Aaai 2006 Pedersen

July 17, 2006 AAAI-2006 Tutorial 1

Language Independent Methods of Clustering Similar Contexts

(with applications)

Ted Pedersen

University of Minnesota, Duluth

[email protected]

http://www.d.umn.edu/~tpederse/SCTutorial.html




Language Independent Methods

• Do not utilize syntactic information– No parsers, part of speech taggers, etc. required

• Do not utilize dictionaries or other manually created lexical resources

• Based on lexical features selected from corpora – Assumption: word segmentation can be done by

looking for white spaces between strings• No manually annotated data of any kind,

methods are completely unsupervised in the strictest sense


Clustering Similar Contexts

• A context is a short unit of text– often a phrase to a paragraph in length,

although it can be longer

• Input: N contexts

• Output: K clusters– Where each member of a cluster is a context

that is more similar to each other than to the contexts found in other clusters


Applications

• Headed contexts (contain target word)– Name Discrimination– Word Sense Discrimination

• Headless contexts – Email Organization– Document Clustering– Paraphrase identification

• Clustering Sets of Related Words


Tutorial Outline• Identifying lexical features

– Measures of association & tests of significance

• Context representations– First & second order

• Dimensionality reduction– Singular Value Decomposition

• Clustering– Partitional techniques– Cluster stopping– Cluster labeling

• Evaluation


SenseClusters

• A package for clustering contexts– http://senseclusters.sourceforge.net– SenseClusters Live! (Knoppix CD)

• Integrates with various other tools– Ngram Statistics Package– CLUTO– SVDPACKC

http://senseclusters.sourceforge.net/


Many thanks…

• Amruta Purandare (M.S., 2004)– Founding developer of SenseClusters (2002-2004)– Now PhD student in Intelligent Systems at the

University of Pittsburgh http://www.cs.pitt.edu/~amruta/

• Anagha Kulkarni (M.S., 2006, expected)– Enhancing SenseClusters since Fall 2004!– Will start as PhD student at CMU/LTI in Fall 2006

http://www.d.umn.edu/~kulka020/

• NSF for supporting Amruta, Anagha and Ted via CAREER award #0092784

http://www.cs.pitt.edu/~amruta/

http://www.d.umn.edu/~kulka020/


Background and Motivations


Headed and Headless Contexts

• A headed context includes a target word– Our goal is to cluster the target words based

on their surrounding contexts – Target word is center of context and our

attention

• A headless context has no target word– Our goal is to cluster the contexts based on

their similarity to each other– The focus is on the context as a whole


Headed Contexts (input)

• I can hear the ocean in that shell.

• My operating system shell is bash.

• The shells on the shore are lovely.

• The shell command line is flexible.

• The oyster shell is very hard and black.


Headed Contexts (output)

• Cluster 1: – My operating system shell is bash.– The shell command line is flexible.

• Cluster 2:– The shells on the shore are lovely.– The oyster shell is very hard and black.– I can hear the ocean in that shell.


Headless Contexts (input)

• The new version of Linux is more stable and has better support for cameras.

• My Chevy Malibu has had some front end troubles.

• Osborne made one of the first personal computers.

• The brakes went out, and the car flew into the house.

• With the price of gasoline, I think I’ll be taking the bus more often!


Headless Contexts (output)

• Cluster 1:– The new version of Linux is more stable and better

support for cameras.– Osborne made one of the first personal computers.

• Cluster 2: – My Chevy Malibu has had some front end troubles.– The brakes went out, and the car flew into the house. – With the price of gasoline, I think I’ll be taking the bus

more often!


Web Search as Application

• Web search results are headed contexts– Search term is target word (found in snippets)

• Web search results are often disorganized – two people sharing same name, two organizations sharing same abbreviation, etc. often have their pages “mixed up”

• If you click on search results or follow links in pages found, you will encounter headless contexts too…


Email Foldering as Application

• Email (public or private) is made up of headless contexts– Short, usually focused…

• Cluster similar email messages together – Automatic email foldering– Take all messages from sent-mail file or inbox

and organize into categories


Clustering News as Application

• News articles are headless contexts– Entire article or first paragraph– Short, usually focused

• Cluster similar articles together


What is it to be “similar”?

• You shall know a word by the company it keeps– Firth, 1957 (Studies in Linguistic Analysis)

• Meanings of words are (largely) determined by their distributional patterns (Distributional Hypothesis)– Harris, 1968 (Mathematical Structures of Language)

• Words that occur in similar contexts will have similar meanings (Strong Contextual Hypothesis)– Miller and Charles, 1991 (Language and Cognitive Processes)

• Various extensions…– Similar contexts will have similar meanings, etc.– Names that occur in similar contexts will refer to the same

underlying person, etc.


General Methodology

• Represent contexts to be clustered using first or second order feature vectors– Lexical features

• Reduce dimensionality to make vectors more tractable and/or understandable– Singular value decomposition

• Cluster the context vectors– Find the number of clusters– Label the clusters

• Evaluate and/or use the contexts!


Identifying Lexical Features

Measures of Association and

Tests of Significance


What are features?

• Features represent the (hopefully) salient characteristics of the contexts to be clustered

• Eventually we will represent each context as a vector, where the dimensions of the vector are associated with features

• Vectors/contexts that include many of the same features will be similar to each other


Where do features come from?

• In unsupervised clustering, it is common for the feature selection data to be the same data that is to be clustered– This is not cheating, since data to be clustered does

not have any labeled classes that can be used to assist feature selection

– It may also be necessary, since we may need to cluster all available data, and not hold out some for a separate feature identification step

• Email or news articles


Feature Selection

• “Test” data – the contexts to be clustered– Assume that the feature selection data is the same as

the test data, unless otherwise indicated

• “Training” data – a separate corpus of held out feature selection data (that will not be clustered)– may need to use if you have a small number of

contexts to cluster (e.g., web search results)– This sense of “training” due to Schütze (1998)


Lexical Features

• Unigram – a single word that occurs more than a given number of times

• Bigram – an ordered pair of words that occur together more often than expected by chance– Consecutive or may have intervening words

• Co-occurrence – an unordered bigram• Target Co-occurrence – a co-occurrence where

one of the words is the target word


Bigrams

• fine wine (window size of 2)• baseball bat• house of representatives (window size of 3)• president of the republic (window size of 4)• apple orchard

• Selected using a small window size (2-4 words), trying to capture a regular (localized) pattern between two words (collocation?)


Co-occurrences

• tropics water• boat fish• law president• train travel

• Usually selected using a larger window (7-10 words) of context, hoping to capture pairs of related words rather than collocations


Bigrams and Co-occurrences

• Pairs of words tend to be much less ambiguous than unigrams– “bank” versus “river bank” and “bank card”– “dot” versus “dot com” and “dot product”

• Three grams and beyond occur much less frequently (Ngrams very Zipfian)

• Unigrams are noisy, but bountiful


“occur together more often than expected by chance…”

• Observed frequencies for two words occurring together and alone are stored in a 2x2 matrix– Throw out bigrams that include one or two stop words

• Expected values are calculated, based on the model of independence and observed values– How often would you expect these words to occur

together, if they only occurred together by chance?– If two words occur “significantly” more often than the

expected value, then the words do not occur together by chance.


2x2 Contingency Table

Intelligence !Intelligence

Artificial 100.0

000.12

300.0

398.8

400

!Artificial 200.0

298.8

99,400.0

99,301.2

99,600

300 99,700 100,000


Measures of Association

2

1,

22

2

1,

2

),(

)],(),([

)),(

),(log*),((

ji ji

jiji

ji

ji

jiji

wwexpected

wwexpectedwwobservedX

wwexpected

wwobservedwwobservedG


Interpreting the Scores…

• G^2 and X^2 are asymptotically approximated by the chi-squared distribution…

• This means…if you fix the marginal totals of a table, randomly generate internal cell values in the table, calculate the G^2 or X^2 scores for each resulting table, and plot the distribution of the scores, you *should* get …


Interpreting the Scores…

• Values above a certain level of significance can be considered grounds for rejecting the null hypothesis – H0: the words in the bigram are independent– 3.841 is associated with 95% confidence that

the null hypothesis should be rejected


Measures of Association

• There are numerous measures of association that can be used to identify bigram and co-occurrence features

• Many of these are supported in the Ngram Statistics Package (NSP)– http://www.d.umn.edu/~tpederse/nsp.html

http://www.d.umn.edu/~tpederse/nsp.html


Summary

• Identify lexical features based on frequency counts or measures of association – either in the data to be clustered or in a separate set of feature selection data– Language independent

• Unigrams usually only selected by frequency– Remember, no labeled data from which to learn, so somewhat

less effective as features than in supervised case

• Bigrams and co-occurrences can also be selected by frequency, or better yet measures of association– Bigrams and co-occurrences need not be consecutive– Stop words should be eliminated– Frequency thresholds are helpful (e.g., unigram/bigram that

occurs once may be too rare to be useful)


Context Representations

First and Second Order Methods


Once features selected…

• We have a set of unigrams, bigrams, co-occurrences or target co-occurrences – We believe/hope that these are descriptive of

the contexts– We also have frequency and measure of

association score that have been used in their selection

• Convert contexts to be clustered into a vector representation based on these features


First Order Representation

• Each context is represented by a vector with M dimensions, each of which indicates whether or not a particular feature occurred in that context– Value may be binary, a frequency count, or an

association score

• Context by Feature representation


Contexts

• Cxt1: There was an island curse of black magic cast by that voodoo child.

• Cxt2: Harold, a known voodoo child, was gifted in the arts of black magic.

• Cxt3: Despite their military might, it was a serious error to attack.

• Cxt4: Military might is no defense against a voodoo child or an island curse.


Unigram Feature Set

• island 1000• black 700• curse 500• magic 400• child 200

• (assume these are frequency counts obtained from some corpus…)


First Order Vectors of Unigrams

island black curse magic child

Cxt1 1 1 1 1 1

Cxt2 0 1 0 1 1

Cxt3 0 0 0 0 0

Cxt4 1 0 1 0 1


Bigram Feature Set• island curse 189.2• black magic 123.5• voodoo child 120.0• military might 100.3• serious error 89.2• island child 73.2• voodoo might 69.4• military error 54.9• black child 43.2• serious curse 21.2

• (assume these are log-likelihood scores based on frequency counts from some corpus)


First Order Vectors of Bigrams

black

magic

island curse

military might

serious error

voodoo child

Cxt1 1 1 0 0 1

Cxt2 1 0 0 0 1

Cxt3 0 0 1 1 0

Cxt4 0 1 1 0 1


First Order Vectors

• Can have binary values or weights associated with frequency, etc.

• Forms a context by feature matrix• May optionally be smoothed/reduced with

Singular Value Decomposition – More on that later…

• The contexts are ready for clustering…– More on that later…


Second Order Features

• First order features encode the occurrence of a feature in a context– Feature occurrence represented by binary value

• Second order features encode something ‘extra’ about a feature that occurs in a context– Feature occurrence represented by word co-occurrences– Feature occurrence represented by context occurrences


Second Order Representation

• First, build word by word matrix from features– Based on bigrams or co-occurrences– First word is row, second word is column, cell is score– (optionally) reduce dimensionality w/SVD– Each row forms a vector of first order co-occurrences

• Second, replace each word in a context with its row/vector as found in the word by word matrix

• Average all the word vectors in the context to create the second order representation– Due to Schütze (1998), related to LSI/LSA


Word by Word Matrix

magic curse might error child

black 123.5 0 0 0 43.2

island 0 189.2 0 0 73.2

military 0 0 100.3 54.9 0

serious 0 21.2 0 89.2 0

voodoo 0 0 69.4 0 120.0


Word by Word Matrix

• …can also be used to identify sets of related words• In the case of bigrams, rows represent the first word in a

bigram and columns represent the second word– Matrix is asymmetric

• In the case of co-occurrences, rows and columns are equivalent– Matrix is symmetric

• The vector (row) for each word represent a set of first order features for that word

• Each word in a context to be clustered for which a vector exists (in the word by word matrix) is replaced by that vector in that context


There was an island curse of black magic cast by that voodoo child.


black 123.5 0 0 0 43.2

island 0 189.2 0 0 73.2

voodoo 0 0 69.4 0 120.0


Second Order Co-Occurrences

• Word vectors for “black” and “island” show similarity as both occur with “child”

• “black” and “island” are second order co-occurrence with each other, since both occur with “child” but not with each other (i.e., “black island” is not observed)



• There was an [curse, child] curse of [magic, child] magic cast by that [might, child] child

• [curse, child] + [magic, child] + [might, child]


There was an island curse of black magic cast by that voodoo child.


Cxt1 41.2 63.1 24.4 0 78.8



• Results in a Context by Feature (Word) Representation

• Cell values do not indicate if feature occurred in context. Rather, they show the strength of association of that feature with other words that occur with a word in the context.


Summary

• First order representations are intuitive, but…– Can suffer from sparsity– Contexts represented based on the features that

occur in those contexts• Second order representations are harder to

visualize, but…– Allow a word to be represented by the words it co-

occurs with (i.e., the company it keeps)– Allows a context to be represented by the words that

occur with the words in the context – Helps combat sparsity…


Related Work• Pedersen and Bruce 1997 (EMNLP) presented first order method of

discrimination http://acl.ldc.upenn.edu/W/W97/W97-0322.pdf

• Schütze 1998 (Computational Linguistics) introduced second order method

http://acl.ldc.upenn.edu/J/J98/J98-1004.pdf

• Purandare and Pedersen 2004 (CoNLL) compared first and second order methods

http://acl.ldc.upenn.edu/hlt-naacl2004/conll04/pdf/purandare.pdf

– First order better if you have lots of data– Second order better with smaller amounts of data

http://acl.ldc.upenn.edu/W/W97/W97-0322.pdf

http://acl.ldc.upenn.edu/J/J98/J98-1004.pdf

http://acl.ldc.upenn.edu/hlt-naacl2004/conll04/pdf/purandare.pdf


Dimensionality Reduction

Singular Value Decomposition


Effect of SVD

• SVD reduces a matrix to a given number of dimensions This may convert a word level space into a semantic or conceptual space– If “dog” and “collie” and “wolf” are

dimensions/columns in a word co-occurrence matrix, after SVD they may be a single dimension that represents “canines”


Effect of SVD

• The dimensions of the matrix after SVD are principal components that represent the meaning of concepts– Similar columns are grouped together

• SVD is a way of smoothing a very sparse matrix, so that there are very few zero valued cells after SVD


How can SVD be used?

• SVD on first order contexts will reduce a context by feature representation down to a smaller number of features– Latent Semantic Analysis typically performs SVD

on a feature by context representation, where the contexts are reduced

• SVD used in creating second order context representations– Reduce word by word matrix


Word by Word Matrixapple blood cells ibm data box tissue graphics memory organ plasma

pc 2 0 0 1 3 1 0 0 0 0 0

body 0 3 0 0 0 0 2 0 0 2 1

disk 1 0 0 2 0 3 0 1 2 0 0

petri 0 2 1 0 0 0 2 0 1 0 1

lab 0 0 3 0 2 0 2 0 2 1 3

sales 0 0 0 2 3 0 0 1 2 0 0

linux 2 0 0 1 3 2 0 1 1 0 0

debt 0 0 0 2 3 4 0 2 0 0 0


Singular Value DecompositionA=UDV’


Word by Word Matrix After SVD

apple blood cells ibm data tissue graphics memory organ plasma

pc .73 .00 .11 1.3 2.0 .01 .86 .77 .00 .09

body .00 1.2 1.3 .00 .33 1.6 .00 .85 .84 1.5

disk .76 .00 .01 1.3 2.1 .00 .91 .72 .00 .00

germ .00 1.1 1.2 .00 .49 1.5 .00 .86 .77 1.4

lab .21 1.7 2.0 .35 1.7 2.5 .18 1.7 1.2 2.3

sales .73 .15 .39 1.3 2.2 .35 .85 .98 .17 .41

linux .96 .00 .16 1.7 2.7 .03 1.1 1.0 .00 .13

debt 1.2 .00 .00 2.1 3.2 .00 1.5 1.1 .00 .00



• These two contexts share no words in common, yet they are similar! disk and linux both occur with “Apple”, “IBM”, “data”, “graphics”, and “memory”

• The two contexts are similar because they share many second order co-occurrences

apple blood cells ibm data tissue graphics memory organ plasma

disk .76 .00 .01 1.3 2.1 .00 .91 .72 .00 .00

linux .96 .00 .16 1.7 2.7 .03 1.1 1.0 .00 .13

• I got a new disk today!

• What do you think of linux?


Relationship to LSA

• Latent Semantic Analysis uses feature by context first order representation – Indicates all the contexts in which a feature

occurs– Use SVD to reduce dimensions (contexts)– Cluster features based on similarity of

contexts in which they occur– Represent sentences using an average of

feature vectors


Feature by Context Representation

Cxt1 Cxt2 Cxt3 Cxt4

black magic 1 1 0 1

island curse 1 0 0 1

military might 0 0 1 0

serious error 0 0 1 0

voodoo child 1 1 0 1


References

• Deerwester, S. and Dumais, S.T. and Furnas, G.W. and Landauer, T.K. and Harshman, R., Indexing by Latent Semantic Analysis, Journal of the American Society for Information Science, vol. 41, 1990

• Landauer, T. and Dumais, S., A Solution to Plato's Problem: The Latent Semantic Analysis Theory of Acquisition, Induction and Representation of Knowledge, Psychological Review, vol. 104, 1997

• Schütze, H, Automatic Word Sense Discrimination, Computational Linguistics, vol. 24, 1998

• Berry, M.W. and Drmac, Z. and Jessup, E.R.,Matrices, Vector Spaces, and Information Retrieval, SIAM Review, vol 41, 1999


Clustering

Partitional Methods

Cluster Stopping

Cluster Labeling


Many many methods…

• Cluto supports a wide range of different clustering methods– Agglomerative

• Average, single, complete link…

– Partitional• K-means (Direct)

– Hybrid• Repeated bisections

• SenseClusters integrates with Cluto– http://www-users.cs.umn.edu/~karypis/cluto/

http://www-users.cs.umn.edu/~karypis/cluto/


General Methodology

• Represent contexts to be clustered in first or second order vectors

• Cluster the context vectors directly– vcluster

• … or convert to similarity matrix and then cluster– scluster


Partitional Methods

• Randomly create centroids equal to the number of clusters you wish to find

• Assign each context to nearest centroid• After all contexts assigned, re-compute

centroids– “best” location decided by criterion function

• Repeat until stable clusters found– Centroids don’t shift from iteration to iteration


Partitional Methods

• Advantages : fast

• Disadvantages– Results can be dependent on the initial

placement of centroids– Must specify number of clusters ahead of time

• maybe not…


Partitional Criterion Functions

• Intra-Cluster (Internal) similarity/distance– How close together are members of a cluster?– Closer together is better

• Inter-Cluster (External) similarity/distance– How far apart are the different clusters?– Further apart is better


Intra Cluster Similarity

• Ball of String (I1)– How far is each member from each other

member

• Flower (I2)– How far is each member of cluster from

centroid


Contexts to be Clustered


Ball of String (I1 Internal Criterion Function)


Flower(I2 Internal Criterion Function)


Inter Cluster Similarity

• The Fan (E1)– How far is each centroid from the centroid of

the entire collection of contexts– Maximize that distance


The Fan(E1 External Criterion Function)


Hybrid Criterion Functions

• Balance internal and external similarity– H1 = I1/E1– H2 = I2/E1

• Want internal similarity to increase, while external similarity decreases

• Want internal distances to decrease, while external distances increase


Cluster Stopping


Cluster Stopping

• Many Clustering Algorithms require that the user specify the number of clusters prior to clustering

• But, the user often doesn’t know the number of clusters, and in fact finding that out might be the goal of clustering


Criterion Functions Can Help

• Run partitional algorithm for k=1 to deltaK– DeltaK is a user estimated or automatically

determined upper bound for the number of clusters

• Find the value of k at which the criterion function does not significantly increase at k+1

• Clustering can stop at this value, since no further improvement in solution is apparent with additional clusters (increases in k)


H2 versus kT. Blair – V. Putin – S. Hussein


PK2

• Based on Hartigan, 1975• When ratio approaches 1, clustering is at a plateau• Select value of k which is closest to but outside of

standard deviation interval

)1(2

)(2)(2

kH

kHkPK


PK2 predicts 3 sensesT. Blair – V. Putin – S. Hussein


PK3• Related to Salvador and Chan, 2004• Inspired by Dice Coefficient• Values close to 1 mean clustering is improving …• Select value of k which is closest to but outside of

standard deviation interval

)1(2)1(2

)(2*2)(3

kHkH

kHkPK


PK3 predicts 3 sensesT. Blair – V. Putin – S. Hussein


References• Hartigan, J. Clustering Algorithms, Wiley, 1975

– basis for SenseClusters stopping method PK2• Mojena, R., Hierarchical Grouping Methods and Stopping Rules: An

Evaluation, The Computer Journal, vol 20, 1977 – basis for SenseClusters stopping method PK1

• Milligan, G. and Cooper, M., An Examination of Procedures for Determining the Number of Clusters in a Data Set, Psychometrika, vol. 50, 1985– Very extensive comparison of cluster stopping methods

• Tibshirani, R. and Walther, G. and Hastie, T., Estimating the Number of Clusters in a Dataset via the Gap Statistic,Journal of the Royal Statistics Society (Series B), 2001

• Pedersen, T. and Kulkarni, A. Selecting the "Right" Number of Senses Based on Clustering Criterion Functions, Proceedings of the Posters and Demo Program of the Eleventh Conference of the European Chapter of the Association for Computational Linguistics, 2006– Describes SenseClusters stopping methods


Cluster Labeling


Cluster Labeling

• Once a cluster is discovered, how can you generate a description of the contexts of that cluster automatically?

• In the case of contexts, you might be able to identify significant lexical features from the contents of the clusters, and use those as a preliminary label


Results of Clustering

• Each cluster consists of some number of contexts

• Each context is a short unit of text• Apply measures of association to the

contents of each cluster to determine N most significant bigrams

• Use those bigrams as a label for the cluster


Label Types

• The N most significant bigrams for each cluster will act as a descriptive label

• The M most significant bigrams that are unique to each cluster will act as a discriminating label


Evaluation Techniques

Comparison to gold standard data


Evaluation

• If Sense tagged text is available, can be used for evaluation– But don’t use sense tags for clustering or

feature selection!

• Assume that sense tags represent “true” clusters, and compare these to discovered clusters– Find mapping of clusters to senses that

attains maximum accuracy


Evaluation

• Pseudo words are especially useful, since it is hard to find data that is discriminated– Pick two words or names from a corpus, and

conflate them into one name. Then see how well you can discriminate.

– http://www.d.umn.edu/~tpederse/tools.html

• Baseline Algorithm– group all instances into one cluster, this will reach “accuracy” equal to majority classifier


Evaluation

• Pseudo words are especially useful, since it is hard to find data that is discriminated– Pick two or more words or names from a

corpus, and conflate them into one name. Then see how well you can discriminate.

– http://www.d.umn.edu/~kulka020/kanaghaName.html


Baseline Algorithm

• Baseline Algorithm – group all instances into one cluster, this will reach “accuracy” equal to majority classifier

• What if the clustering said everything should be in the same cluster?


Baseline Performance

S1 S2 S3 Totals

C1 0 0 0 0

C2 0 0 0 0

C3 80 35 55 170

Totals 80 35 55 170

S3 S2 S1 Totals

C1 0 0 0 0

C2 0 0 0 0

C3 55 35 80 170

Totals 55 35 80 170

(0+0+55)/170 = .32 if C3 is S1 (0+0+80)/170 = .47 if C3 is S3


Evaluation• Suppose that C1 is labeled S1, C2 as S2, and C3 as S3• Accuracy = (10 + 0 + 10) / 170 = 12% • Diagonal shows how many members of the cluster actually belong to

the sense given on the column • Can the “columns” be rearranged to improve the overall accuracy?

– Optimally assign clusters to senses

S1 S2 S3 Totals

C1 10 30 5 45

C2 20 0 40 60

C3 50 5 10 65

Totals 80 35 55 170


Evaluation

• The assignment of C1 to S2, C2 to S3, and C3 to S1 results in 120/170 = 71%

• Find the ordering of the columns in the matrix that maximizes the sum of the diagonal.

• This is an instance of the Assignment Problem from Operations Research, or finding the Maximal Matching of a Bipartite Graph from Graph Theory.

S2 S3 S1 Totals

C1 30 5 10 45

C2 0 40 20 60

C3 5 10 50 65

Totals 35 55 80 170


Alternatives?

• Unsupervised methods may not discover clusters equivalent to the classes learned in supervised learning

• Evaluation based on assuming that sense tags represent the “true” cluster are likely a bit harsh. Alternatives?– Humans could look at the members of each cluster and

determine the nature of the relationship or meaning that they all share

– Use the contents of the cluster to generate a descriptive label that could be inspected by a human


Thank you!

• Questions or comments on tutorial or SenseClusters are welcome at any time

[email protected]

• SenseClusters is freely available via LIVE CD, the Web, and in source code form

http://senseclusters.sourceforge.net

• SenseClusters papers available at:http://www.d.umn.edu/~tpederse/senseclusters-pubs.html

mailto:[email protected]

http://senseclusters.sourceforge.net/

http://www.d.umn.edu/~tpederse/senseclusters-pubs.html

Aaai 2006 Pedersen

Technology

Transcript of Aaai 2006 Pedersen