applied sequentially
    • each phase consists of a set of commands
    • sample convention: Of the rules in a compound command, select the one that applies to the longest suffix.
  • Typical rules
    • ssesss
    • iesi
    • ationalate
    • tionaltion

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Categories of Stemmer

The following diagram illustrate the various categories of stemmer. Porter's algorithm is shown by the red path.

Conflation methods

Manual Automatic (stemmers)

Affix Successor Table n-gram

removal variety lookup

Longest Simple

match removal

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Comparison of stemmers

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Stemming in Practice

Evaluation studies have found that stemming can affect retrieval

performance, usually for the better, but the results are mixed.

• Effectiveness is dependent on the vocabulary. Fine distinctions may be lost through stemming.

• Automatic stemming is as effective as manual conflation.

• Performance of various algorithms is similar.

Porter's Algorithm is entirely empirical, but has proved to be an

effective algorithm for stemming English text with trained users.

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Language-specificity

  • Many of the above features embody transformations that are
    • Language-specific and
    • Often, application-specific
  • These are “plug-in” addenda to the indexing process
  • Both open source and commercial plug-ins available for handling these

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Normalization: other languages

  • Accents: résumé vs. resume.
  • Most important criterion:
    • How will your users write their queries for these words?

  • Even in languages that standardly have accents, users often may not type them

  • German: Tuebingen vs. Tübingen
    • Should be equivalent

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Normalization: other languages

  • Need to “normalize” indexed text as well as query terms into the same form

  • Character-level alphabet detection and conversion
    • Tokenization not separable from this.
    • Sometimes ambiguous:

7月30日 vs. 7/30

Morgen will ich in MIT

Is this

German “mit”?

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Dictionary entries – first cut

ensemble.french

時間.japanese

MIT.english

mit.german

guaranteed.english

entries.english

sometimes.english

tokenization.english

These may be grouped by language. More on this in ranking/query processing.

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Interface

Query Engine

Indexer

Index

Crawler

Users

Web

A Typical Web Search Engine

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Content Analysis of Text

  • Automated Transformation of raw text into a form that represent some aspect(s) of its meaning
  • Including, but not limited to:
    • Token creation
    • Matrices and Vectorization
    • Phrase Detection
    • Categorization
    • Clustering
    • Summarization

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Techniques for Content Analysis

  • Statistical / vector
    • Single Document
    • Full Collection
  • Linguistic
    • Syntactic
    • Semantic
    • Pragmatic
  • Knowledge-Based (Artificial Intelligence)
  • Hybrid (Combinations)

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  • Very common words, such as of, and, the, are rarely of use in information retrieval.
  • A stop list is a list of such words that are removed during lexical analysis.
  • NOT INDEXED
  • A long stop list saves space in indexes, speeds processing, and eliminates many false hits.
  • However, common words are sometimes significant in information retrieval, which is an argument for a short stop list. (Consider the query, "To be or not to be?")

Stop Lists

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Suggestions for Including Words in a Stop List

Include the most common words in the English language (perhaps 50 to 250 words).

Do not include words that might be important for retrieval (Among the 200 most frequently occurring words in general literature in English are time, war, home, life, water, and world).

• In addition, include words that are very common in context (e.g., computer, information, system in a set of computing documents).

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Example: the WAIS stop list�(first 84 of 363 multi-letter words)

about above according across actually adj after afterwards again against all almost alone along already also although always among amongst an another any anyhow anyone anything anywhere are aren't around at be became because become becomes becoming been before beforehand begin beginning behind being below beside besides between beyond billion both but by can can't cannot caption co could couldn't

did didn't do does doesn't don't down during each eg eight eighty

either else elsewhere end ending enough

etc even ever every everyone everything

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Stop list policies

How many words should be in the stop list?

• Long list lowers recall

Which words should be in list?

• Some common words may have retrieval importance:

-- war, home, life, water, world

• In certain domains, some words are very common:

-- computer, program, source, machine, language

There is very little systematic evidence to use in selecting a stop list.

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Stop Lists in Practice

The modern tendency is:

  1. have very short stop lists for broad-ranging or multi-lingual document collections, especially when the users are not trained (or none at all – Moore’s law)
  2. have longer stop lists for document collections in well-defined fields, especially when the users are trained professional.
  3. Web search engines have no stop lists

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Token generation - stemming

  • What are tokens for documents?
    • Words (things between spaces)
  • Some words equivalent
  • Stemming finds equivalences among words
  • Removal of grammatical suffixes

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Stemming

  • Reduce terms to their roots before indexing
    • language dependent
    • e.g., automate(s), automatic, automation all reduced to automat.

for example compressed

and compression are both

accepted as equivalent to

compress.

for exampl compres and

compres are both accept as

equival to compres.

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Analyzer: �Lucene Tokenization

  • Tokenizes the input text
  • Common Analyzers
    • WhitespaceAnalyzer�Splits tokens on whitespace
    • SimpleAnalyzer�Splits tokens on non-letters, and then lowercases
    • StopAnalyzer�Same as SimpleAnalyzer, but also removes stop words
    • StandardAnalyzer�Most sophisticated analyzer that knows about certain token types, lowercases, removes stop words, ...

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Analysis example

  • “The quick brown fox jumped over the lazy dog”
  • WhitespaceAnalyzer
    • [The] [quick] [brown] [fox] [jumped] [over] [the] [lazy] [dog]
  • SimpleAnalyzer
    • [the] [quick] [brown] [fox] [jumped] [over] [the] [lazy] [dog]
  • StopAnalyzer
    • [quick] [brown] [fox] [jumped] [over] [lazy] [dog]
  • StandardAnalyzer
    • [quick] [brown] [fox] [jumped] [over] [lazy] [dog]

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Another analysis example

  • “XY&Z Corporation – xyz@example.com”
  • WhitespaceAnalyzer
    • [XY&Z] [Corporation] [-] [xyz@example.com]
  • SimpleAnalyzer
    • [xy] [z] [corporation] [xyz] [example] [com]
  • StopAnalyzer
    • [xy] [z] [corporation] [xyz] [example] [com]
  • StandardAnalyzer
    • [xy&z] [corporation] [xyz@example.com]

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Example of tokenizing a document with different Lucene Analyzers

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What’s inside an Analyzer?

  • Analyzers need to return a TokenStreampublic TokenStream tokenStream(String fieldName,� Reader reader)

TokenStream

Tokenizer

TokenFilter

Reader

Tokenizer

TokenFilter

TokenFilter

lemmatization

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Lucene Tokenizers and TokenFilters

  • Tokenizer
    • WhitespaceTokenizer
    • KeywordTokenizer
    • LetterTokenizer
    • StandardTokenizer
    • ...
  • TokenFilter
    • LowerCaseFilter
    • StopFilter
    • PorterStemFilter
    • ASCIIFoldingFilter
    • StandardFilter
    • ...

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Other Analyzers

  • Also available
    • GermanAnalyzer
    • RussianAnalyzer
    • (Lucene Sandbox)
      • BrazilianAnaylzer
      • ChineseAnalyzer (UTF-8)
      • CzechAnalyzer
      • DutchAnalyzer
      • FrenchAnalyzer
      • GreekAnalyzer
      • KoreanAnalyzer
      • JapaneseAnalyzer

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Analyzer for Lucene

  • Tokenization: Create an Analyser
    • Options
      • WhitespaceAnalyzer
        • divides text at whitespace
      • SimpleAnalyzer
        • divides text at non-letters
        • convert to lower case
      • StopAnalyzer
        • SimpleAnalyzer
        • removes stop words
      • StandardAnalyzer
        • good for most European Languages
        • removes stop words
        • convert to lower case

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Summary of Text

  • Text is reduced to tokens (terms)
  • Stop words can be removed
  • Tokenizer has many features
  • Stemmers widely used for token generation
    • Porter stemmer most common

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Selection of tokens, weights, stop lists and stemming

Special purpose collections (e.g., law, medicine, monographs)

Best results are obtained by tuning the search engine for the characteristics of the collections and the expected queries.

It is valuable to use a training set of queries, with lists of relevant documents, to tune the system for each application.

General purpose collections (e.g., web search)

The modern practice is to use a basic weighting scheme (e.g., tf.idf), a simple definition of token, a short stop list and no stemming except for plurals, with minimal conflation.

Web searching combine similarity ranking with ranking based on document importance.

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Indexing Subsystem

Documents

break into tokens

stop list*

stemming*

term weighting*

Index database

text

non-stoplist tokens

tokens

stemmed terms

terms with weights

*Indicates optional operation.

assign document IDs

documents

document numbers and *field numbers

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Search Subsystem

Index database

query

parse query

stemming*

stemmed terms

stop list*

non-stoplist tokens

query tokens

Boolean operations*

ranking*

relevant document set

ranked document set

retrieved document set

*Indicates optional operation.

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Try out queries on Google

  • fish
  • fishs
  • fishes
  • fishing

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Google Translate Example - problems

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Statistical Properties of Text

  • Token occurrences in text are not uniformly distributed
  • They are also not normally distributed
  • They do exhibit a Zipf distribution
    • Also known as “discrete Pareto distribution”

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Zipf Distribution

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A More Standard Collection

8164 the

4771 of

4005 to

2834 a

2827 and

2802 in

1592 The

1370 for

1326 is

1324 s

1194 that

973 by

969 on

915 FT

883 Mr

860 was

855 be

849 Pounds

798 TEXT

798 PUB

798 PROFILE

798 PAGE

798 HEADLINE

798 DOCNO

1 ABC

1 ABFT

1 ABOUT

1 ACFT

1 ACI

1 ACQUI

1 ACQUISITIONS

1 ACSIS

1 ADFT

1 ADVISERS

1 AE

Government documents, 157734 tokens, 32259 unique

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Plotting Word Frequency by Rank

  • Main idea: count
    • How many times tokens occur in the text
      • Over all texts in the collection
  • Now rank these according to how often they occur. This is called the rank.

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Rank Freq Term�1 37 system�2 32 knowledg�3 24 base�4 20 problem�5 18 abstract�6 15 model�7 15 languag�8 15 implem�9 13 reason�10 13 inform�11 11 expert�12 11 analysi�13 10 rule�14 10 program�15 10 oper�16 10 evalu�17 10 comput�18 10 case�19 9 gener�20 9 form

150 2 enhanc

151 2 energi

152 2 emphasi

153 2 detect

154 2 desir

155 2 date

156 2 critic

157 2 content

158 2 consider

159 2 concern

160 2 compon

161 2 compar

162 2 commerci

163 2 clause

164 2 aspect

165 2 area

166 2 aim

167 2 affect

Most and Least Frequent Terms

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Rank Freq�1 37 system�2 32 knowledg�3 24 base�4 20 problem�5 18 abstract�6 15 model�7 15 languag�8 15 implem�9 13 reason�10 13 inform�11 11 expert�12 11 analysi�13 10 rule�14 10 program�15 10 oper�16 10 evalu�17 10 comput�18 10 case�19 9 gener�20 9 form

The Corresponding Zipf Curve

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43 6 approach�44 5 work�45 5 variabl�46 5 theori�47 5 specif�48 5 softwar�49 5 requir�50 5 potenti�51 5 method�52 5 mean�53 5 inher�54 5 data�55 5 commit�56 5 applic�57 4 tool�58 4 technolog�59 4 techniqu

Zoom in on the Knee of the Curve

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Zipf Distribution

  • The Important Points:
    • a few elements occur very frequently
    • a medium number of elements have medium frequency
    • many elements occur very infrequently
    • Self similarity
      • Same shape for large and small frequency words
    • Long tail
    • Not necessarily obeys central limit theorem

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Zipf Distribution

  • The product of the frequency of words (f) and their rank (r) is approximately constant
    • Rank = order of words’ frequency of occurrence

  • Another way to state this is with an approximately correct rule of thumb:
    • Say the most common term occurs C times
    • The second most common occurs C/2 times
    • The third most common occurs C/3 times

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Zipf Distribution�(linear and log scale)

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What Kinds of Data Exhibit a Zipf Distribution?

  • Words in a text collection
    • Virtually any language usage
  • Library book checkout patterns
  • Incoming Web Page Requests (Nielsen)
  • Outgoing Web Page Requests (Cunha & Crovella)
  • Document Size on Web (Cunha & Crovella)
  • Many sales with certain retailers

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Prevalence of Zipfian Laws

  • Many items exhibit a Zipfian distribution.
    • Population of cities
    • Wealth of individuals
      • Discovered by sociologist/economist Pareto in 1909
    • Popularity of books, movies, music, web-pages, etc.
    • Popularity of consumer products
      • Chris Anderson’s “long tail”

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Power Laws

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Power Law Statistics - problems with means

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Power-law distributions

  • The degree distributions of most real-life networks follow a power law

  • Right-skewed/Heavy-tail distribution
    • there is a non-negligible fraction of nodes that has very high degree (hubs)
    • scale-free: no characteristic scale, average is not informative

  • In stark contrast with the random graph model!
    • Poisson degree distribution, z=np

    • highly concentrated around the mean
    • the probability of very high degree nodes is exponentially small

p(k) = Ck-α

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Power-law signature

  • Power-law distribution gives a line in the log-log plot

  • α : power-law exponent (typically 2 ≤ α ≤ 3)

degree

frequency

log degree

log frequency

α

log p(k) = -α logk + logC

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Examples of degree distribution for power laws

Taken from [Newman 2003]

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Power Law Statistics - long tails

Power of the long tail:

The phrase The Long Tail, as a proper noun, was first coined by Chris Anderson. The concept drew in part from an influential February 2003 essay by Clay Shirky, "Power Laws, Weblogs and Inequality" that noted that a relative handful of weblogs have many links going into them but "the long tail" of millions of weblogs may have only a handful of links going into them. Beginning in a series of speeches in early 2004 and culminating with the publication of a Wired magazine article in October 2004, Anderson described the effects of the long tail on current and future business models. Anderson later extended it into the book The Long Tail: Why the Future of Business is Selling Less of More (2006).

Anderson argued that products that are in low demand or have low sales volume can collectively make up a market share that rivals or exceeds the relatively few current bestsellers and blockbusters, if the store or distribution channel is large enough. Examples of such mega-stores include the online retailer Amazon.com and the online video rental service Netflix. The Long Tail is a potential market and, as the examples illustrate, the distribution and sales channel opportunities created by the Internet often enable businesses to tap into that market successfully.

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Word Frequency vs. Resolving Power

The most frequent words are not the most descriptive.

van Rijsbergen 79

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Fit to Zipf for Brown Corpus

k = 100,000

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Does Real Data Fit Zipf’s Law?

  • A law of the form y = kxc is called a power law.
  • Zipf’s law is a power law with c = –1
  • On a log-log plot, power laws give a straight line with slope c.

  • Zipf is quite accurate except for very high and low rank.

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Mandelbrot (1954) Correction

  • The following more general form gives a bit better fit:

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Mandelbrot Fit

P = 105.4, B = 1.15, ρ = 100

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Explanations for Zipf’s Law

  • Zipf’s explanation was his “principle of least effort.” Balance between speaker’s desire for a small vocabulary and hearer’s desire for a large one.
  • Debate (1955-61) between Mandelbrot and H. Simon over explanation.
  • Simon explanation is “rich get richer.”
  • Li (1992) shows that just random typing of letters including a space will generate “words” with a Zipfian distribution.

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Zipf’s Law Impact on IR

  • Good News:
    • Stopwords will account for a large fraction of text so eliminating them greatly reduces inverted-index storage costs.
    • Postings list for most remaining words in the inverted index will be short since they are rare, making retrieval fast.
  • Bad News:
    • For most words, gathering sufficient data for meaningful statistical analysis (e.g. for correlation analysis for query expansion) is difficult since they are extremely rare.

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Vocabulary Growth

  • How does the size of the overall vocabulary (number of unique words) grow with the size of the corpus?
  • This determines how the size of the inverted index will scale with the size of the corpus.
  • Vocabulary not really upper-bounded due to proper names, typos, etc.

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Heaps’ Law

  • If V is the number of distinct words, size of the vocabulary, and the n is the length of the corpus in words:

  • Typical constants:
    • K 10100
    • β 0.40.6 (approx. square-root)

H.S. Heaps, G. Herdon

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Heaps’ Law Data

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Explanation for Heaps’ Law

  • Can be derived from Zipf’s law by assuming documents are generated by randomly sampling words from a Zipfian distribution.

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Consequences for Heaps’ Law

  • Heaps' law means that as more instance text is gathered, there will be diminishing returns in terms of discovery of the full vocabulary from which the distinct terms are drawn.
  • Heaps' law also applies to situations in which the "vocabulary" is just some set of distinct types which are attributes of some collection of objects. For example, the objects could be people, and the types could be country of origin of the person. If persons are selected randomly (that is, we are not selecting based on country of origin), then Heaps' law says we will quickly have representatives from most countries (in proportion to their population) but it will become increasingly difficult to cover the entire set of countries by continuing this method of sampling. Heaps' law has been observed also in single-cell transcriptomes[4] considering genes as the distinct objects in the "vocabulary".

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Consequences of Zipf for IR

  • There are always a few very frequent tokens that are not good discriminators.
    • Called “stop words” in IR
    • Usually correspond to linguistic notion of “closed-class” words
      • English examples: to, from, on, and, the, ...
      • Grammatical classes that don’t take on new members.
  • There are always a large number of tokens that occur once and can mess up algorithms.
  • Medium frequency words most descriptive

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Text Metadata

  • Information about a document that may not be a part of the document itself (data about data).
  • Descriptive metadata is external to the meaning of the document:
    • Author
    • Title
    • Source (book, magazine, newspaper, journal)
    • Date
    • ISBN
    • Publisher
    • Length

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Metadata (cont)

  • Semantic metadata concerns the content:
    • Abstract
    • Keywords
    • Subject Codes
      • Library of Congress
      • Dewey Decimal
      • UMLS (Unified Medical Language System)
  • Subject terms may come from specific ontologies (hierarchical taxonomies of standardized semantic terms).

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Web Metadata

  • META tag in HTML
    • <META NAME=“keywords” CONTENT=“pets, cats, dogs”>
  • META “HTTP-EQUIV” attribute allows server or browser to access information:
    • <META HTTP-EQUIV=“expires” CONTENT=“Tue, 01 Jan 02”>
    • <META HTTP-EQUIV=“creation-date” CONTENT=“23-Sep-01”>

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Markup Languages

  • Language used to annotate documents with “tags” that indicate layout or semantic information.
  • Most document languages (Word, RTF, Latex, HTML) primarily define layout.
  • History of Generalized Markup Languages:

GML(1969)

SGML (1985)

HTML (1993)

XML (1998)

Standard

HyperText

eXtensible

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Markup Languages

  • More about this later when we talk about the semantic web

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Text as queries

  • Text is a natural query model.
  • Discuss this next.

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Lemmatization vs stemming

  • In general, lemmatization offers better precision than stemming, but at the expense of recall.
  • Stemming and lemmatization are effective techniques to expand recall 
  • lemmatization gives up some recall to increase precision.
  • But both techniques can feel like crude instruments, but Google uses them
  • Lemmatization and stemming are special cases of normalization. They identify a canonical representative for a set of related word forms. The entire process is often called normalization
  • Some use lemmatization to refer to both

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Text - Summary

  • Perform lexical analysis - processing text into tokens or terms
    • Many issues: normalization, lemmatization
    • Most language dependent
    • Languages on the internet
  • Stemming reduces the number of tokens
    • Porter stemmer most common
  • Lemmatization reduces the number of tokes
    • Can operate on stimms
    • can include stemming
  • Stop words removed to improve performance
    • Can be omitted
  • Lucene Analyzers perform tokenization
    • Many tokenizers available (Python)
  • What remains are terms to be indexed
  • Text has power law distribution (Zipf)
    • Words with resolving power in the middle and tail of the distribution
    • Heap/s law shows how vocab growth tapers off
  • Text as metadata and queries

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