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Problem

• Compress Text Algorithms (6EAP) – Text – Images, , sound, … Compression • Reduce space, efficient communicaon, etc… Jaak Vilo – Data deduplicaon 2012 fall • Exact compression/decompression

Jaak Vilo MTAT.03.190 Text Algorithms 1 •

Links

• Managing Gigabytes: • hp://datacompression.info/ Compressing and Indexing • hp://en.wikipedia.org/wiki/Data_compression Documents and Images • Debra A. Lelewer and Daniel S. Hirschberg • Ian H. Wien, Alistair Moffat, – hp://www.ics.uci.edu/~dan/pubs/DataCompression.html Timothy C. Bell • Compression FAQ hp://www.faqs.org/faqs/compression-faq/ • Hardcover: 519 pages Publisher: Morgan Kaufmann; 2nd Revised • Informaon Theory Primer With an edion edion (11 May 1999) Appendix on Logarithms by Tom Language English ISBN-10: Schneider hp://www.lecb.ncifcrf.gov/~toms/paper/primer/ 1558605703 • hp://www.cbloom.com/algs/index.html

Problem What it’s about?

• Informaon transmission • Eliminaon of redundancy • Informaon storage • Being able to predict… • The data sizes are huge and growing – fax - 1.5 x 106 /page • Compression and decompression – photo: 2M pixels x 24bit = 6MB – Represent data in a more compact way – X-ray image: ~ 100 MB? – Decompression - restore original form – Microarray scanned image: 30-100 MB – Tissue-microarray - hundreds of images, each tens of MB • Lossy and – Large Hardon Collider (CERN) - The device will produce few peta (1015) bytes of stored – Lossless - restore in exact copy data in a year. – Lossy - restore almost the same informaon – TV (PAL) 2.7 · 108 bit/s • Useful when no 100% accuracy needed – CD-sound, super-audio, DVD, ... • voice, image, movies, ... • Decompression is determinisc (lossy in compression phase) – Human genome – 3.2Gbase. 30x sequencing => 100Gbase + quality info (+ raw data) • Can achieve much more effecve results – 1000 genomes, all individual genomes …

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Methods covered: Model

• Code words (Huffman coding) Model Model • Run-length encoding • Arithmec coding • Lempel-Ziv family (compress, gzip, zip, pkzip, ...)

• Burrows-Wheeler family (bzip2) Compressed data • Other methods, including images Data Data Encoder Decoder • Kolmogorov • Search from compressed texts

• Let pS be a of message S • The informaon content can be represented in terms of

• I(S) = -log( pS ) bits • If the p=1 then the informaon content is 0 (no new informaon) – If Pr[s]=1 then I(s) = 0. – In other words, I(death)=I(taxes)=0 • I( heads or tails ) = 1 -- if the coin is fair • Entropy H(S) is the average informaon content of S

– H(S) = pS · I(S) = -pS log( pS ) bits hp://en.wikipedia.org/wiki/Informaon_entropy

• Shannon's experiments with human predictors show an informaon rate of between .6 and 1.3 bits per character, depending on the experimental setup; the PPM compression algorithm can achieve a compression rao of 1.5 bits per character.

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http://prize.hutter1.net/ • The data compression world is all abuzz about Marcus Huer’s recently announced 50,000 euro prize for record-breaking data compressors. Marcus, of the Swiss Dalle Molle Instute for Arficial Intelligence, apparently in cahoots with Florida compression maven Ma Mahoney, is offering cash prizes for what amounts to the most • No compression can on average achieve beer compression impressive ability to compress 100 MBytes of Wikipedia data. (Note that nobody is going to than the entropy win exactly 50,000 euros - the prize amount is prorated based on how well you beat the current record.) • Entropy depends on the model (or choice of symbols) • This prize differs considerably from my Million Digit Challenge, which is really nothing more • Let M={ m , .. m } be a set of symbols of the model A and let than an aempt to silence people foolishly claiming to be able to compress random data. 1 n Marcus is instead looking for the most effecve way to reproduce the Wiki data, and he’s p(mi) be the probability of the symbol mi pung up real money as an incenve. The benchmark that contestants need to beat is that set by Ma Mahoney’s paq8f , the current record holder at 18.3 MB. (Alexander • The entropy of the model A, H(M) is -∑i=1..n p(mi) · log( p(mi) ) Ratushnyak’s submission of a variant looks to clock in at a dy 17.6 MB, and should soon bits be confirmed as the new standard.) • So why is an AI guy inserng himself into the world of compression? Well, Marcus realizes • Let the message S = s1, .. sk, and every symbol si be in the that good data compression is all about modeling the data. The beer you understand the model M. The informaon content of model A is -∑ log p data stream, the beer you can predict the incoming tokens in a stream. Claude Shannon i=1..k empirically found that humans could model English text with an entropy of 1.1 to 1.6 0.6 to (si) 1.3 bits per character, which at at best should mean that 100 MB of Wikipedia data could be reduced to 13.75 7.5 MB, with an upper bound of perhaps 20 16.25 MB. The theory is that • Every symbol has to have a probability, otherwise it cannot be reaching that 7.5 MB range is going to take such a good understanding of the data stream coded if it is present in the data that it will amount to a demonstraon of Arficial Intelligence. hp://marknelson.us/2006/08/24/the-huer-prize/#comment-293

Model Stac or adapve

• Stac model does not change during the Model Model compression • Adapve model can be updated during the process • Symbols not in message cannot have 0-probability

Compressed • Semi-adapve model works in 2 stages, off-line. Data data Data • First create the code table, then encode the message Encoder Decoder with the code table

How to compare compression Shorter code words… techniques? • Rao (t/p) t: original message length • S = 'aa bbb cccc ddddd eeeeee fffffffgggggggg' • p: compressed message length • Alphabet of 8 • In texts - bits per symbol • Length = 40 symbols • The me and memory used for compression • Equal length codewords • The me and memory used for decompression • 3-bit a 000 b 001 c 010 d 011 e 100 f 101 g 110 • error tolerance (e.g. self-correcng code) space 110 • S compressed - 3*40 = 120 bits

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Run-length encoding Alphabecally ordered word-lists

• hp://michael.dipperstein.com/rle/index.html • The string:

• "aaaabbcdeeeeefghhhij"

• may be replaced with resume 0resume

• "a4b2c1d1e5f1g1h3i1j1". retail 2tail • This is not shorter because 1-leer repeat takes more characters... retain 5n • "a3b1cde4fgh2ij" • Now we need to know which characters are followed by run-length. retard 4rd • E.g. use escape symbols. retire 3ire • Or, use the symbol itself - if repeated, then must be followed by run- length • "aa2bb0cdee3fghh1ij"

Coding techniques Variable length encoders

• Coding refers to techniques used to encode • How to use codes of variable length? tokens or symbols. • Decoder needs to know how long is the • Two of the best known coding algorithms are symbol Huffman Coding and Arithmec Coding. • Coding algorithms are effecve at • Prefix-free code: no code can be a prefix of compressing data when they use fewer bits another code for high probability symbols and more bits for low probability symbols.

Algoritm Shannon-Fano

• Calculate the frequencies and probabilies of • Input: probabilies of symbols symbols: • Output: Codewords in prefix free coding • S = 'aa bbb cccc ddddd eeeeee fffffffgggggggg'

freq ratio p(s) a 2 2/40 0.05 1. Sort symbols by frequency b 3 3/40 0.075 c 4 4/40 0.1 2. Divide to two almost probable groups d 5 5/40 0.125 space 5 5/40 0.125 3. First group gets prefix 0, other 1 e 6 6/40 0.15 f 7 7/40 0.175 4. Repeat recursively in each group unl 1 g 8 8/40 0.2 symbol remains

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Example 1 Example 1

Code: a 1/2 0 a 1/2 0 b 1/4 10 b 1/4 10 c 1/8 110 c 1/8 110 d 1/16 1110 d 1/16 1110 e 1/32 11110 e 1/32 11110 f 1/32 11111 f 1/32 11111

Shannon-Fano Shannon-Fano S = 'aa bbb cccc ddddd eeeeee fffffffgggggggg' • S = 'aa bbb cccc ddddd eeeeee fffffffgggggggg' p(s) code • S in compressed is 117 bits g 0.2 00 0.2 0.525 • 2*4 + 3*4 + 4*3 + 5*3 + 5*3 + 6*3 + 7*3 + 8*2 f 0.175 010 0.175 0.325 0.15 = 117 e 0.15 011 1 d 0.125 100 • Shannon-Fano not always opmal space 0.125 101 0.475 • Somemes 2 equal probable groups cannot be c 0.1 110 achieved b 0.075 1110 a 0.05 1111 • Usually beer than H+1 bits per symbol, when H is entropy.

Char Freq Code Huffman code space 7 111 Huffman example a 4 010 • Works the opposite way. e 4 000 f 3 1101 • Start from least probable symbols and separate them with 0 h 2 1010 and 1 (sufix) i 2 1000 • Add probabilies to form a "new symbol" with the new m 2 0111 probability n 2 0010 • Prepend new bits in front of old ones. s 2 1011 t 2 0110 l 1 11001 o 1 00110 p 1 10011 r 1 11000 u 1 00111 "this is an example of a huffman tree" x 1 10010

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Properes of Huffman coding

• Huffman coding is opmal when the • Error tolerance quite good frequencies of input characters are powers of • In case of the loss, adding or change of a two. Arithmec coding produces slight gains single bit, the differences remain local to the over Huffman coding, but in pracce these place of the error gains have not been large enough to offset • Error usually remains quite local (proof?) arithmec coding's higher computaonal • complexity and patent royales Has been shown, the code is opmal • (as of November 2001/Jul2006, IBM owns patents on • Can be shown the average result is H+p the core concepts of arithmec coding in several +0.086, where H is the entropy and p is the jurisdicons). probability of the most probable symbol hp://en.wikipedia.org/wiki/Arithmec_coding#US_patents_on_arithmec_coding

Move to Front Arithmec (en)coding

• Move to Front (MTF), Least recently used • Arithmec coding is a method for lossless data compression. • It is a form of , but where other entropy encoding (LRU) techniques separate the input message into its component symbols and replace each symbol with a code word, arithmec coding encodes the • Keep a list of last k symbols of S enre message into a single number, a fracon n where (0.0 n < 1.0). • Huffman coding is opmal for character encoding (one character-one code • Code word) and simple to program. Arithmec coding is beer sll, since it can – use the code for symbol. allocate fraconal bits, but more complicated. • Wikipedia hp://en.wikipedia.org/wiki/Arithmec_encoding – if in codebook, move to front • Enre message is a single floang point number, a fracon n where (0.0 n – if not in codebook, move to first, remove the last < 1.0). • Every symbol gets a probability based on the model • c.f. the handling of memory paging • Probabilies represent non-intersecng intervals • Other heuriscs ... • Every text is such an

Let P(A)=0.1, P(B)=0.4, P(C)=0.5

A [0,0.1) AA [0 , 0.01) AB [0.01 , 0.05) AC [0.05 , 0.1 )

B [0.1,0.5) BA [0.1 , 0.14) BB [0.14 , 0.3 ) BC [0.3 , 0.5 )

C [0.5,1) CA [0.5 , 0.55 ) CB [0.55 , 0.75 ) CC [0.75 , 1 )

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• Add a EOF symbol. • Invented by Jorma Rissanen (then at IBM) • Arithmec coding revisited by Alistair Moffat, Radford M. • Problem with infinite precision arithmecs Neal, Ian H. Wien - hp://portal.acm.org/citaon.cfm?id=874788 • Alternave - blockwise, use integer- arithmecs • Models for arithmec coding - • • Works, if smallest p not too small HMM Hidden Markov Models i • ... • Best rao • Context methods: Abrahamson dependency model • Problem - the speed, and error tolerance, • Use the context to maximum, to predict the next symbol small change has catastrophic effect • PPM - Predicon by Paral Matching • Several contexts, choose best • Variaons

Diconary based compression Lempel-Ziv family, LZ, LZ-77

• Diconary (symbol table) , list codes • Use the diconary to memorise the previously compressed parts • LZ-77 • If not in disconary, use escape • Sliding window of previous text; and text to be compressed

• Usual heuriscs searches for longest repeat /bbaaabbbaaffacbbaa…./...abbbaabab... • With fixed table one can search for opmal • Lookahead - longest prefix that begins within the moving window, is code encoded with [posion,length] • With adapve diconary the opmal coding is • In example, [5,6] • Fast! (Commercial soware, e.g. PKZIP, Stacker, DoubleSpace, ) NP-complete • Several alternave codes for same string (alternave substrings will match) • Quite good for English language texts, for • Lempel-Ziv compression from McGill Univ. hp://www.cs.mcgill.ca/~cs251/OldCourses/1997/topic23/ example

Original LZ77 LZ-78 • Triples [posion,length,next char] • If output [a,b,c], advance by b+1 posions • Diconary • Store strings from processed part of the message • For each part of the triple the nr of bits is • Next symbol is the longest match from diconary, that reserved depending on window length matches the text to be processed ⎡ log(n-f) ⎤ + ⎡ log(f) ⎤ + 8 • LZ78 (Ziv and Lempel 1978) where n is window size, and f is lookahead • First, diconary is empty, with index 0 size • Code [i,c] - refers to diconary (word u at pos. i) and c is the next symbol • Example: abbbbabbc • Add uc to diconary [0,0,a] [0,0,b] [1,3,a] [3,2,c] • Example: ababcabc → [0,a][0,b][1,b][0,c][3,c] • In example the match actually overlaps with lookahead window

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LZW LZJ

• Code consists of indices only! • Coding - search for longest prefix. • First, diconary has every symbol /alphabet/ • Update diconary like LZ78 • Code - address of the trie node • In decoding there is a danger: See abcabca • From the root of the trie, there is a transion – If abc is in diconary – add abca to diconary on every symbol (like in LZW). – next is abca, output that code – But when decoding, aer abc it is not known that abca is in the • If out of memory, remove these nodes/ diconary branches that have been used only once • Soluon - if the diconary entry is used immediately aer its creaon, the 1st and last characters have to match • In pracce, h=6, diconary has 8192 nodes

• Many representaons for the diconary. • List, hash, sorted list, combinaon, binary tree, trie, suffix tree, ...

LZFG Burrows-Wheeler

• See FAQ hp://www.faqs.org/faqs/compression-faq/part2/secon-9.html • Effecve LZ method • The method described in the original paper is really a composite of three different algorithms: • From LZJ – the block sorng main engine (a lossless, very slightly expansive preprocessor), – the move-to-front coder (a byte-for-byte simple, fast, locally adapve noncompressive coder) and • – a simple stascal compressor (first order Huffman is menoned as a candidate) eventually doing Create a suffix tree for the window the compression. • Of these three methods only the first two are discussed here as they are what constutes the • Code - node address plus nr of characters heart of the algorithm. These two algorithms combined form a completely reversible (lossless) transformaon that - with typical input - skews the first order symbol distribuons from teh edge. to make the data more compressible with simple methods. Intuively speaking, the method transforms slack in the higher order probabilies of the input block (thus making them more • The internal and leaf nodes with different even, whitening them) to slack in the lower order stascs. This effect is what is seen in the histogram of the resulng symbol data. codes • Please, read the arcle by Mark Nelson: • Data Compression with the Burrows-Wheeler Transform Mark Nelson, Dr. Dobb's Journal • small match directly... (?) September, 1996. hp://marknelson.us/1996/09/01/bwt/

Burrows-Wheeler Transform (BWT)

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Example

CODE: t: hat acts like this:<13><10><1 t: hat buffer to the constructor • Decode: errktreteoe.e t: hat corrupted the heap, or wo W: hat goes up must come down<13 t: hat happens, it isn't likely w: hat if you want to dynamicall • t: hat indicates an error.<13><1 Hint: . Is the last character, t: hat it removes arguments from alphabecally first… t: hat looks like this:<13><10>< t: hat looks something like this t: hat looks something like this t: hat once I detect the mangled

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Syntacc compression

• Context Free Grammar for presenng the • Many images, photos, sound, video, ... syntax tree • Usually for source code • Assumpon - program is syntaccally correct • Comments • Features, constants - group by group

Fax group 3

• Fax/group 3 • Joint Photographic Experts Group JPEG 2000 • Black/white, 0/1 code hp://www.jpeg.org/jpeg2000/ • Image Compression -- JPEG from W.B. Pennebaker, • Run-length: 000111001000 → 3,3,2,1,3 J.L. Mitchell, "The JPEG Sll Image Data Compression • Variable-length codes for represenng run- Standard", Van Nostrand Reinhold, 1993. lengths. • Color image, 8 or 12 bits per pixel per color. • Four modes Sequenal Mode • Lossless Mode • Progressive Mode • Hierarchical Mode • DCT (Discrete Cosine Transform)

Lena

• from hp://www.utdallas.edu/~aria/mcl/post/ • Lossy signal compression works on the basis of transming the "important" signal content, while oming other parts (Quanzaon). To perform this quanzaon effecvely, a linear de-correlang transform is applied to the signal prior to quanzaon. All exisng image and video coding standards use this approach. The most commonly used transform is the Discrete Cosine Transform (DCT) used in JPEG, MPEG-1, MPEG-2, H.261 and H.263 and its descendants. For a detailed discussion of the theory behind quanzaon and jusficaon of the usage of linear transforms, see reference [1] below. • A brief overview of JPEG compression is as follows. The JPEG encoder parons the image into 8x8 blocks of pixels. To each of these blocks it applies a 2- dimensional DCT. The transform matrix is normalized (element-wise) by a 8x8 quanzaon matrix and then rounded to the nearest integer. This operaon is equivalent to applying different uniform quanzers to different frequency bands of the image. The high-frequency image content can be quanzed more coarsely than the low-frequency content, due to two factors. • L9_Compression/lena/

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Vector quanzaon Discrete cosine transform

• • A discrete cosine transform (DCT) expresses a sequence of finitely many Vector quanzaon data points in terms of a sum of cosine funcons oscillang at different • Diconary-meetod frequencies. DCTs are important to numerous applicaons in science and engineering, from lossy compression of audio and images (where small • 2-dimensional blocks high-frequency components can be discarded), to spectral methods for the numerical soluon of paral differenal equaons. The use of cosine rather than sine funcons is crical in these applicaons: for compression, it turns out that cosine funcons are much more efficient (as explained below, fewer are needed to approximate a typical signal), whereas for differenal equaons the cosines express a parcular choice of boundary condions.

• hp://en.wikipedia.org/wiki/Discrete_cosine_transform

• In parcular, a DCT is a Fourier-related transform 2d DCT (type II) compared to the DFT. similar to the discrete (DFT), but For both transforms, using only real numbers. DCTs are equivalent to DFTs there is the magnitude of the spectrum on left of roughly twice the length, operang on real data and the histogram on with even symmetry (since the Fourier transform of right; both spectra are cropped to 1/4, to a real and even funcon is real and even), where in zoom the behaviour in some variants the input and/or output data are the lower frequencies. The DCT concentrates shied by half a sample. There are eight standard most of the power on the lower frequencies. DCT variants, of which four are common.

• Digital Image Processing: hp://www-ee.uta.edu/dip/

Block Diagram of JPEG Baseline s EE330 (Princeton) (Princeton) s EE330 ’ From Wallace’s JPEG tutorial (1993) JPEG tutorial Wallace’s From From Liu 475 x 330 x 3 = 157 KB luminance ENEE631 Digital Image ENEE631 Digital Image Lec13 – Transf. Coding & JPEG [65] Lec13 – Transf. Coding & JPEG [66] Processing (Spring'04) Processing (Spring'04)

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RGB Components Y U V (Y Cb Cr) Components s EE330 (Princeton) (Princeton) s EE330 (Princeton) s EE330 ’ ’ From Liu From Liu Assign more bits to Y, less bits to Cb and Cr ENEE631 Digital Image ENEE631 Digital Image Lec13 – Transf. Coding & JPEG [67] Lec13 – Transf. Coding & JPEG [68] Processing (Spring'04) Processing (Spring'04)

JPEG Compression (Q=75%) JPEG Compression (Q=75%) s EE330 (Princeton) (Princeton) s EE330 (Princeton) s EE330 ’ ’

From Liu 45 KB, compression ration ~ 4:1 From Liu 45 KB, compression ration ~ 4:1

ENEE631 Digital Image ENEE631 Digital Image Lec13 – Transf. Coding & JPEG [69] Lec13 – Transf. Coding & JPEG [70] Processing (Spring'04) Processing (Spring'04)

JPEG Compression (Q=75% & 30%)

Uncompressed (100KB)

JPEG 75% (18KB) s EE330 (Princeton) (Princeton) s EE330 ’ UMCP ENEE408G Slides (created by M.Wu & R.Liu2002)& © ENEE408G Slides (created byM.Wu UMCP JPEG 50% (12KB)

JPEG 30% (9KB) From Liu 45 KB 22 KB JPEG 10% (5KB) ENEE631 Digital Image ENEE631 Digital Image Lec13 – Transf. Coding & JPEG [71] Lec13 – Transf. Coding & JPEG [72] Processing (Spring'04) Processing (Spring'04)

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1.4-billion-pixel digital camera compression

• Monday, November 24, 2008 • group at Waterloo hp://www.technologyreview.com/compung/21705/page1/ hp://links.uwaterloo.ca/.home.html • Giant Camera Tracks Asteroids • A "Hitchhiker's Guide to Fractal Compression" • The camera will offer sharper, broader views For Beginners of the sky. p://links.uwaterloo.ca/pub/Fractals/Papers/ • The focal plane of each camera contains an almost complete 64 x 64 array of CCD devices, each containing approximately 600 x 600 pixels, for a total of about 1.4 gigapixels. The CCDs Waterloo/vr95.pdf themselves employ the innovave technology called "orthogonal transfer", which is described below. • Encode using fractals.

Diagram showing how an OTA chip • Search for regions that with a simple is made up of 64 OTCCD cells, each of which has 600 x 600 pixels transformaon can be similar to each other. • Compressin rao 20-80

• When one compresses files, can we sll use fast search techniques without decompressing • Moving Pictures Experts Group ( frst? • Somemes, yes hp://www.chiariglione.org/mpeg/ ) • e.g. Udi Manber has developed a method • Approximate Matching of Run-Length Compressed Strings • MPEG Compression : hp://www.cs.cf.ac.uk/Dave/Mulmedia/node255.html Veli Mäkinen, Gonzalo Navarro, Esko Ukkonen

• Screen divided into 256 blocks, where the • We focus on the problem of approximate matching of strings that have been compressed using run-length encoding. Previous studies have concentrated on the problem of compung changes and movements are tracked the longest common subsequence (LCS) between two strings of length m and n , compressed to m' and n' runs. We extend an exisng algorithm for the LCS to the • Only differences from previous frame are achieving O(m'n+n'm) complexity. Furthermore, we extend this algorithm to a weighted edit distance model, where the weights of the three basic edit operaons can be chosen shown arbitrarily. This approach also gives an algorithm for approximate searching of a paern of m leers (m' runs) in a text of n leers (n' runs) in O(mm'n') me. Then we propose improvements for a greedy algorithm for the LCS, and conjecture that the improved • Compression rao 50-100 algorithm has O(m'n') expected case complexity. Experimental results are provided to support the conjecture.

Kolmogorov (or Algorithmic) complexity • Kolmogorov, Chain, ... • Algorithmic informaon theory is a field of study which • What is the compressed version of sequence aempts to capture the concept of complexity using tools '1234567891011121314151617181920212223242526...' ? from theorecal . The chief idea is to define • Every symbol appears almost equally frequently, almost the complexity (or Kolmogorov complexity) of a string as the "random" by entropy length of the shortest program which, when run without any input, outputs that string. Strings that can be produced by • for i=1 to n do print i ; short programs are considered to be not very complex. This • Algorithmic complexity (or Kolmogorov complexity) for string noon is surprisingly deep and can be used to state and prove S is the length of the shortest program that reproduces S, impossibility results akin to Gödel's incompleteness theorem oen noted K(S) and Turing's halng problem. • Condional complexity : K(S|T). Reproduce S given T. • The field was developed by and • hp://en.wikipedia.org/wiki/Algorithmic_informaon_theory Gregory Chain starng in the late 1960s.

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Kolmogorov complexity: size of circle in bits... G J Chain

Model Model • hp://www.cs.umaine.edu/~chain/

Compressed Data data Data Encoder Decoder

• Distance using K. • Use of Kolmogorov Distance Idenficaon of • d(S,T) = ( K(S|T) + K(T|S) ) / ( K(S) + K(T) ) Web Page Authorship, Topic and Domain • We cannot calculate K, but we can David Parry (PPT) in OSWIR 2005, 2005 approximate it workshop on Open Source Web Informaon Retrieval • E.g. by compression LZ, BWT, etc • Informatsioonikaugus by Mart Sõmermaa, Fall • d(S,T) = ( C(ST) + C(TS) ) / ( C(S) + C(T) ) 2003 (in Data Mining Research seminar) hp://www.egeen.ee/u/vilo/edu/2003-04/DM_seminar_2003_II/Raport/P06/main.pdf

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