111111111111111111111111111111111111111111111111111111111111111111111111111
`US007158961Bl
`
`c12) United States Patent
`Charikar
`
`(IO) Patent No.:
`(45) Date of Patent:
`
`US 7,158,961 B1
`Jan.2,2007
`
`(54) METHODS AND APPARATUS FOR
`ESTIMATING SIMILARITY
`
`(75)
`
`Inventor: Moses Samson Cbarlkar, Princeton,
`NJ (US)
`
`(73) Assignee: Google, Inc., Mountain View, CA (US)
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 611 days.
`
`(21) Appl. No.: 10/029,883
`
`(22) Filed:
`
`Dec. 31, 2001
`
`(51)
`
`Int. Cl.
`G06F 7104
`(2006.01)
`(52) U.S. Cl ............................................ 707/2; 707/102
`(58) Field of Classification Search ................ 70711-3,
`707/5, 10, 100, 102, 104.1; 708/200, 422-424;
`345/418,419, 427; 382/10, 154, 181, 190,
`382/191,209,217-220,276-278
`See application file for complete search history.
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`5,067,152 A • 1111991 Kisor eta! ............... 348/422.1
`5,101,475 A • 3/1992 Kaufinan et a! . ........... 345/424
`5,469,354 A • lli1995 Hatakeyama et a!. . ......... 707/3
`5,612,865 A • 3/1997 Dasgupta ..................... 1oon9
`5,794,178 A • 8/1998 Caid e1 al ...................... 704/9
`5,806,061 A • 9/1998 Chaudhuri et al. ............ 707/3
`6,061,734 A • 5/2000 London ...................... 709/238
`6,134,532 A • 10/2000 Lazarus et a!. ............... 705/14
`2/2002 Broder et a! ................... 707/3
`6,349,296 B1 •
`6,603,470 B1 * 8/2003 Deering ...................... 345/419
`
`OTHER PUBLICATIONS
`
`Moses Sampspn Charikar, "Algorithms for Clustering Problems",
`2001, Stanford University, vol. 62/01-B of Dissertation Abstracts
`International. •
`
`SRC Technical Note; 1997-015; Jul. 25, 1997; "Syntactic Clustering
`of the Web"; Andrei Z. Broder eta!.; pp. 1·14; Digital Equipment
`Corporation
`http://gatekeeper.dec.com/pubiDEC/SRCitechnical(cid:173)
`notesiSRC-1997 -0 15-html/.
`"Similarity Search in High Dimensions via Hashing"; Aristides
`Gionis et al.; Department of Computer Science; Stanford Univer-
`sit}i;pp.518:529iT999:---~~~- ····
`~ -----
`~ ~ -~- - --
`
`"Approximate Nearest Neighbors: Towards Removing the Curse of
`Dimensionality (preliminary version)"; Piotr Indyk et al.; Depart(cid:173)
`ment of Computer Science; Stanford University; Jul. 21, 1999; pp.
`1·13 and i-vii.
`"Chapter 26-Improved approximation algorithms for network
`design problems"; M.X. Goemans et al.; pp. 223-232.
`"Approximation Algorithms for Classification Problems with
`Pairwise Relationships: Metric Labeling and Markov Random
`Fields"; Jon Kleinberg et al.
`"Scalable Techniques for Clustering the Web"; Taher H. Haveliwala
`et al.
`"Efficient Search for Approximate Nearest Neighbor in High
`Dimensional Spaces"; Eyal Kushilevitz eta!.; pp. 1-17.
`"On the resemblance and containment of documents"; Andrei Z.
`Broder; Digital Systems Research Center, Palo Alto, CA; pp. 1-9.
`* cited by examiner
`Primary Examiner-Greta Robinson
`Assistant Examiner-Harold E. Dodd, Jr.
`(74) Attorney, Agent, or Firm-Hartity Snyder LLP
`
`(57)
`
`ABSTRACT
`
`A similarity engine generates compact representations of
`objects called sketches. Sketches of different objects can be
`compared to determine the similarity between the two
`objects. The sketch for an object may be generated by
`creating a vector corresponding to the object, where each
`coordinate of the vector is associated with a corresponding
`weight. The weight associated with each coordinate in the
`vector is multiplied by a predetermined hashing vector to
`generate a product vector, and the product vectors are
`summed. The similarity engine may then generate a compact
`representation of the object based on the su=ed product
`vector.
`
`24 Claims, 4 Drawing Sheets
`
`EXHIBIT 2106
`Facebook, Inc. et al.
`v.
`Software Rights Archive, LLC
`CASE IPR2013-00479
`
`

`

`U.S. Patent
`
`Jan.2,2007
`
`Sheet 1 of 4
`
`US 7,158,961 B1
`
`102
`
`NETWORK
`
`110
`r _______ MEMORY ____ .1.1!S
`120
`122
`124 r
`1
`I
`I
`~
`E
`a>
`·g
`~
`-~
`I
`I
`e
`I
`I
`~
`w
`:E'
`I
`I
`a.
`..c
`-&
`~
`I
`I
`m
`~
`~
`:~
`I
`I
`I
`I
`~-------f _______ J
`I
`I
`
`(f)
`
`111
`
`Fig. 1
`
`-
`PROCESSOR
`
`

`

`U.S. Patent
`
`Jan.2,2007
`
`Sheet 2 of 4
`
`US 7,158,961 B1
`
`Create vector
`representation of input
`object.
`
`201
`
`202
`
`Multply each coordinate in
`created vector by a
`predetermined hashing
`vector.
`
`203
`
`Sum the resulting products
`obtained in Act 202 to
`obtain result vector.
`
`204
`
`205
`
`Convert each coordinate in
`result vector to a single bit
`based on the sign of the
`coordinate's value.
`
`Concatenate the obtained
`bits to obtain similarity
`sketch.
`
`Fig. 2
`
`

`

`U.S. Patent
`
`Jan.2,2007
`
`Sheet 3 of 4
`
`US 7,158,961 B1
`
`301
`JL
`
`302
`JJf
`
`coordinate value
`1
`four
`1
`score
`and
`1
`seven
`1
`years
`1
`ago
`1
`
`Fig. 3A
`
`coordinate value
`four
`0.3
`0.4
`score
`and
`0.05
`seven
`0.3
`years
`0.4
`ago
`0.2
`
`Fig. 38
`
`

`

`U.S. Patent
`
`Jan.2,2007
`
`Sheet 4 of 4
`
`US 7,158,961 B1
`
`r - - - - - - - - - - - - - - - - - - - - - - - -
`401
`rJ
`Coordinate Value
`
`four 0.3
`score 0.4
`
`Hashing Vectors
`(-4, 2, 6)
`...-"\...402
`
`(8, -9, -4)
`
`...-"\...403
`
`404
`
`"'
`
`Result Vector= ( -4 x 0.3, 2 x 0.3, 6 x 0.3)
`+
`(8 X 0.4, -9 X 0.4, -4 X 0.4)
`= (2.0, 3.0, 0.2)
`
`405 "'
`Similarity Sketch = 111
`-------------------------'
`
`Fig. 4
`
`

`

`US 7,158,961 B1
`
`1
`METHODS AND APPARATUS FOR
`ESTIMATING SIMILARITY
`
`BACKGROUND OF THE INVENTION
`
`A. Field of the Invention
`The present invention relates generally to similarity esti(cid:173)
`mation, and more particularly, to calculating similarity met(cid:173)
`rics for objects such as web pages.
`B. Description of Related Art
`The World Wide Web ("web") contains a vast amount of
`information. Locating a desired portion of the information,
`however, can be challenging. Search engines catalog web
`pages to assist web users in locating the information they
`desire. Typically, in response to a user's request, the search 15
`engine returns references to documents relevant to the
`request.
`From the search engine's perspective, one problem in
`cataloging the large number of available web pages is that
`multiple ones of the web documents are often identical or 20
`nearly identical. Separately cataloging similar documents is
`inefficient and can be frustrating for the user if, in response
`to a request, a list of nearly identical documents is returned.
`Accordingly, it is desirable for the search engine to identify
`documents that are similar or "roughly the same" so that this 25
`type of redundancy in search results can be avoided.
`In addition to improving web search results, the identifi(cid:173)
`cation of similar documents can be beneficial in other areas.
`For example, storage space may be reduced by storing only 30
`one version of a set of similar documents. Or, a collection of
`documents can be grouped together based on document
`similarities, thereby improving efficiency when compressing
`the collection of documents.
`One conventional technique for determining similarity is
`based on the concept of sets. A document, for example, may
`be represented as a sub-set of words from a corpus of
`possible words. The similarity, or resemblance of two docu(cid:173)
`ments to one another is then defined as the intersection of the
`two sets divided by the union of the two sets. One problem
`with this set-based similarity measure is that there is limited
`flexibility in weighting the importance of the elements
`within a set. A word is either in a set or it is not in a set. In
`practice, however, it may be desirable to weight certain
`words, such as words that occur relatively infrequently in the 45
`corpus, more heavily when determining the similarity of
`documents.
`Accordingly, there is a need in the art for improved
`techniques for determining similarity between documents.
`
`10
`
`2
`A second method consistent with the present invention
`includes creating a similarity sketch for each of first and
`second objects based on the application of a hashing func(cid:173)
`tion to a vector representation of the first and second objects.
`Additionally, the method compares, on a bit-by-bit basis, the
`similarity sketches for the first and second objects, and
`generates a value defining the similarity between the first
`and second objects based on a correspondence in the bit(cid:173)
`by-bit comparison.
`Another aspect of the present invention is directed to a
`server that includes at least one processor, a database con(cid:173)
`taining a group of objects, and a memory operatively
`coupled to the processor. The memory stores program
`instructions that when executed by the processor, cause the
`processor to remove similar objects from the database by
`comparing similarity sketches of pairs of objects in the
`database and removing one of the objects of the pair when
`the comparison indicates that the pair of objects are more
`similar than a threshold level of similarity. The processor
`generates the similarity sketches for each of the pair of
`objects based on an application of a hashing function to
`vector representations of the objects.
`Yet another aspect of the invention is directed to a method
`for generating a compact representation of a first object. The
`method includes identifYing a set of features corresponding
`to the object and generating, for each feature, a hashing
`vector having n coordinates. The hashing vectors are
`sUllillled to obtain a sUllillled vector, and an n*x-bit repre(cid:173)
`sentation of the sUllillled vector is obtained by calculating an
`x-bit value for each coordinate of the summed vector.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`35
`
`The accompanying drawings, which are incorporated in
`and constitute a part of this specification, illustrate an
`embodiment of the invention and, together with the descrip(cid:173)
`tion, explain the invention. In the drawings,
`FIG. 1 is a diagram illustrating an exemplary system in
`40 which concepts consistent with the present invention may be
`implemented;
`FIG. 2 is a flow chart illustrating methods consistent with
`principles of the present invention for generating similarity
`sketches;
`FIGS. 3A and 3B illustrate exemplary object vectors; and
`FIG. 4 is a diagram conceptually illustrating the calcula(cid:173)
`tion of a result vector for an exemplary object vector based
`on two corresponding hashing vectors.
`
`SUMMARY OF THE INVENTION
`
`50
`
`DETAILED DESCRIPTION
`
`Systems and methods consistent with the present inven(cid:173)
`tion address this and other needs by providing a similarity
`engine that generates compact representations of objects that
`can be compared to determine similarity between the
`objects.
`In one aspect, the present invention is a method for
`generating a compact representation of an object. The
`method includes generating a vector corresponding to the
`object, each coordinate of the vector being associated with
`a corresponding weight and multiplying the weight associ(cid:173)
`ated with each coordinate in the vector by a corresponding
`hashing vector to generate a product vector. The method
`further includes summing the product vectors and generating
`the compact representation of the object using the summed
`product vectors.
`
`55
`
`The following detailed description of the invention refers
`to the accompanying drawings. The detailed description
`does not limit the invention. Instead, the scope of the
`invention is defined by the appended claims and equivalents.
`As described herein, a similarity engine generates com(cid:173)
`pact representations, called similarity sketches, for object
`vectors. The object vectors can be created for objects, such
`60 as document files. The similarity sketch for two different
`object vectors can be quickly and easily compared to gen(cid:173)
`erate an indication of the similarity between the two objects.
`FIG. 1 is a diagram illustrating an exemplary system in
`which concepts consistent with the present invention may be
`implemented. The system includes multiple client devices
`102, a server device 110, and a network 101, which may be,
`for example, the Internet. Client devices 102 each include a
`
`65
`
`

`

`US 7,158,961 B1
`
`25
`
`3
`computer-readable medium 109, such as random access
`memory, coupled to a processor 108. Processor 108 executes
`program instructions stored in memory 109. Client devices
`102 may also include a number of additional external or
`internal devices, such as, without limitation, a mouse, a
`CD-ROM, a keyboard, and a display.
`Tbrough client devices 102, users 105 can communicate
`over network 101 with each other and with other systems
`and devices coupled to network 101, such as server device
`110.
`Similar to client devices 102, server device 110 may
`include a processor 111 coupled to a computer readable
`memory 112. Server device 110 may additionally include a
`secondary storage element, such as database 130.
`Client processors 108 and server processor 111 can be any 15
`of a number of well known computer processors, such as
`processors from Intel Corporation, of Santa Clara, Calif. In
`general, client device 102 may be any type of computing
`platform connected to a network and that interacts with
`application programs, such as a digital assistant or a "smart" 20
`cellular telephone or pager. Server 110, although depicted as
`a single computer system, may be implemented as a network
`of computer processors.
`Memory 112 may contain a number of programs, such as
`search engine program 120, spider program 122, and simi(cid:173)
`larity engine 124. Search engine program 120 locates rel(cid:173)
`evant information in response to search queries from users
`105. In particular, users 105 send search queries to server
`device 110, which responds by returning a list of relevant
`information to the user 105. Typically, users 105 ask server
`device 110 to locate web pages relating to a particular topic
`and stored at other devices or systems connected to network
`101. The general implementation of search engines is well
`known in the art and therefore will not be described further
`herein.
`Search engine program 120 may access database 130 to
`obtain results from a document corpus 135, stored in data(cid:173)
`base 130, by comparing the terms in the user's search query
`to the documents in the corpus. The information in docu- 40
`ment corpus 135 may be gathered by spider program 122,
`which "crawls" web documents on network 101 based on
`their hyperlinks.
`In one embodiment consistent with the principles of the
`present invention, memory 112 additionally includes simi(cid:173)
`larity engine 124. Similarity engine 124 generates similarity
`information between documents in document corpus 135.
`More particularly, similarity engine 124 may generate a
`relatively small "sketch" (e.g., a 64 bit value) for each
`document in corpus 135 and may compare the sketches
`between pairs of documents. If two documents, based on
`their sketches, are more similar than a predefined similarity
`threshold, similarity generator 124 may, for example,
`remove one of the two documents from document corpus
`135. In this manner, search engine program 120 is less likely
`to return redundant or overly similar results in response to
`user queries. Alternately, instead of removing documents
`from the corpus based on the similarity sketches, similarity
`generator 124 may remove duplicate documents "on the fly."
`In other words, search engine program 120 may generate a 60
`set of documents in response to a user query and similarity
`generator 124 may cull the generated set of documents based
`on similarity sketches.
`FIG. 2 is a flow chart illustrating methods consistent with
`principles of the present invention for generating similarity
`sketches for objects by similarity engine 124. In general,
`similarity engine 124 processes objects, such as web docu-
`
`4
`ments, to generate the sketches. Sketches of different objects
`can be compared to generate a quantitative metric of the
`similarity of the objects.
`To begin, similarity engine 124 creates a vector represen(cid:173)
`tation of the input object. (Act 201). The input object may
`be a document such as a web page. More generally, the
`object can be any item that contains a series of discrete
`elements, and the representation of the input object can be
`10 a set of associated features rather than a vector per se. The
`vector coordinates are indexed by the elements of the object.
`In the case of documents, for example, the elements may be
`the words in the document.
`FIG. 3A illustrates an example of a vector 301 for the
`object phrase "four score and seven years ago." The vector
`for this phrase contains six non-zero coordinates corre(cid:173)
`sponding to the six words in the phrase. Conceptually, the
`vector can be thought of as containing as many coordinates
`as there are elements in the universe of elements (e.g., the
`number of unique words in the corpus), with each coordinate
`other than those in the phrase having a value of zero.
`In FIG. 3A, each non-zero coordinate is given an equal
`vector weight (i.e., it has the value one). More generally,
`however, different elements can be given different weights.
`This is illustrated in FIG. 3B, in which words that are
`considered "more important" are more heavily weighted in
`object vector 302. For example, "years" and "score,"
`because they are less common words, may be given a higher
`weighting value, while "and" is given a low weight. In this
`manner, the object vector can emphasize certain elements in
`the similarity calculation while de-emphasizing others. In
`the implementation of FIG. 3B, valid values are in the range
`between zero and one.
`The weights for an element can be calculated using any
`number of possible weighting formulas. In one implemen(cid:173)
`tation, for vectors associated with documents, the weight for
`a word is set as the number of occurrences of the word
`within the document divided by the number of documents in
`the corpus containing the word.
`After constructing the object vector 301 or 302 for the
`45 object, similarity engine 124 multiplies every coordinate in
`the object vector by a corresponding predetermined hashing
`vector having a preset number of coordinates (dimensions),
`where each coordinate in the hashing vector corresponds to
`a number, such as a random number, provided that the same
`50 input object vector coordinate yields the same hashing
`vector coordinate. (Act 202). A different hashing vector may
`be used for each possible coordinate (e.g., word). The
`number of preset coordinates in the hashing vector corre(cid:173)
`sponds to the size of the resulting sketch. For example, to
`55 produce a 64-bit sketch for each object, a 64-dimensional
`hashing vector would be chosen.
`For a particular input vector coordinate, the correspond(cid:173)
`ing hashing vector could be generated from a pseudo ran(cid:173)
`dom number generator seeded based on the input vector
`coordinate (ignoring the actual value of the input vector
`coordinate). The values of the coordinates of the hashing
`vector could be selected based on the output of the pseudo
`random number generator so that the values are random
`65 numbers drawn from a chosen distribution. For example,
`coordinates could be drawn from the normal distribution
`with probability density function
`
`30
`
`35
`
`

`

`US 7,158,961 B1
`
`5
`
`Another possibility is to choose coordinates to be either + 1
`or -1 with equal probability. A hash function could be used
`to map input vector coordinates to hashing vectors directly.
`For example, a 64-bit hash value obtained from a hash
`function could be mapped to a 64-dimensional hashing
`vector by choosing the i'h coordinate of the hashing vector
`to be + 1 or -1 based on whether the i'h bit in the hash value
`is 1 or 0.
`The product vectors generated in Act 202 are summed for
`all elements in the object to generate a result vector having
`the same number of coordinates as each of the predeter(cid:173)
`mined hashing vectors. (Act 203).
`Stated more formally, the operations performed in Acts
`202-203 generate the result vector based on a hashing
`function defined as,
`
`6
`of the three coordinates in result vector 404. As shown,
`because each of the three coordinate values is positive, the
`similarity sketch is "111."
`The values of the coordinates in hashing vectors 402 and
`403 can be chosen at random. For a large corpus (e.g., a
`million possible words) and a larger similarity sketch (e.g.,
`128 bits), such a large number of hashing vectors (i.e., one
`million), each made up of 128 random values, can be
`burdensome to store and subsequently access. Accordingly,
`10 the random numbers for each hash vector could be dynami(cid:173)
`cally generated using a pseudo random number generator
`seeded with a value based on the hash vector's coordinate.
`Furthermore, if it is determined that two coordinates in the
`object vector are "similar", it may be desirable to make the
`15 hashing vectors similar for these two object vector coordi(cid:173)
`nates. In this mauner, one may incorporate information
`about the similarity of object vector coordinates into their
`associated hashing vectors.
`Although the above description of similarity engine 124
`20 generally describes a similarity engine operating in the
`context of web documents, the concepts described could
`also be implemented based on any object that contains a
`series of discrete elements.
`As mentioned, similarity sketches generated by similarity
`25 engine 124 may be used to refine the entries in database 130
`to reduce the occurrence of redundant or nearly redundant
`documents returned in response to a user's search query. The
`similarity sketches can be used in a number of other appli(cid:173)
`cations. For example, spider program 122, when crawling
`30 web sites, may use similarity engine 124 to determine sites
`that are substantial duplicates of one another. Mirror sites are
`one example of duplicate sites that occur frequently on the
`web. In future crawls, spider program 122 may more effi(cid:173)
`ciently crawl the web by avoiding crawling the sites that are
`35 determined to be substantial duplicates.
`As another example of the application of similarity engine
`124, similarity engine 124 may generate object vectors for
`a web document based on the list of hyperlinks in the
`document. Accordingly, similarity engine 124 may develop
`similarity sketches based on a document's list of links.
`As yet another example of the application of similarity
`engine 124, the similarity engine may operate on "snippets"
`of text associated with documents returned from a search
`query. A snippet is an abstraction of the document that is
`initially returned to a user in response to a search query.
`Based on the snippets, users select full documents to view.
`Similarity engine 124 may compare snippets from a search
`query and exclude those snippets and/or search results that
`exceed a similarity threshold.
`As yet another example of the application of similarity
`engine 124, similarity engine 124 may quantitatively deter(cid:173)
`mine the similarity between two words or phrases based on
`the context surrounding those words or phrases from the
`document corpus. More specifically, similarity engine 124
`may create an object vector for a word, such as "shop",
`based on the words within a certain distance (e.g., 10 words)
`of each occurrence of shop in the corpus. The coordinates of
`this object vector would be all the words in the corpus. The
`60 value for the coordinates may be, for example, the number
`of times the coordinate word occurs within the context
`distance. If, for example, the word "cart" occurs frequently
`in the document corpus within the selected context distance
`to the word "shop," then the value for "cart" would be
`65 relatively high in the object vector. Two different words with
`close similarity sketches, as determined by similarity engine
`124, are likely to be used as synonyms in the corpus.
`
`---;.
`
`where R is the result vector, c 1 is the weight value for the
`i'h coordinate (a scalar), --:;, is the predetermined hashing
`vector for the i'h coordinate in the object vector, and the sum
`is taken over all the possible coordinates in the object vector.
`The result vector can be used as the similarity sketch for
`the object. Optionally, the result vector may be further
`simplified to obtain the similarity sketch by generating, for
`each coordinate in the resultant vector, a single bit corre(cid:173)
`sponding to the sign of the coordinate's value. (Act 204).
`The generated bits are then concatenated together to form
`the object's sketch. (Act 205). In the above example, for a 40
`64-coordinate hashing vector, and thus, a 64-coordinate
`result vector, the similarity sketch would be a 64-bit value.
`When comparing the similarity sketches for two objects
`generated by Act 205, similarity generator 124 may create a
`similarity value based on a bit-by-bit comparison of the 45
`sketches. In one implementation, a final similarity measure
`between two sketches can be obtained by logically exclu(cid:173)
`sive-ORing (XOR) the two sketch values and summing the
`complements of the individual result bits to yield a value
`between zero (not similar) and 64 (very similar) for a 64-bit 50
`similarity sketch. If the similarity measure is above a pre(cid:173)
`determined threshold (e.g., greater than 50), the two objects
`may be considered to be similar to one another.
`FIG. 4 is a diagram conceptually illustrating the calcula(cid:173)
`tion of a result vector for an exemplary object vector 401 and 55
`two corresponding hashing vectors 402 and 403. In practice,
`object vectors are likely to be significantly more complex
`than object vector 401 and the hashing vectors are likely to
`contain more than the three coordinates illustrated in hash(cid:173)
`ing vectors 402 and 403.
`Object vector 401 contains two non-zero elements, "four"
`and "score," each associated with a weight value. Hashing
`vectors 402 and 403 each have three coordinates, which will
`thus yield a three-bit similarity sketch. Result vector 404 is
`the sum of hashing vectors 402 and 403 after being multi(cid:173)
`plied by the value of the corresponding coordinate in object
`vector 401. Similarity sketch 405 is derived from the signs
`
`

`

`US 7,158,961 B1
`
`7
`Similarity engine 124 may also be used outside of the
`context of web search engines. For example, a collection of
`objects may be grouped based on their similarity. Grouping
`objects in this manner may be used to gain increased
`compression ratios for the objects or to increase access
`speed from a storage medium.
`The similarity sketches described above have a number of
`advantages. Because the similarity sketches are based on
`vector representations, different elements of the vectors can
`be given different weights, thus allowing vector elements to 10
`be more or less important than one another. In contrast, in
`conventional set-based similarity techniques, elements are
`simply either in a set or not in the set. Additionally, the
`sketches generated above are relatively compact compared
`to similarity measures generated with the conventional set- 15
`based techniques.
`The foregoing description of preferred embodiments of
`the present invention provides illustration and description,
`but is not intended to be exhaustive or to limit the invention
`to the precise form disclosed. Modifications and variations 20
`are possible in light of the above teachings or may be
`acquired from practice of the invention. For example,
`although the preceding description generally discussed the
`operation of search engine 120 in the context of a search of
`documents on the world wide web, search engine 120 and
`similarity engine 124 could be implemented on any corpus.
`Moreover, while a series of acts have been presented with
`respect to FIG. 2, the order of the acts may be different in
`other implementations consistent with the present invention.
`No element, act, or instruction used in the description of 30
`the present application should be construed as critical or
`essential to the invention unless explicitly described as such.
`Also, as used herein, the article "a" is intended to include
`one or more items. Where only one item is intended, the term
`"one" or similar language is used.
`The scope of the invention is defined by the claims and
`their equivalents.
`What is claimed is:
`1. A computer-implemented method for generating a
`compact representation of a first object, comprising:
`(a) identifying a set of features corresponding to the first
`object;
`(b) generating for each feature a hashing vector having n
`coordinates;
`(c) snnnning the hashing vectors to obtain a summed 45
`vector; and
`(d) creating an n·x-bit representation of the summed
`vector by calculating an x-bit value for each coordinate
`of the snnnned vector, the n·x-bit representation of the
`summed vector defining the compact representation of 50
`the first object.
`2. The computer-implemented method of claim 1,
`wherein the set of features is a vector.
`3. The computer-implemented method of claim 1,
`wherein generating for each feature a hashing vector com- 55
`prises:
`determining a weight associated with each feature; and
`multiplying each hashing vector by the weight determined
`for the corresponding feature.
`4. The computer-implemented method of claim 1, 60
`wherein the object is a document.
`5. The computer-implemented method of claim 4,
`wherein each feature is a word within the document.
`6. The computer-implemented method of claim 1,
`wherein the object is a summary of another object.
`7. The computer-implemented method of claim 1,
`wherein x is equal to 1.
`
`8
`8. The computer-implemented method of claim 1,
`wherein n is equal to 64.
`9. The computer-implemented method of claim 1, further
`comprising:
`repeating acts (a)-(d) for a second object to create a
`second n·x-bit representation; and
`comparing the first and second n·x-bit representations to
`determine whether the first and second objects are
`similar.
`10. The computer-implemented method of claim 9, fur(cid:173)
`ther comprising discarding either one of the first or second
`objects.
`11. The computer-implemented method of claim 1, further
`comprising:
`repeating acts (a)-(d) form objects to create m n·x-bit
`representations; and
`grouping the m objects based on their corresponding
`n·x-bit representations.
`12. The computer-implemented method of claim 11, fur(cid:173)
`ther comprising compressing the objects by group.
`13. The computer-implemented method of claim 1,
`wherein act (b) comprises generating for each feature a
`hashing vector having n coordinates, such that the hashing
`25 vectors are similar for similar features.
`14. A computer-implemented method for generating a
`compact representation of an object, comprising:
`generating a vector corresponding to the object, each
`coordinate of the vector being associated with a corre(cid:173)
`sponding weight;
`multiplying the weight associated with each coordinate in
`the vector by a corresponding hashing vector to gen(cid:173)
`erate a product vector;
`summing the product vectors to obtain a summed product
`vector; and
`generating a compact representation of the object using
`the snnnned product vectors.
`15. The computer-implemented method of claim 14,
`40 wherein the weights are real numbers.
`16. The computer-implemented method of claim 15,
`wherein the weights include values between zero and one.
`17. The computer-implemented method of claim 14,
`wherein the object is a web document.
`18. The computer-implemented method of claim 17,
`wherein the coordinates in the vector correspond to words in
`the web document.
`19. The computer-implemented method of claim 18, fur(cid:173)
`ther comprising:
`assigning the weights for each coordinate of the vector as
`the number of occurrences of the word within the web
`document divided by the number of web documents
`contained in a collection of web documents that contain
`the word.
`20. The computer-implemented method of claim 14,
`wherein values in the hashing vectors are generated using a
`pseudo random number generator seeded based on the
`coordinate corresponding to the hashing vector.
`21. The computer-implemented method of claim 14,
`wherein each bit is generated based on the sign of the value
`of the coordinate.
`22. A system for generating a compact representation of
`an object, comprising:
`means for generating a vector corresponding to the object,
`each coordinate of the vector being associated with a
`corresponding weight;
`
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`65
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`US 7,158,961 B1
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`9
`means for multiplying the weight associated with eac