Processing of large document collections

Processing of large document collections

Part 4

Text compression

Despite a continuous increase in storage and transmission capacities, more and more effort has been put into using compression to increase the amount of data that can be handled

no matter how much storage space or transmission bandwidth is available, someone always finds ways to fill it with

Text compression

Efficient storage and representation of information is an old problem (before the computer era) Morse code: uses shorter

representations for common characters Braille code for the blind: includes

contractions, which represent common words with 2 or 3 characters

Text compression

On a computer: changing the representation of a file so that it takes less space to store or less time to transmit original file can be reconstructed exactly from

the compressed representationdifferent than data compression in general

text compression has to be lossless compare with sound and images: small

changes and noise is tolerated

Text compression methods

Huffman coding (in the 50’s) compressing English: 5 bits/character

Ziv-Lempel compression (in the 70’s) 4 bits/character

arithmetic coding 2 bits/char (more processing power

needed)prediction by partial matching (80’s)


Since 80’s compression rate has been about the same

improvements are made in processor and memory utilization during compression

also: amount of compression may increase when more memory (for compression and uncompression) is available


Most text compression methods can be placed in one of two classes: symbolwise methods dictionary methods

Symbolwise methods

Work by estimating the probabilities of symbols (often characters) coding one symbol at a time using shorter codewords for the most

likely symbols (in the same way as Morse code does)

Dictionary methods

Achieve compression by replacing words and other fragments of text with an index to an entry in a ”dictionary” the Braille code is a dictionary method

since special codes are used to represent whole words

Symbolwise methods

Usually based on Huffman coding or arithmetic coding

variations differ mainly in how they estimate probabilities for symbols the more accurate these estimates are, the

greater the compression that can be achieved to obtain good compression, the probability

estimate is usually based on the context in which a symbol occurs

Symbolwise methods

Modeling estimating probabilities there does not appear to be any single

”best” methodCoding

converting the probabilities into a bitstream for transmission

well understood, can be performed effectively

Dictionary methods

Generally use quite simple representations to code references to entries in the dictionary

obtain compression by representing several symbols as one output codeword

Dictionary methods

often based on Ziv-Lempel coding replaces strings of characters with a

reference to a previous occurrence of a string adaptive effective: most characters can be coded as

part of a string that has occurred earlier in the text

compression is achieved if the reference is stored in fewer bits than the string it replaces

Models

Compression methods obtain high compression by forming good models of the data that is to be coded

the function of a model is to predict symbols e.g. during the encoding of a text , the

”prediction” for the next symbol might include a probability of 2% for the letter ’u’, based on its relative frequency in a sample of text

Models

The set of all possible symbols is called the alphabet

the probability distribution provides an estimated probability for each symbol in the alphabet

Encoding, decoding

the model provides the probability distribution to the encoder, which uses it to encode the symbol that actually occurs

the decoder uses an identical model together with the output of the encoder to find out what the encoded symbol was

Information content of a symbol

The number of bits in which a symbol s should be coded is called the information content I(s) of the symbol

the information content I(s) is directly related to the symbol’s predicted probability P(s), by the function I(s) = -log P(s) bits


The average amount of information per symbol over the whole alphabet is known as the entropy of the probability distribution, denoted by H:

ss

sPsPsIsPH )(log)()()(


Provided that the symbols appear independently and with the assumed probabilities, H is a lower bound on compression, measured in bits per symbol, that can be achieved by any coding method


If the probability of symbol ’u’ is estimated to be 2%, the corresponding information content is 5.6 bits

if ’u’ happens to be the next symbol that is to be coded, it should be transmitted in 5.6 bits

predictions can usually be improved by taking account of the previous symbol


predictions can usually be improved by taking account of the previous symbol

if a ’q’ has just occurred, the probability of ’u’ may jump to 95 %, based on how often ’q’ is followed by ’u’ in a sample of text

information content of ’u’ in this case is 0.074 bits


Models that take a few immediately preceding symbols into account to make a prediction are called finite-context models of order m m is the number of previous symbols

used to make a prediction

Adaptive models

There are many ways to estimate the probabilities in a model

we could use static modelling: always use the same probabilities for

symbols, regardless of what text is being coded

compressing system may not perform well, if different text is receivede.g. a model for English with a file of numbers

Adaptive models

One solution is to generate a model specifically for each file that is to be compressed

an initial pass is made through the file to estimate symbol probabilities, and these are transmitted to the decode before transmitting the encoded symbols

this is called semi-static modelling

Adaptive models

Semi-static modelling has the advantage that the model is invariably better suited to the input than a static one, but the penalty paid is having to transmit the model first, as well as the preliminary pass over the

data to accumulate symbol probabilities

Adaptive models

Adaptive model begins with a bland probability distribution and gradually alters it as more symbols are encountered

as an example, assume a zero-order model, i.e., no context is used to predict the next symbol

Adaptive models

Assume that a encoder has already encoded a long text and come to a sentence: It migh

now the probability that the next character is ’t’ is estimated to be 49,983/768,078 = 6.5 %, since in the previous text, 49,983 characters of the total of 768,078 characters were ’t’

Adaptive models

Using the same system, ’e’ has the probability 9.4 % and ’x’ has probability 0.11 %

the model provides this estimated probability distribution to an encoder

the decoder is able to generate the same model since it has the same probability estimates as the encoder

Adaptive models

For a higher-order model, such as a first-order model, the probability is estimated by how often that character has occurred in the current context

in a zero-order model earlier, a symbol ’t’ occurred in a context: It migh , but the model made no use of the characters of the phrase

Adaptive models

A first-order model would use the final ’h’ as a context with which to condition the probability estimates

the letter ’h’ has occurred 37,525 times in the prior text, and 1,133 of these times it was followed by a ’t’

the probability of ’t’ occurring after an ’h’ can be estimated to be 1,133/37,525=3.02 %

Adaptive models

For ’t’, a prediction of 3.2% is actually worse than in the zero-order model because ’t’ is rare in this context (’e’ follows ’h’ much more often)

second-order model would use the relative frequency that the context ’gh’ is followed by ’t’, which is the case in 64,6%

Adaptive models

Good: robust, reliable, flexibleBad: not suitable for random access

to compressed files a text can be decoded only from the

beginning: the model used for coding a particular part of the text is determined from all the preceding text

-> not suitable for full-text retrieval

Coding

Coding is the task of determining the output representation of a symbol, based on a probability distribution supplied by a model

general idea: the coder should output short codewords for likely symbols and long codewords for rare ones

symbolwise methods depend heavily on a good coder to achieve compression

Huffman coding

A phrase is coded by replacing each of its symbols with the codeword given by a table

Huffman coding generates codewords for a set of symbols, given some probability distribution for the symbols

the type of code is called prefix-free code no codeword is the prefix of another symbol’s

codeword

Huffman coding

The codewords can be stored in a tree (a decoding tree)

Huffman’s algorithm works by constructing the decoding tree from the bottom up

Huffman codingAlgorithm

create for each symbol a leaf node containing the symbol and its probability

two nodes with the smallest probabilities become siblings under a new parent node, which is given a probability equal to the sum of its two children’s probabilities

the combining operation is repeated until there is only one node without a parent

the two branches from every nonleaf node are then labeled 0 and 1

Huffman coding

Huffman coding is generally fast for both encoding and decoding, provided that the probability distribution is static adaptive Huffman coding is possible, but

needs either a lot of memory or is slowcoupled with a word-based model

(rather than character-based model), gives a good compression

Canonical Huffman codes

The frequency of each word is countedthe codewords are chosen for each word

to minimize the size of the compressed file -> static zero-order word-level model

the codewords are shown in decreasing order of length (and therefore in increasing order of word frequency) within each block of codes of the same

length, words are ordered alphabetically


The list begins with the thousands of words (and numbers) that appear only once

when the codewords are sorted in lexical order, they are also in order from the longest to the shortest codeword


A word’s encoding can be determined quickly from the length of its codeword, how far through the list it is, and the codeword for the first word of that length


It is not necessary to store a decode tree

all the is required is a list of the symbols ordered according

to the lexical order of the codewords an array storing the first codeword of

each distinct length

Dictionary models

Dictionary-based compression methods use the principle of replacing substrings in a text with a codeword that identifies that substring in a dictionary

dictionary contains a list of substrings and a codeword for each substring

often fixed codewords used reasonable compression is obtained even if

coding is simple

Dictionary models

The simplest dictionary compression methods use small dictionaries

for instance, digram coding selected pairs of letters are replaced

with codewords a dictionary for the ASCII character set

might contain the 128 ASCII characters, as well as 128 common letter pairs

Dictionary modelsDigram coding…

the output codewords are eight bits each the presence of the full ASCII character set

ensures that any (ASCII) input can be represented

at best, every pair of characters is replaced with a codeword, reducing the input from 7 bits/character to 4 bits/characters

at worst, each 7 bit character will be expanded to 8 bits

Dictionary models

Natural extension: put even larger entries in the dictionary, e.g.

common words like ’and’, ’the’,… or common components of words like ’pre’, ’tion’…

a predefined set of dictionary phrases make the compression domain-dependent or very short phrases have to be used ->

good compression is not achieved

Dictionary modelsOne way to avoid the problem of the

dictionary being unsuitable for the text at hand is to use a semi-static dictionary scheme constuct a new dictionary for every text that

is to be compressed overhead of transmitting or storing the

dictionary is significant decision of which phrases should be included

is a difficult problem

Dictionary models

Solution: use an adaptive dictionary scheme

Ziv-Lempel coders (LZ77 and LZ78)a substring of text is replaced with a

pointer to where it has occurred previously

dictionary: all the text prior to the current position

codewords: pointers

Dictionary models

Ziv-Lempel… the prior text makes a very good

dictionary since it is usually in the same style and language as upcoming text

the dictionary is transmitted implicitly at no extra cost, because the decoder has access to all previously encoded text

LZ77

Key benefits: relatively easy to implement decoding can be performed extremely

quickly using only a small amount of memorysuitable when the resources required for

decoding must be minimized, like when data is distributed or broadcast from a central source to a number of small computers

LZ77

The output of an encoder consists of a sequence of triples, e.g. <3,2,b> the first component of a triple indicates

how far back to look in the previous (decoded) text to find the next phrase

the second component records how long the phrase is

the third component gives the next character from the input

LZ77

The components 1 and 2 consitute a pointer back into the text

the component 3 is actually necessary only when the character to be coded does not occur anywhere in the previous input

LZ77

Encoding for the text from the current point ahead:

search for the longest match in the previous textoutput a triple that records the position and

length of the matchthe search for a match may return a length of

zero, in which case the position of the match is not relevant

search can be accelerated by indexing the prior text with a suitable data structure

LZ77limitations on how far back a pointer can

refer and the maximum size of the string referred to

e.g. for English text, a window of a few thousand characters

the length of the phrase e.g. maximum of 16 characters

otherwise too much space wasted without benefit

LZ77

The decoding program is very simple, so it can be included with the data at very little cost

in fact, the compressed data is stored as part of the decoder program, which makes the data self-expanding

common way to distribute files

Synchronization

Good compression methods perform best when compressing large files

this tends to preclude random access because the decompression algorithms are sequential by nature

full-text retrieval systems require random access, and special measures need to be taken to facilitate this

Synchronization

There are two reasons that the better compression methods require files to be decoded from the beginning they use variable-length codes their models are adaptive

Synchronization

With variable-length codes, it is not possible to begin decoding at an arbitrary position in the file we cannot be sure of starting on the

boundary between two codewordsadaptive modelling: even if the

codeword boundary is known, the model required for decoding can be constructed only using all the preceding text

Synchronization

To achieve synchronization with adaptive modelling, large files must be broken up into small sections of a few kilobytes

a good compression cannot be obtained by compressing the small sections separately ->the compression model has to be constructed based on a sample text of the whole data

Synchronization

For full-text retrieval, it is usually preferable to use a static model rather than an adaptive one

static models are more appropriate given the static nature of a large textual database

SynchronizationIn a full-text retrieval system, the main

text usually consists of a number of documents, which represent the smallest unit to which random access is required

in an uncompressed text, a document can be identified simply by specifying how many bytes it is from the start of the file when a variable-length code is used, a

document may not start on a byte boundary

Synchronization

A solution is to insist that documents begin on byte boundaries, which means that the last byte may contain some wasted bits

there has to be some way to tell the decoder that it should not interpret some bits

Processing of large document collections

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