Part-of-speech tagging using latent analogy
First Claim
1. A method, comprising:
- analyzing a corpus having first training sequences of words in a semantic vector space;
extracting a global semantic information associated with an input sequence of words from the semantic vector space;
selecting second training sequences of words having part-of-speech tags in the semantic vector space based on the global semantic information and the first training sequences; and
assigning a part-of-speech tag to at least one word of the input sequence based on the part-of-speech tags of the second training sequences, wherein at least one of the analyzing, extracting, selecting, and assigning is performed by a processor.
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Abstract
Methods and apparatuses to assign part-of-speech tags to words are described. An input sequence of words is received. A global fabric of a corpus having training sequences of words may be analyzed in a vector space. A global semantic information associated with the input sequence of words may be extracted based on the analyzing. A part-of-speech tag may be assigned to a word of the input sequence based on POS tags from pertinent words in relevant training sequences identified using the global semantic information. The input sequence may be mapped into a vector space. A neighborhood associated with the input sequence may be formed in the vector space wherein the neighborhood represents one or more training sequences that are globally relevant to the input sequence.
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26 Claims
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1. A method, comprising:
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analyzing a corpus having first training sequences of words in a semantic vector space;
extracting a global semantic information associated with an input sequence of words from the semantic vector space;selecting second training sequences of words having part-of-speech tags in the semantic vector space based on the global semantic information and the first training sequences; and assigning a part-of-speech tag to at least one word of the input sequence based on the part-of-speech tags of the second training sequences, wherein at least one of the analyzing, extracting, selecting, and assigning is performed by a processor. - View Dependent Claims (2, 3, 4, 5)
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6. A method to assign part-of-speech tags to words, comprising:
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receiving an input sequence of words; mapping the input sequence into a semantic vector space, wherein the semantic vector space includes representations of a first plurality of training sequences of words; and forming a neighborhood associated with the input sequence in the semantic vector space to obtain a part-of-speech tag for at least one word of the input sequence, wherein the neighborhood represents one or more second training sequences having part-of-speech tags selected from the first plurality of training sequences that are globally semantically relevant to the input sequence in the semantic vector space wherein at least one of the receiving, mapping, and forming is performed by a processor. - View Dependent Claims (7, 8, 9, 10, 11, 12)
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13. An article of manufacture comprising:
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a non-transitory machine-accessible medium including data that, when accessed by a machine, cause the machine to perform operations comprising, analyzing a corpus having first training sequences of words in a semantic vector space; extracting a global semantic information associated with an input sequence of words from the semantic vector space; selecting second training sequences of words having part-of-speech tags in the semantic vector space based on the global semantic information and the first training sequences; and assigning a part-of-speech tag to to at least one word of the input sequence based on the part-of-speech tags of the second training sequences. - View Dependent Claims (14, 15, 16, 17)
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18. An article of manufacture comprising:
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a non-transitory machine-accessible medium including data that, when accessed by a machine, cause the machine to perform operations to assign part-of-speech tags to words, comprising; receiving an input sequence of words; mapping the input sequence into a semantic vector space, wherein the semantic vector space includes representations of a first plurality of training sequences of words; and forming a neighborhood associated with the input sequence in the semantic vector space to obtain part-of-speech tag for at least one word of the input sequence, wherein the neighborhood represents one or more second training sequences having part-of-speech tags selected from the first plurality of training sequences that are globally semantically relevant to the input sequence in the semantic vector space. - View Dependent Claims (19, 20, 21, 22, 23, 24)
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25. A data processing system, comprising:
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means for analyzing a corpus having first having training sequences of words in a semantic vector space; means for extracting a global semantic information associated with an input sequence of words from the semantic vector space; means for identifying selecting second training sequences of words having part-of-speech tags in the semantic vector space based on the global semantic information and the first training sequences; and means for assigning a part-of-speech tag to a-at least one word of the input sequence based on the part-of-speech tags of the second training sequences.
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26. A data processing system, comprising:
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means for receiving an input sequence of words; means for mapping the input sequence into a semantic vector space, wherein the semantic vector space includes representations of a first plurality of training sequences of words; and means for forming a neighborhood associated with the input sequence in the semantic vector space to obtain a part-of-speech tag for at least one word of the input sequence, wherein the neighborhood represents one or more second training sequences having part-of-speech tags selected from the first plurality of training sequences that are globally semantically relevant to the input sequence in the semantic vector space.
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1 Specification
A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. Copyright ©2007, Apple Inc., All Rights Reserved.
The present invention relates generally to language processing. More particularly, this invention relates to automatic discovery of the syntactic structure in language.
Part-of-speech (“POS”) tagging is used in many natural language processing (“NLP”) tasks. As POS tags augment the information contained within words by indicating some of the structure inherent in language, their accuracy is often critical to NLP applications. In text-to-speech (TTS) synthesis POS information is often relied upon to determine how to pronounce a word properly. A word may be pronounced differently depending on a part of speech and/or a tense. For example, a word “read” may be pronounced differently depending on a tense. A word “advocate” may be pronounced differently depending on whether the word “advocate” is a noun or verb.
POS tags may help to decide whether the synthesized word should be accented or not. For example, a noun may be accented more than a verb. Accordingly, POS tags may greatly influence how natural synthetic speech sounds. Typically, a POS tag is assigned to a word based on the local information contained in a text. For example, to assign a POS tag to a word in the text, adjacent words are typically considered.
Conceptually, the POS tags may be assigned to words in a text according to predetermined rules. For example, if a determiner, such as “the” or “a”, precedes a word in the text, than the word may be assigned an adjective or a noun tag. In another example, if word “to” precedes a word in the text, than the word may be assigned a verb tag.
In the past, numerous rules were manually generated for the POS tagging. An answer to one rule, however, may conflict with the answer to another rule. Accordingly, the POS tagging may strongly depend on how the rules are ordered. Accordingly, the accuracy of the POS tagging by rules may be poor.
Current methods of POS tagging involve sophisticated statistical models, such as maximum entropy Markov models (“MEMMs”) and conditional random fields (“CRFs”). Both types of modeling rely on a set of feature functions to ensure that important characteristics of the empirical training distribution are reflected in the trained model. These types of modeling, however, may suffer directly or indirectly from the so-called “label bias problem”, whereby certain characteristics are unduly favored over other characteristics.
Hence, the tagging accuracy of both MEMMs and CRFs may depend on how many feature functions are selected and how relevant they are to the task at hand. Such selection may require application-specific linguistic knowledge, complicating deployment across different applications. Moreover, it is basically impossible to specify a set of feature functions that will work well in every environment. For example, a set of feature functions that is selected for the POS tagging of the text from the Wall Street Journal may not be appropriate for the POS tagging of the text from the Word Book Encyclopedia, or from a web blog. Typically, the accuracy of both MEMMs and CRFs may increase as the number of feature functions increases. Increasing the number of feature functions to assign POS tags to words in the text dramatically increases the processing time and/or work load on the processing resources and may be very expensive.
Methods and apparatuses to assign part-of-speech tags to words are described. An input sequence of words, for example, a sentence, is received. A global fabric of a training corpus containing training sequences of words is analyzed in a vector space. The vector space may include a latent semantic (“LS”) space. Global semantic information associated with the input sequence of words is extracted based on the analyzing. A part-of-speech (“POS”) tag is assigned to a word of the input sequence based on POS tags from words in training sequences that are identified using the global semantic information. In one embodiment, analyzing of the global fabric of the training corpus is performed using a latent semantic mapping. In one embodiment, the global semantic information is used to identify which training sequences from the training corpus are globally relevant. In one embodiment, the characteristics of the words of the identified training sequences that are globally relevant to the input sequence are obtained. In one embodiment, the characteristics of the words of the training sequences that are globally relevant to the input sequence include part-of-speech characteristics.
In one embodiment, an input sequence of words is mapped into a vector space. The vector space may include representations of a plurality of training sequences of words. A neighborhood associated with the input sequence may be formed in the vector space. The neighborhood may represent one or more training sequences of the corpus that are globally relevant to the input sequence. A part-of-speech tag to assign to a word of the input sequence may be determined based on characteristics of the words of the training sequences from the neighborhood.
In one embodiment, an input sequence is mapped into a vector space, for example, a LS space. The vector space may include representations of a plurality of training sequences of words. A closeness measure between each of the training sequences and the input sequence may be determined in the vector space. One or more training sequences may be selected out of the plurality of the training sequences based on the closeness measure, to form the neighborhood of the input sequence in the vector space. The neighborhood may represent one or more training sequences of a training corpus that are globally relevant to the input sequence. A part-of-speech tag to assign to the word of the input sequence may be determined based on one or more part-of-speech characteristics of words from the training sequences represented in the neighborhood.
In one embodiment, an input sequence is mapped into a vector space, for example, a LS space. The vector space may include representations of a plurality of training sequences of words. A neighborhood of the input sequence in the vector space is formed. The neighborhood of the input sequence in the vector space may contain representations of the training sequences that are globally relevant to the input sentence. In one embodiment, determination is made whether a training sequence in the neighborhood contains a word that is similar to an input word of the input sequence. One or more sub-sequences of the training sequence that contain one or more words that are similar to the input words of the input sequence are determined. The one or more sub-sequences that contain the words that are similar to the input words may be aligned to obtain one or more part-of-speech characteristics. One or more part-of-speech tags to assign to one or more words of the input sequence may be determined based on the one or more part-of-speech characteristics.
Other features will be apparent from the accompanying drawings and from the detailed description which follows.
The present invention is illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar elements.
The subject invention will be described with references to numerous details set forth below, and the accompanying drawings will illustrate the invention. The following description and drawings are illustrative of the invention and are not to be construed as limiting the invention. Numerous specific details are described to provide a thorough understanding of the present invention. However, in certain instances, well known or conventional details are not described in order to not unnecessarily obscure the present invention in detail.
Reference throughout the specification to “one embodiment”, “another embodiment”, or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
Methods and apparatuses to assign part-of-speech (“POS”) tags to words using a latent analogy and a system having a computer readable medium containing executable program code to assign part-of-speech tags to words using a latent analogy are described below. Other methods and other features are also described. A machine-readable medium may include any mechanism for storing information in a form readable by a machine (e.g., a computer). For example, a machine-readable medium includes read only memory (“ROM”); random access memory (“RAM”); magnetic disk storage media; optical storage media; and flash memory devices.
As shown in
It will be appreciated that data processing system 113 is one example of many possible data processing systems which have different architectures. For example, personal computers based on an Intel microprocessor often have multiple buses, one of which can be an input/output (I/O) bus for the peripherals and one that directly connects the processing unit 101 and the memory 102 (often referred to as a memory bus). The buses are connected together through bridge components that perform any necessary translation due to differing bus protocols.
Network computers are another type of data processing system that can be used with the embodiments of the present invention. Network computers do not usually include a hard disk or other mass storage, and the executable programs are loaded from a network connection into the memory 102 for execution by the processing unit 101. A Web TV system, which is known in the art, is also considered to be a data processing system according to the embodiments of the present invention, but it may lack some of the features shown in
It will also be appreciated that the data processing system 113 is controlled by operating system software which includes a file management system, such as a disk operating system, which is part of the operating system software. One example of operating system software is the family of operating systems known as Macintosh® Operating System (Mac OS®) or Mac OS X® from Apple Inc. of Cupertino, Calif. Another example of operating system software is the family of operating systems known as Windows® from Microsoft Corporation of Redmond, Wash., and their associated file management systems. The file management system is typically stored in the non-volatile storage 107 and causes the processing unit 101 to execute the various acts required by the operating system to input and output data and to store data in memory, including storing files on the non-volatile storage 107.
As shown in
As shown in
Given a natural language sentence comprising z words, POS tagging aims at annotating each observed word wi with some suitable part-of-speech pi, (each typically associated with a particular state si, 1≦i≦z). Representing the overall sequence of words by W and the corresponding sequence of POS by P, typical statistical models try to maximize the conditional probability Pr (P/W) over all possible POS sequences P.
Maximum entropy models such as MEMMs and CRFs approach this problem by considering state-observation transition distributions expressed as log-linear models of the form:
which represent the probability of moving from state si to state si+1 conditioned upon observation wi. In expression (1), fk(Ci, wi) is a feature function of the current observation and any entity belonging to the appropriate clique Ci of the underlying undirected graph, λk is a parameter to be estimated, and Z(S, W) is a normalization factor. Each feature function expresses some characteristic of the empirical training distribution, which is deemed important to require of the trained model as well. For natural language, however, it is essentially impossible to achieve a systematic and exhaustive determination of empirical importance. In practice, this means that the accuracy of models like expression (1) is largely contingent on the pertinence of the feature functions selected for the particular task at hand.
The usual way out of this dilemma is to throw in as many feature functions as computational resources will allow. Even so, due to the intrinsic lopsided sparsity of language, many distributional aspects will still be missing. And therefore, in those specific contexts where they happen to matter, this may result in erroneous tagging. Consider, for example, the sentence:
Jet streams blow in the troposphere. (2)
The correct tagging for sentence (2) would read as follows:
jet/NN streams/NNS blow/VBP in/IN the/DT troposphere/NN (3)
In expression (3) POS tag “NN” may indicate a noun singular, POS tag “NNS” may indicate a noun with a plural, POS tag “VBP” may indicate a verb in present tense, and POS tag “IN” may indicate a preposition. POS tags are known to one of ordinary skill in the art of natural language processing.
The CRF model provides, however, the following POS tagging:
jet/NN streams/VBZ blow/NN in/IN the/DT troposphere/NN (4)
As expression (4) indicates, CRF model incorrectly resolves the inherent POS ambiguity in the sub-sequence “streams blow.” As shown in (4), word “streams” is assigned a tag VBZ that is third person verb instead of tag NN, as shown in (3) Word “blow” is assigned a tag NN instead of tag VBP, as shown in (3). The problem is that from purely a syntactic viewpoint both interpretations are perfectly acceptable (a frequent situation due to the many dual noun-verb possibilities in English).
What would clearly help in this case is taking into account the semantic information available. Indeed the word “troposphere,” for example, would seem to make the verbal usage of “blow” substantially more likely. That is, the semantic of the sentence (2) can be used to disambiguate between two sequences of words, such as sequence (3) and sequence (4). The semantic information may include a general topic of the sentence and meaning of the words in the sentence.
For example, the semantic information may be obtained from determination whether words “jet” and “streams” mostly co-occur in a database, such that word “jet” is in most of the times accompanied by word “streams” and vice versa. If the words “jet” and “streams” mostly co-occur, then it means that “jet stream” is a compound. That is, the meaning of the words “jet” and “streams” in the input sentence (2) can be determined. The POS tags may be assigned to words “jet” and “streams” based on the determined meaning of the words, and/or the general topic of the sentence. Tagging using latent analogy may be an attempt to systematically generalize this observation, as described in further detail below.
Semantic information can be extracted from an analysis of the global fabric of the training corpus of word sequences. In one embodiment, the analysis of the global fabric of the training corpus is performed using latent semantic mapping. For each sequence of words under consideration, a neighborhood of globally relevant training word sequences may be generated. For example, the neighborhood of the globally relevant training word sequences may be the training sequences that belong to the same general topic, as the sequence of words under consideration.
The POS characteristics of the words of the globally relevant training word sequences from the neighborhood may be extracted. The POS characteristics of the globally relevant training sequences may be used to assign POS tags to the words of the sequence under consideration. The POS disambiguation may emerge automatically as a by-product of latent semantic mapping (“LSM”)-based semantic consistency, which practically bypasses the need for an explicit linguistic knowledge. Additionally, POS tagging using latent analogy takes substantially less time than currently available methods, such as MEMMs and CRFs, described above.
In one embodiment, the analysis of the global fabric of the training corpus is performed using latent semantic mapping. In one embodiment, the analyzing of the global fabric of the training corpus in the vector space comprises mapping the input sequence into the vector space, and forming a neighborhood associated with the input sequence in the vector space. In one embodiment, the neighborhood associated with the input sequence of words in the vector space represents one or more training sequences that are globally relevant to the input sequence, as described in further detail below. In one embodiment, the one or more training sequences that are globally relevant to the input sequence are the training sentences that have the substantially the same general topic, as the input sequence of words. In one embodiment, the analyzing of the global fabric of the training corpus in the vector space comprises determining a closeness measure between the training sequences and the input sequence in the vector space, as described in further detail below.
As shown in
Each entry wij of matrix W may be expressed as follows:
where cij is the number of times gi occurs in sentence hj, nj is the total number of n-grams present in this sentence, and εi, is the normalized entropy of gi, in V 203. The global weighting implied by 1−εi, reflects the fact that two n-grams appearing with the same count in a particular sentence do not necessarily convey the same amount of information; this is subordinated to the distribution of the n-grams in the entire set V 203. That means, for example, that for a word like ‘the’, which occurs in almost every sentence, normalized entropy εi would be very close to 1, which means that global weighting implied by 1−εi would be very close to zero, and therefore may be not informative. For a word that has normalized entropy εi close to zero, global weighting implied by 1−εi would be close to one, meaning that this word may be informative.
W=USVT, (6)
where U is the (M×R) left singular matrix 503 with row vectors ui (1≦i≦M), S is the (R×R) diagonal matrix 505 of singular values s1≧s2≧ . . . ≧sR≧0, V is the (N×R) right singular matrix 507 with row vectors vJ (1≦j≦N), wherein R<<M, N is the order of the decomposition, and T denotes matrix transposition. Both left and right singular matrices U 503 and V 507 are column-orthonormal, i.e., UTU=VTV=IR (the identity matrix of order R). Thus, the column vectors of matrices U and V each define an orthonormal basis for the space of dimension R spanned by the (R-dimensional) ui'"'"'s and vj'"'"'s. This space may be referred as a vector space, such as vector space 205 of
The basic idea behind (6) is that the rank-R decomposition captures the major structural associations in W and ignores higher order effects. Hence, the relative positions of the sentence vector representations (anchors) in the vector space reflect a parsimonious encoding of the semantic concepts used in the training data. This means that any input sequence of words; e.g., a sentence, mapped onto a vector space “close” (in some suitable metric) to a particular sentence anchor would be expected to be closely related to the corresponding training sentence, and any training sequence of words (e.g., sentence) whose representation (“anchor”) is “close” to a vector representation of input sequence of words in the space L would tend to be related to this input sentence. This offers a basis for determining sentence neighborhoods.
Referring back to
In one embodiment, if the input sequence of words is globally relevant to training sequences of words, for example, the input sentence has substantially the same style, general topic, matrices U 513 and S 514 will be substantially similar to matrices U 503 and S 505. Therefore, assuming the matrices U and S do not change appreciably, so that matrix U 513 is substantially similar to matrix U 503, and matrix S 514 is substantially similar to matrix S 505, the SVD expansion (6) will read as follows:
{tilde over (h)}p=US{tilde over (v)}pT (7)
where the R-dimensional vector {tilde over (v)}pT acts as an additional (N+1) column 516 of the matrix VT. This in turn leads to the definition:
In one embodiment, one or more training sequences that are globally relevant to the received sequence of words are selected from the plurality of training sequences selected to form the neighborhood, and the training sequences that are not globally relevant to the received sequence of words are rejected. In one embodiment, a closeness measure, for example, a distance, between representations of a training sequence of the plurality of the training sequences and the input sequence in the vector space is determined to form the neighborhood. A training sequence may be selected out of the plurality of the training sequences based on the closeness measure, as described in further detail below. Next, at operation 1004, a POS tag is assigned to a word of the received sequence based on the POS characteristics (e.g., POS values) obtained from the neighborhood.
Referring back to
In one embodiment, each of the closeness measures 602 and 603 are compared to a predetermined threshold. The training sequence may be selected if the closeness measure 602 exceeds the predetermined threshold. The training sequence 211 may be rejected if closeness measure 603 is less or equal to the predetermined threshold. The predetermined threshold may be chosen depending on a particular application or task at hand. In another embodiment, to form neighborhood 611, the training sequences are ranked according to their closeness measures to the input sequence in vector space 205. The training sequence that has a rank equal or higher than a predetermined rank may be selected to form neighborhood 611, and the training sequence that has the rank lower than the predetermined rank may be rejected. The predetermined rank may be any number 2, 3, . . . N and may be chosen according to a particular application or task at hand.
Referring back to expression (8), it remains to specify a suitable closeness measure to compare
for any 1≦j≦N. Using (9), all training sentences can be ranked in decreasing order of closeness to the representation of the input sentence 609. The associated sentence neighborhood 609 may be formed by retaining only those training sequences whose closeness measure is higher than a predetermined threshold.
Next, a determination is made whether closeness measures of vector representations of all training sequences have been checked at operation 1104. If not all training sequences have been checked, the operation 1102 method 1100 returns to operation 1102. If closeness measures of vector representations of all training sequences have been checked, method 1100 continues with operation 1105 that involves forming a neighborhood in the vector space that includes representations of the retained training sequences. Next, at operation 1106, a determination is made whether a training sequence represented in the neighborhood contains a word that is substantially similar to (e.g., the same as) the word of the input sequence of words. Next, operation 1107 is performed that includes forming one or more sub-sequences of the training sequence having vector representation in the neighborhood. The sub-sequences contain the words that are substantially similar to the words of the input sequence. Next, one or more sub-sequences are aligned at operation 1108 to obtain one or more POS characteristics (e.g., values) of the words from the sub-sequences. Method 1100 continues with operation 1109 that involves determining a POS tag for the word from the input sequence based on the obtained POS characteristics (e.g., POS values).
Referring back to
The final POS sequence may read as follows:
Jet/NN streams/NNS blow/VBP in/IN the/DT troposphere/NN (10)
In one embodiment, when the number of one POS values and the number of another POS values that label the words from the sub-sequences are substantially equal, for example, when 50% of the POS values represent nouns and 50% of POS values represent verbs, then the statistics from the whole training corpus can be used to determine the proper POS tag for the input word. A comparison with (3) and (4) shows that POS tagging using latent analogy is able to satisfactorily resolve the inherent POS ambiguity discussed previously. This bodes well for its general deployability across a wide range of applications.
At operation 1206 determination is made whether the training sequence represented in the neighborhood contains a word that is substantially similar to the input word. If the training sequence does not contain the word that is substantially similar to the input word, the training sentence is disregarded at operation 1211. If the training sequence contains the word that is substantially similar to the input word, the training sentence is retained, and a sub-sequence of such training sequence is selected that contains the word that is substantially similar to the input word at operation 1207.
Next, at operation 1208 determination is made have all or a predetermined number of training sequences of words represented in the vector neighborhood been checked. If not all or predetermined number of training sequences represented in the neighborhood have been checked, method 1200 returns to operation 1206. If all or a predetermined number of training sequences represented in the neighborhood have been checked, method 1200 continues at operation 1209 that involves aligning the selected sub-sequences to obtain POS characteristics (e.g., POS values) of the words from the sub-sequences. Next, assigning a POS tag to the input word is performed based on the obtained one or more POS characteristics (e.g., POS values) of the word from the sub-sequences that is substantially similar to the input word.
Some portions of the preceding detailed descriptions have been presented in terms of algorithms and symbolic representations of operations on data bits within a computer memory. These algorithmic descriptions and representations are the ways used by those skilled in the data processing arts to most effectively convey the substance of their work to others skilled in the art. An algorithm is here, and generally, conceived to be a self-consistent sequence of operations leading to a desired result. The operations are those requiring physical manipulations of physical quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like.
It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the above discussion, it is appreciated that throughout the description, discussions utilizing terms such as “processing”, “computing”, “calculating”, “determining” and the like, refer to the action and processes of a data processing system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the data processing system'"'"'s registers and memories into other data similarly represented as physical quantities within the data processing system memories or registers or other such information storage, transmission or display devices.
The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose systems may be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method operations. The required structure for a variety of these systems will appear from the description below. In addition, embodiments of the present invention are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of embodiments of the invention as described herein.
In the foregoing specification, embodiments of the invention have been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.