research article augmenting weak semantic...

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2013 Article ID 308176 10 pageshttpdxdoiorg1011552013308176

Research ArticleAugmenting Weak Semantic Cognitive Maps with anlsquolsquoAbstractnessrsquorsquo Dimension

Alexei V Samsonovich and Giorgio A Ascoli

Krasnow Institute for Advanced Study George Mason University 4400 University Drive MS 2A1 Fairfax VA 22030-4444 USA

Correspondence should be addressed to Alexei V Samsonovich asamsonogmuedu

Received 14 December 2012 Accepted 29 April 2013

Academic Editor Rajan Bhattacharyya

Copyright copy 2013 A V Samsonovich and G A Ascoli This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The emergent consensus on dimensional models of sentiment appraisal emotions and values is on the semantics of the principaldimensions typically interpreted as valence arousal and dominance The notion of weak semantic maps was introduced recentlyas distribution of representations in abstract spaces that are not derived from human judgments psychometrics or any other apriori information about their semantics Instead they are defined entirely by binary semantic relations among representationssuch as synonymy and antonymy An interesting question concerns the ability of the antonymy-based semantic maps to captureall ldquouniversalrdquo semantic dimensions The present work shows that those narrow weak semantic maps are not complete in thissense and can be augmented with other semantic relations Specifically including hyponym-hypernym relations yields a newsemantic dimension of the map labeled here ldquoabstractnessrdquo (or ontological generality) that is not reducible to any dimensionsrepresented by antonym pairs or to traditional affective space dimensions It is expected that including other semantic relations(eg meronymyholonymy) will also result in the addition of new semantic dimensions to the map These findings have broadimplications for automated quantitative evaluation of the meaning of text and may shed light on the nature of human subjectiveexperience

1 Introduction

The idea of representing semantics geometrically is increas-ingly popular Many mainstream approaches use vectorspace models in which concepts words documents andso forth are associated with vectors in an abstract multi-dimensional vector space Other approaches use manifoldsof more complex topology and geometry In either casethe resultant space or manifold together with its allocatedrepresentations is called a semantic space or a semantic(cognitive) map Examples include spaces constructed withLatent Semantic Analysis (LSA) [1] and Latent DirichletAllocation (LDA) [2] as well as many related techniques forexample ConceptNet [3 4] Other examples of techniquesinclude Multi-Dimensional Scaling (MDS) [5] includingIsomap [6] and related manifold-learning techniques [7]Gardenforsrsquo conceptual spaces [8] very popular in the pastmodels of self-organizing feature maps and more

The majority of these approaches are based on the ideaof a dissimilarity metrics which is to capture semantic

dissimilarity between representations (words documentsconcepts etc) with a geometrical distance between associ-ated space elements (points or vectors) In other words themetrics that determines the allocation of representations inspace is a function of their semantic dissimilarity In this casetwo representations allocated at close points in space musthave similar semantics and vice versa two representationswith similar semantics must be close to each other in spaceConversely representations unrelated to each other must beseparated by significant distance

We introduced the term ldquoweak semantic cognitive map-pingrdquo to denote an alternative approach exploited herewhich is not based on dissimilarity [9ndash11] The idea is not toseparate all differentmeanings fromeach other (like inMDS)nor to allocate them based on their individual semanticcharacteristics given a priori (as in LSA) but rather to arrangethem in space based on their mutual semantic relationsThe notion of weak semantic cognitive maps was originallyintroduced in a narrow sense where these relations werelimited to synonymy and antonymy only [9ndash11] In a more

2 Computational Intelligence and Neuroscience

general sense as discussed below weak semantic cognitivemaps may capture other binary semantic relations as wellincluding hypernymy-hyponymy holonymy-meronymy tro-ponymy causality and dependence

While the understanding of dissimilarity as the basis ofantonymy is widespread many examples of the dictionaryantonym pairs used in our analysis suggest that dissimilarityand antonymy are distinct notions Most unrelated wordsmay be considered dissimilar (eg ldquoapplerdquo and ldquoinequalityrdquo)yet do not constitute antonym pairs In contrast antonympairs include words that are related to each other and in acertain sense are similar to each other in their meaning andusage for example king and queen major and minor andascent and descent It appears that most antonym pairs (atleast in the dictionaries that we used) are consistent with thenotion of ldquooppositerdquo rather than ldquodissimilarrdquo

More generally the method of weak semantic map-ping is essentially different from most vector-space-basedapproaches including LSA LDA MDS and ConceptNet [1ndash4] primarily because there is no a priori attribution of seman-tic features to representations in the constructive definitionof the map Only relations but not semantic features aregiven as input As a result semantic dimensions of the mapthat are not predefined to emerge naturally starting froma randomly generated initial distribution of words in anabstract space with no a priori given semantics and followingthe strategy to pull synonyms together and antonyms apart[10 11] (see Section 2 Methods) In contrast to LSA principalcomponent analysis is used here to reveal the main emergentsemantic dimensions at the final stage only The advan-tage of the antonymy-based weak semantic cognitive mapcompared to ldquostrongrdquo maps based on dissimilarity metricsis that its dimensions have clearly identifiable semantics(naturally given by the corresponding pairs of antonyms) thatare domain-independent For example the notion of ldquogoodversus badrdquo that corresponds to the first principal componentapplies to all domains of human knowledge

Interestingly semantics of the emergent dimensions ofantonym-based weak semantic cognitive maps are closelyrelated to those of another broad category of ldquodimensionalmodelsrdquo of affects [12] that attempt to capture humanemotions feelings affects appraisals sentiments and atti-tudes Examples range from original classical models suchas Osgoodrsquos semantic differential [13] Russellrsquos circumplex[14] and Plutchikrsquos wheel [15] to many more recent deriva-tive integrated frameworks like PAD (pleasure arousaland dominance) [16] ANEW (Affective Norms for EnglishWords) [17] EPA (evaluation potency and arousal) [18] anda recent 3D model linking emotions to main neurotrans-mitters [19] These dimensional models are usually derivedfrom human experimental studies involving psychometricsor introspective judgment evaluated on the Likert scale [20]While these models provide the most common bases foropinionmining or sentiment analysis [21] the weak semanticmap is more complete in the sense that (i) it assigns valuesto all words not only to emotionally meaningful words (ii)it measures semantics associated with all antonym pairs notonly emotionally meaningful antonym pairs and thereforeis applicable to all domains of knowledge and (iii) its

dimensions are orthogonal and independent of each otherThe combination of these featuresmakesweak semanticmapsextremely valuable for numerous applications

It is surprising that the well-known dimensions of thesemantic differential PAD EPA and related models canbe recognized in the main principal components (PC) ofthe above cited weak semantic map where PC1 is relatedto valence PC2 to arousal and PC3 to dominance [11](This correspondence is approximate because the principalcomponents have zero correlations with each other whilethe variables of eg ANEW are strongly correlated) Forexample ldquoloverdquo and ldquojoyrdquo have top values of valence in theaffective database ANEW and also top values of PC1 of weaksemantic cognitive mapWords like ldquoangerrdquo and ldquoexcitementrdquohave top values of arousal in the affective database ANEWand also top values of PC2 in weak semantic cognitive mapThis correspondence is consistent in weak semantic mapsconstructed based on different corpora in several majorlanguages [11] The observation is unexpected because theweak semantic map is not derived from any semantic featuresof words given a priori and is not explicitly related toemotions and feelings by its construction In fact any pair ofantonyms defines a map dimension including antonym pairsthat are not associated with affects for example ldquoabstract-specificrdquo It is also surprising that the weak semantic map islow-dimensional the number of PCs that account for 95of the variance of the multidimensional distribution typicallyvaries from 4 to 6 depending on the corpus [11]

How complete is the weak semantic map narrowlydefined only by antonym pairs Certainly at least somesemantic differences cannot be captured by antonymy rela-tions because not all concepts have antonyms (eg thenumber 921714083) Here we address a different questionwhether all universal semantic dimensions can be capturedby antonymy relations For example it may seem obvious thatcausality cannot be captured by antonymyHowever the issueis nontrivial as there are many examples of causally relatedantonyms (eg attack-defend begin-end send-receive andeven cause-effect) Thus two logical possibilities stand

(1) Antonym-based semantic maps separate representa-tions along all semantic dimensions that make sensefor all domains of knowledge Thus if there is asemantic characteristic 119883 that makes sense for alldomains of knowledge such that some concepts canbe characterized as having more 119883 than others thenthere is a direction on the narrow weak semantic mapalong which those concepts are separated based ontheir value of X

(2) The alternative there is at least one general seman-tic characteristic 119883 defined for all domains that isignored by the antonym-based weak semantic mapIn other words the variance in 119883 measured acrossall concepts is not accounted by the map coordinatesof concepts and vice versa no significant part of thevariance of the map can be accounted by X

Here we argue for (2) quantifying the notion of ldquoabstract-nessrdquo (or ontological generality) as an example of 119883 Our

Computational Intelligence and Neuroscience 3

minus3 minus2 minus1 0 1 2 3minus25

minus2

minus15

minus1

minus05

0

05

1

15

2

PC1 valence

PC2

arou

sal

Good

Bad

Calm

Exciting

Screw

Tired

Action

WithdrawalObject

Figure 1 A sample from the antonymy-based weak semanticcognitive map constructed by Samsonovich and Ascoli [11] Greydots show all 15783 words from the MS Word English dictionarySimilar results were obtained by WordNet Words shown in colorare examples of hypernym-hyponym pairs ldquoaction-withdrawalrdquo andldquoobject-screwrdquo Selected examples illustrate that there is no clearseparation of hypernyms and hyponyms on the map

technical definition of ldquoabstractnessrdquo is based on hyponym-hypernym relations among words

Before presenting results of the computational study webriefly discuss the hypothesis at an intuitive level Whileldquoabstract-specificrdquo is a pair of antonyms which correspondsto a direction on the narrow weak semantic map the twoantonyms ldquoabstractrdquo and ldquospecificrdquo themselves have approx-imately the same measure of ldquoabstractnessrdquo (the 119883 value)associated with them Intuitively this observation must holdfor most antonym pairs because antonyms pairs do nottypically constitute a hypernym-hyponym couple Thereforeit is unlikely that there is a hyperplane on the map thatseparates more abstract frommore specific wordsThereforewe do not expect to find a dimension of the map basedon synonyms and antonyms that could separate words byldquoabstractnessrdquo (see Figure 1) In contrast there is a hyperplane(PC1 = 0) that separates ldquogoodrdquo and ldquobadrdquo words and ahyperplane (PC2 = 0) that separates ldquocalmingrdquo and ldquoexcitingrdquowords That is to say ldquogood wordsrdquo tend to be synonyms ofthe word ldquogoodrdquo but ldquoabstract wordsrdquo are not synonyms ofthe word ldquoabstractrdquo or of each other

2 Methods

21 Weak Semantic Cognitive Mapping The general idea ofsemantic cognitive mapping is to allocate representations(eg words) in an abstract space based on their semanticsThis paradigm is common for a large number of techniquesoverviewed in Introduction While most studies in semanticcognitive mapping are based on the notion of a dissimilaritymetrics andor on a set of semantic features given a prioriweak semantic mapping ignores dissimilarity as well as anyindividually predefined semantics

The algorithm for antonymy-based weak semantic map-ping is described in our previous work [11] The semanticspace is created by minimization of the ldquoenergyrdquo of the entiredistribution of words on themap starting from a randomdis-tribution Then the emergent semantics of the map dimen-sions are defined by the entire distribution of representationson themap and typically are best characterized by the pairs ofantonyms that are separated by the greatest distance along thegiven dimensionThe main semantic dimensions are definedby the principal components of the emergent distributionof words on the map Semantics associated with the firstthree PCs can be characterized as ldquogoodrdquo versus ldquobadrdquo (PC1)ldquocalming easyrdquo versus ldquoexciting hardrdquo (PC2) and ldquofreeopenrdquo versus ldquodominated closedrdquo (PC3) [11] When limitedto affects these semantics approximately correspond to thethree PAD dimensions pleasure arousal and dominance

More precisely the narrow weak semantic cognitive mapis a distribution of words in an abstract vector space (with nosemantics preassociatedwith its elements or dimensions) thatminimizes the following energy function [11]

119867(x) = minus12

119873

sum

119894119895 =1

119882119894119895x119894sdot x119895+1

4

119873

sum

119894 =1

1003816100381610038161003816x1198941003816100381610038161003816

4 x isin R119873 otimesR119863 (1)

Here x119894is a D-vector representing the 119894th word (out of

N) The 119882119894119895entries of the symmetric relation matrix equal

+1 for pairs of synonyms ndash1 for pairs of antonyms and zerootherwiseD is set to any integer (eg 100) that is substantiallygreater than the number of resulting significant principalcomponents of the distribution which typically ranges from4 to 6 and determines the dimensionality of the map Inthis case the choice of 119863 does not change the outcome Theenergy function (1) follows the principle of parsimony it isthe simplest analytical expression that creates balanced forcesof desired signs between synonyms and antonyms preservessymmetries of semantic relations and increases indefinitelyat the infinity keeping the resultant distribution localizednear the origin of coordinates

The procedure is that the initial coordinates of all wordsare sampled by a random number generatorThen the energy(1) minimization process starts that pulls synonym vectorstogether and antonym vectors apart Then principal compo-nent analysis is used to reveal the main emergent semanticdimensions of the optimized map [10 11] Thus the initialspace coordinates are not associated with any semantics apriori instead words are allocated randomly in an abstractmultidimensional space In contrast the starting point oftraditional techniques based on LSA [1 22] is a feature spacewhere dimensions have definite semantics a priori

The representative weak semantic map shown in Figure 1includes 119873 = 15783 words and was constructed based onthe dictionary of English synonyms and antonyms availableas part ofMicrosoftWord (MSWord) [11] A similar map wasalso constructed using WordNet in the same work [11] and isalso used in this study together withmaps constructed in [11]for other languages Figure 1 represents the first two PCs ofthe distribution of words on the map constructed using theEnglish MSWord thesaurus The axes of the map are definedby the PCs Selected words shown on the map in black at


minus6 minus4 minus2 0 2 4 60

1000

2000

3000

4000

5000

6000

7000

8000

9000

ldquoAbstractnessrdquo

Wor

d co

unts

Figure 2 Distribution histogram of the 124408WordNet 30 wordsalong the ldquoabstractnessrdquo dimension

Table 1The tails of the list of 124408 words sorted by ldquoabstractnessrdquoin descending order

The beginning of the list The end of the listEntity Chain wrenchPhysical entity Francis turbinePsychological feature Tricolor television tubeAuditory communication Tricolor tubeUnmake Tricolour television tubeCognition Tricolour tubeKnowledge EdmontoniaNoesis CoelophysisNatural phenomenon DeinocheirusAbility StruthiomimusSocial event DeinonychusCraniate DromaeosaurVertebrate Mononychus olecranusHigher cognitive process OviraptoridPhysiological property SuperslasherMammal UtahraptorMammalian Velociraptor

their map locations characterize the semantics of the mapThe two hypernym-hyponym pairs ldquoobject-screwrdquo (shown inpink) and ldquoaction-withdrawalrdquo (in blue) illustrate the mapinability to capture the ldquoabstractnessrdquo dimension confirmedquantitatively by correlation analysis in the next sectionIt should be pointed out here that the negative valence ofldquoobjectrdquo can be attributed to the meaning of the verb ldquoobjectrdquothat is merged with the noun ldquoobjectrdquo on this string-basedsemantic map

22 Measuring the ldquoAbstractnessrdquo of Words Here we refer tothe ldquoabstractnessrdquo of a concept as its ontological generalityThe WordNet database contains information that allowsus to arrange English words on a line according to their

ldquoabstractnessrdquo (or ontological generality) This informationis contained in the hyponym-hypernym relations amongwords The goal is to separate hypernym-hyponym pairs inone dimension tentatively labeled ldquoabstractnessrdquo so that eachhyponym has a lower ldquoabstractnessrdquo value compared to itshypernymsGiven a consistent hierarchy a solutionwould befor example to interpret the order of a word in the hierarchyas a measure of its ldquoabstractnessrdquo Unfortunately the systemof hyponym-hypernym relations among words available inWordNet is internally inconsistent it has numerous loopsand conflicting links Therefore we use an optimizationapproach analogous to the antonymy-based weak semanticmapping based on (1) The underlying idea is to give eachword 119894 its ldquoabstractnessrdquo coordinate 119909

119894in such a way that the

overall correlation between the difference in word ldquoabstract-nessrdquo coordinates 119909 and the reciprocal hypernym-hyponymrelations of the two words is maximized Unfortunately anenergy function similar toH (1) cannot be used here becausethe symmetry of hypernym-hyponym relations is differentfrom the symmetry of antonym and synonym relationsNevertheless we showed in previous work [23] that the goalcan be achieved by using the following definition of wordldquoabstractnessrdquo values 119909

= argminR119899

[

[

119899

sum

119894119895 =1

119882119894119895(119909119894minus 119909119895minus 1)2

+ 120583

119899

sum

119894 =1

1199092

119894]

]

(2)

where 119899 is the number of words 120583 is a regularizationparameter and 119882

119894119895= 1 if the word 119894 is a hypernym of the

word j and zero otherwise Here the first sum is taken overall ordered hyponym-hypernym pairs

The publicly available WordNet 30 database (httpwordnetprincetonedu) was used in this study The hyper-nym-hyponym relations among 119899 = 124408 English wordswere extracted from the database as a connected graphdefining thematrixW whichwas used to compute the energyfunction (2) Optimization was carried out with standardMATLAB functions as described in [23]

3 Results

31 Measuring Correlations of Augmented Map DimensionsThe one-dimensional semantic map of ldquoabstractnessrdquo wascomputed as described in Section 2 The resultant distribu-tion of 124408WordNet words in one dimension is shown inFigure 2 The two ends of the sorted list of words along theirldquoabstractnessrdquo are given in Table 1

This map was then combined with several antonymy-based weak semantic maps that are previously constructed[11] The ldquoabstractnessrdquo map was merged with any givennarrow weak semantic map as the following First the set ofwords was limited to those that are common for both mapsThen the augmented map was defined as a direct sum of thetwo vector spaces that is the ldquoabstractnessrdquo dimension wasadded as a new word coordinate

The resultant augmented maps were used to com-pute the correlation between ldquoabstractnessrdquo and other map


minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

3

minus5 0 5 minus5 0 5

PC1

val

ence

PC2

arou

sal

minus4

minus2

0

2

4

PC3

free

dom

dom

inan

ce

ldquoAbstractnessrdquo ldquoAbstractnessrdquo ldquoAbstractnessrdquo

(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan

celdquoAbstractnessrdquo ldquoAbstractnessrdquo ldquoAbstractnessrdquo

(b)

Figure 3 Correlations of ldquoabstractnessrdquo with principal components of the antonymy-based weak semantic cognitive maps (a) The mapconstructed using WordNet 30 (b) the map constructed using the Microsoft Word thesaurus

Table 2 Pearson correlation coefficient 119877 and the corresponding accounted variance (1198772) of ldquoabstractnessrdquo with PC1 valence PC2 arousaland PC3 freedomdominance measured in four augmented maps constructed based onWordNet 30 and theMSWord English French andGerman thesauri

PC1 valence PC2 arousal PC3 freedom dominance119877 119877

2119877 119877

2119877 119877

2

WordNet 009 08 minus007 05 minus001 0 (NS)MSWord English 012 14 001 0 (NS) minus003 01 (NS)MSWord French 011 12 002 0 (NS) 001 0 (NS)MSWord German 014 20 minus002 0 (NS) 0 0 (NS)

dimensions The main question was how if at all is the newldquoabstractnessrdquo dimension related to the principal componentsof the antonymy-based weak semantic map Figure 3 illus-trates the scatterplots of word ldquoabstractnessrdquo values derivedfromWordNet with the dimensions of narrowweak semanticmaps derived fromWordNet data (Figure 3(a)) and fromMSWord (Figure 3(b))ThePearson correlation coefficient119877 andthe corresponding accounted variance1198772 are given in Table 2for each PC

Similar results were obtained for augmentedweak seman-tic maps in other languages (constructed based on the MSWord thesaurus as described in [11]) French (Figure 4(a))

and German (Figure 4(b)) Automated Google translationwas used to merge maps in different languages

In all cases ldquoabstractnessrdquo is only positively correlatedwith valence (119875 lt 10minus8 in all corpora) while none of thecorrelation coefficients with the other two dimensions(arousal and freedom) are statistically significant in a con-sistent way across corpora Even in the case of valence thecorrelation coefficient remains small (Table 2) This findingis further addressed in Section 4

Overall the results (Figures 3 and 4) show that the newldquoabstractnessrdquo dimension is practically orthogonal to thenarrowly defined weak semantic map dimensions Indeed


minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)

Figure 4 Correlations of ldquoabstractnessrdquo with principal components of the antonymy-based weak semantic cognitivemaps in other languages(a) The map constructed using the French dictionary of MSWord (b) The map constructed using the German dictionary of MSWord

in most cases the correlation is not significant In theminority of the cases where the correlation is statisticallysignificant the correlation coefficient is sufficiently small asto become marginal Specifically little information is lost bydisregarding the fraction of the variance of the distributionof words on the weak semantic map accounted by the wordldquoabstractnessrdquo or vice versa the fraction of the variance inthe word ldquoabstractnessrdquo accounted by the weak semantic mapdimensions (Table 2)

In conclusion the previous weak semantic map dimen-sions do not account for a substantial fraction of variance inldquoabstractnessrdquo and word ldquoabstractnessrdquo values do not accountfor a substantial fraction of variance in the distribution ofwords on antonymy-based weak semantic maps

32 Examples of Document Mapping with the AugmentedSemantic Map Traditionally only the valence dimensionis used in sentiment analysis At the same time otherdimensions including ldquoabstractnessrdquo are frequently indi-cated as useful (eg [24]) We previously applied theweak semantic map to analysis of Medline abstracts [25]As an extension of that study we now applied the aug-mented semantic map to analyze various kinds of docu-ments

Using the MS Word English narrow weak semantic mapmerged with the WordNet-based ldquoabstractnessrdquo map thispart of the study asked the following key research questionshow informative is the new dimension compared to familiardimensions at the document level Specifically how well aredifferent kinds of documents separated from each other onthe augmented map compared to the narrow weak semanticmap How capable is the new ldquoabstractnessrdquo dimensioncompared to antonymy-based dimensions in terms of doc-ument separation Being aware of more advanced methodsof sentiment analysis [21 26] here we adopted the simplestldquobag of wordsrdquo method (computing the ldquocenter of massrdquo ofwords in the document not to be confused with LSA) Thisparsimonious choice is justified because at this point we areinterested in assessing the value of the new dimension com-pared to familiar dimensions of the narrow weak semanticmap rather than achieving practically significant results

For each document the average augmented map coor-dinates of all words were computed together with thestandard error in each dimensionThe results are representedin Figure 5 by crossed ovals with the center of the crossrepresenting the average and the size of the oval representingthe standard error (ie the standard deviation divided bythe square root of the number of identified words) Thelarge black crosses in each panel represent the average ofall words in the dictionary weighted by their overall usage


1 11 12 13 14 15

02

03

04

05

06

07

Vale

nce 1

2 3

4

56

7

8

9

1011

1213


(a)

1 11 12 13 14 15

01

015

02

Aro

usal

1

2

3

4

56

7

8

9

10

11

12

13


(b)

Valence

01

015

02

Aro

usal

02 04 06 08

1

2

3

4

56

7

8

9

10

11

12

13

(c)

minus01 minus006 minus002 0

minus002

0

002

004Ri

chne

ss

Freedom

1

2

3

4

5

6

7

8

9

10

11

1213

(d)

Figure 5 Representations of 13 documents (details in the text) on the augmented semantic map The Pearson correlation coefficient 119877 andthe corresponding 119875 value were computed for each panel None of the correlations are significant (a) Valence versus ldquoabstractnessrdquo R = 054119875 = 006 (b) Arousal versus ldquoabstractnessrdquo R = 050 119875 = 009 (c) Arousal versus valence R = 054 119875 = 0057 (d) Richness (PC4) versusfreedom (PC3) R = 046 119875 = 012

frequency not limited to materials of this study and derivedas in [11] Colors and numbers of ovals in Figure 5 correspondto RGB values and item numbers given in the following list ofcorpora

(1) Project Gutenbergrsquos A Text-Book of Astronomyby George C Comstock (httpwwwgutenbergorgfiles3483434834-0txt) 9626 words rgb = (0 0 6)

(2) Martha Stewart Living Radio Thanksgivings HotlineRecipes 2011 (httpwwwhunt4freebiescomfree-martha-stewart-thanksgiving-recipes-ebook-down-load) 2091 words rgb = (0 0 9)

(3) AlQaida InspireMagazine Issue 9 (httpwwwenwi-kipediaorgwikiInspire (magazine)) 2555 wordsrgb = (0 2 10)

(4) A suicide blog (httpwwwtumblrcomtaggedsuic-ideblog) 387 words rgb = (0 5 10)

(5) 152 Shakespeare sonnets [27] 4170 words rgb = (0 810)

(6) TheHitchhikerrsquos Guide to the Galaxy by Douglas Ad-ams (httpwwwpaulyhartblogspotcom201110hi-tchhikers-guide-to-galaxy-text 28html) 4187 wordsrgb = (1 10 9)

(7) 10 abstracts of award-winning NSF grant propos-als (downloaded from httpwwwnsfgovaward-search) 585 words rgb = (4 10 6)

(8) 196 reviews of the film ldquoIronManrdquo 2008 (httpwwwmrqecommovie reviewsiron-man-m100052975)3902 words rgb = (8 10 2)

(9) 170 reviews of the film ldquoSuperhero Movierdquo 2008(httpwwwmrqecommovie reviewssuperhero-movie-m100071304) 2204 words rgb = (10 9 0)


(10) 160 reviews of the film ldquoProm Nightrdquo 2008(httpwwwmrqecommovie reviewsprom-night-m100076394) 2114 words rgb = (10 6 0)

(11) 47 anecdotes ofabout famous scientists (retri-eved from httpjcdverhahomexs4allnlscijokes10html) 919 words rgb = (10 3 0)

(12) transcript of Obamarsquos speech at the DNC onSeptember 6 2012 (httpwwwfoxnewscompoli-tics20120906transcript-obama-speech-at-dnc)491 words rgb = (10 0 0)

(13) ldquoTopological strings and their physical applica-tionsrdquo by Andrew Neitzke and Cumrun Vafa (httpwwwarxivorgabshep-th0410178v2) 1909 wordsrgb = (7 0 0)

The selected documents are mostly well separated in3 dimensions including valence (PC1) arousal (PC2) andldquoabstractnessrdquo (Figure 5) At the same time the ovals morefrequently overlap on the plane freedom-richness (PC3-PC4) Visually ldquoabstractnessrdquo is approximately as efficient asvalence (PC1) in its ability to separate documents and appearsto be more efficient than other dimensions however the ovalseparation on the valence-arousal projection (Figure 5(c))looks slightly better than on the valence-ldquoabstractnessrdquo pro-jection (Figure 5(a)) This observation suggests that disre-garding ldquoabstractnessrdquo may not significantly affect the qualityof results while disregarding valence would substantiallyimpair the quality of document separation (eg on theldquoabstractness-rdquoarousal plane Obamarsquos speech overlaps sub-stantially with the suicide blog while valence separates thetwo documents significantly)

Differences between the above 13 documents along these5 dimensions were quantified with analysis of varianceSpecifically the MANOVA 119875 value was 0027 suggesting thatall five semantic dimensions are mutually independent incharacterizing the selected 13 corpora Moreover in orderto compare how informative different semantic dimensionsare relative to each other two sets of characteristics werecomputed (Table 3) namely (i) the ANOVA119875 values to rejectthe null hypothesis that all 13 corpora have the same mean ineach selected semantic dimension and (ii) the MANOVA 119875values to reject the null hypothesis that the means of all 13corpora belong to a low-dimensional hyperplane within thespace of all but one semantic dimensions

These results can be interpreted as follows The lower the119875 value for ANOVA is the more informative the selectedsemantic dimension is On the contrary the lower the119875 valuefor MANOVA is the less informative the selected semanticdimension is because MANOVA was computed in the spaceof all semantic dimensions except the one selectedThereforeresults represented in Table 3 indicate that ldquoabstractnessrdquo(dimension 0) is nearly as informative as valence (dimension1) and could be more informative than arousal (dimension2 based on ANOVA only) freedom (dimension 3) andrichness (dimension 4) More data are needed to verify thisinterpretation

4 Discussion

Statistical analysis indicates that ldquoabstractnessrdquo is positively (ifmarginally) correlated with valence consistently across cor-pora which is not the case with other semantic dimensionsOn the one hand the amount of variance in the distributionsof words that can be attributed to interaction between valenceand ldquoabstractnessrdquo is not substantial (only 2 of varianceor less) therefore the two dimensions can be consideredorthogonal for practical purposes On the other hand theconsistent significance of this negligibly small correlationacross datasets and languages indicates that there may be auniversal factor responsible for it This factor could be theusage frequency of words that affects the probability of wordselection for dictionaries Stated simply abstract positivewords and specific negative words are used more frequentlythan abstract negative words and specific positive wordsSpecifically our previous study [11] showed that the meanvalence (normalized to unitary standard deviation) of allwords weighted by their usage frequency is significantly posi-tive (050 using frequency data from a database of Australiannewspapers and 059 using frequency data from the BritishNational Corpus) Using the results in the present study themean normalized ldquoabstractnessrdquo is between 099 (weighted byldquoAustralianrdquo frequency) and 139 (weighted by ldquoBritishrdquo fre-quency) An equivalent explanation is that abstract words andpositive words are both used more frequently than specificwords and negative words Specifically the correlation withfrequency is small but significantly positive both for valence(0064 Australian 0061 British) and for ldquoabstractnessrdquo (0036Australian 0019 British) This interpretation is consistentwith data at the level of documents (Figure 5(a)) wherethe correlation coefficient is even higher yet not significant(not shown) Another potential source of correlation is theselection of words for inclusion in dictionaries It seemshowever counterintuitive that the overall picture should beaffected bymarginal inclusions of rare words Nevertheless itwould be interesting to check elsewhere how the correlationchanges across sets of words found in various types ofdocuments

The method of weak semantic mapping is an alterna-tive to other vector-space-based approaches including LSALDA MDS and ConceptNet [1ndash4] primarily because (i)no semantic features of words are given as input and (ii)the abstract space of the map has no semantics associated apriori with its dimensions It is therefore not surprising thatemergent semantic features (dimensions) in weak semanticmapping are substantially different from emergent semanticdimensions obtained by LSAand related techniques the latterare typically domain specific and harder to interpret [22]

From another perspective it is interesting that emergentsemantic dimensions of a weak semantic map are so familiarAll generally accepted dimensional models of sentimentappraisal emotions and values attitudes feelings and soforth converge on semantics of their principal dimensionstypically interpreted as valence arousal and dominance[12ndash14 16ndash18] Antonymy-based weak semantic mappingappears to be consistent with this emergent consensus [9ndash11] despite the stark difference in methodologies (human


Table 3 ANOVA and MANOVA 119875 values for selected semantic dimensions characterizing the means of the 13 corpora Dimensions arenumbered as follows 0 ldquoabstractnessrdquo 1 PC1 (valence) 2 PC2 (arousal) 3 PC3 (freedomdominance) and 4 PC4 (richness)

Semantic Dimension 0 1 2 3 4One dimension ANOVA 12119890 minus 36 59119890 minus 57 31119890 minus 15 21119890 minus 7 62119890 minus 11

All but one MANOVA 0018 0040 0041 51119890 minus 7 14119890 minus 7

judgment or psychometrics versus automated calculationsbased on subject-independent data)The number of semanticdimensions or factors used in the literature varies from2 to 7 which roughly corresponds to the variability in thenumber of significant principal components of the narrowweak semantic map [11] Why do antonyms relating to theldquodimensionalmodelsrdquo of affect and not othersmake for goodPCs This interesting question remains open and should beaddressed by future studies

The present study unambiguously demonstrates theinability of narrow weak semantic maps to capture all univer-sal semantic dimensions Here we presented one dimensionldquoabstractnessrdquo that is not captured by ldquoantonymy-rdquo definedweak semantic maps This is due to the fact that in generalhypernym-hyponym pairs are not antonym pairs and viceversa Therefore hypernym-hyponym relations cannot becaptured with the map defined by antonym relations and themap needs to be augmented The example of ldquoabstractnessrdquothat we found is probably not unique we expect a similaroutcome for the holonym-meronym relation which will beaddressed elsewhere Our previous results indicated thatantonym relations are essential for weak semantic mappingwhile synonym relations are not [28]

Thus the present work shows that narrow weak semanticmaps (and related dimensional models of emotions) arenot complete in this sense and need to be augmented byincluding other kinds of semantic relations in their definitionA question remains open as to whether any augmentedsemantic map may be considered completemdashor there willalways be new semantic dimensions that can be added tothe map We speculate that there exists a complete finite-dimensional weak semantic map Moreover the number ofits dimensions can be relatively small This is because thenumber of distinct semantic relationships in natural languageis limited as is the number of primary categories [29] orthe number of primary semantic elements of metalanguageknown as semantic primes [31 32] This notion of ldquocomplete-nessrdquo however may only be applicable to a limited scope forexample all existing natural languages

We found that hyponym-hypernym relations induce anew semantic dimension on the weak semantic map thatis not reducible to any dimensions represented by antonympairs or to the traditional PAD or EPA dimensions Itstentative labeling as ldquoabstractnessrdquo or ontological generalityhowever remains speculative In any case it is not ourambition here to define the notion of ldquoabstractnessrdquo or toestablish a precise connection between the real notion ofabstractness and our new ldquoabstractnessrdquo dimension a topicthat should be addressed elsewhere

Findings of this study have broad implications forautomated quantitative evaluation of the meaning of text

including semantic search opinionmining sentiment analy-sis andmood sensing as exemplified in Figure 5 and Table 3While multidimensional approaches in opinion mining arenowadays popular the problem is finding good multidi-mensional ranking of all words in the dictionary Tradi-tional bootstrapping methods (eg based on cooccurrenceof words) to extend the ranking of positivity from a smallsubset of words to all words may not work for example forldquoabstractnessrdquo The approach presented here should be usefulfor such applications

Finally we speculate that this approachmay shed light onthe nature of human subjective experience [30] by revealingfundamental semantics of qualia as PCs of the weak semanticcognitive map In addition we suggest other connections ofour findings for example to semantic primes [31 32]

Acknowledgments

The authors are grateful to Mr Thomas Sheehan for helpwith extraction of the relation data from WordNet Part ofGiorgio A Ascolirsquos time was supported by the IntelligenceAdvanced Research Projects Activity (IARPA) via Depart-ment of the Interior (DOI) Contract no D10PC20021 TheUS Government is authorized to reproduce and distributereprints for governmental purposes notwithstanding anycopyright annotation thereon The views and conclusionscontained herein are those of the authors and should not beinterpreted as necessarily representing the official policies orendorsements either expressed or implied of IARPA DOIor the US Government

References

[1] T K Landauer and S T Dumais ldquoA solution to Platorsquos problemthe Latent Semantic Analysis theory of acquisition inductionand representation of knowledgerdquo Psychological Review vol104 no 2 pp 211ndash240 1997

[2] T L Griffiths and M Steyvers ldquoFinding scientific topicsrdquoProceedings of the National Academy of Sciences of the UnitedStates of America vol 101 no 1 pp 5228ndash5235 2004

[3] C Havasi R Speer and J Alonso ldquoConceptNet 3 a flexiblemultilingual semantic network for common sense knowl-edgerdquo in Proceedings of the International Conference onRecent Advances in Natural Language Processing (RANLP rsquo07)Borovets Bulgaria 2007

[4] E Cambria TMazzocco andAHussain ldquoApplication ofmulti-dimensional scaling and artificial neural networks for biologi-cally inspired opinion miningrdquo Biologically Inspired CognitiveArchitectures vol 4 pp 41ndash53 2013

[5] R F Cox and M A Cox Multidimensional Scaling Chapmanamp Hall 1994


[6] J B Tenenbaum V de Silva and J C Langford ldquoA globalgeometric framework for nonlinear dimensionality reductionrdquoScience vol 290 no 5500 pp 2319ndash2323 2000

[7] L K Saul K Q Weinberger J H Ham F Sha and DD Lee ldquoSpectral methods for dimensionality reductionrdquo inSemisupervised Learning O Chapelle B Schoelkopf and AZien Eds pp 293ndash308 MIT Press Cambridge Mass USA2006

[8] P Gardenfors Conceptual Spaces The Geometry of ThoughtMIT Press Cambridge Mass USA 2004

[9] A V Samsonovich R F Goldin and G A Ascoli ldquoToward asemantic general theory of everythingrdquo Complexity vol 15 no4 pp 12ndash18 2010

[10] A V Samsonovich and G A Ascoli ldquoCognitive map dimen-sions of the human value system extracted from natural lan-guagerdquo in Advances in Artificial General Intelligence ConceptsArchitectures and Algorithms Proceedings of the AGI Workshop2006 B Goertzel and P Wang Eds vol 157 of Frontiers inArtificial Intelligence and Applications pp 111ndash124 IOS PressAmsterdam The Netherlands 2007

[11] A V Samsonovich and G A Ascoli ldquoPrincipal semanticcomponents of language and the measurement of meaningrdquoPLoS ONE vol 5 no 6 Article ID e10921 2010

[12] E Hudlicka ldquoGuidelines for designing computational modelsof emotionsrdquo International Journal of Synthetic Emotions no 1pp 26ndash79 2011

[13] C E Osgood G Suci and P TannenbaumTheMeasurement ofMeaning University of Illinois Press Urbana Ill USA 1957

[14] J A Russell ldquoA circumplex model of affectrdquo Journal of Person-ality and Social Psychology vol 39 no 6 pp 1161ndash1178 1980

[15] R Plutchik ldquoA psychoevolutionary theory of emotionsrdquo SocialScience Information vol 21 no 4-5 pp 529ndash553 1982

[16] A Mehrabian Nonverbal Communication 2007[17] P J Lang M M Bradley and B N Cuthbert ldquoEmotion and

motivation measuring affective perceptionrdquo Journal of ClinicalNeurophysiology vol 15 no 5 pp 397ndash408 1998

[18] C E Osgood W H May and M S Miron Cross-CulturalUniversals of Affective Meaning University of Illinois PressUrbana Ill USA 1975

[19] H Lovheim ldquoA new three-dimensionalmodel for emotions andmonoamine neurotransmittersrdquoMedicalHypotheses vol 78 no2 pp 341ndash348 2012

[20] R Likert ldquoA technique for the measurement of attitudesrdquoArchives of Psychology vol 22 no 140 pp 1ndash55 1932

[21] B Pang and L Lee ldquoOpinion mining and sentiment analysisrdquoFoundations and Trends in Information Retrieval vol 2 no 1-2pp 1ndash135 2008

[22] T K Landauer D S McNamara S Dennis and W KintschEds 2007Handbook of Latent Semantic Analysis LawrenceErlbaum Associates Mahwah NJ USA

[23] A V Samsonovich ldquoA metric scale for ldquoAbstractnessrdquo of thewordmeaningrdquo in Intelligent Techniques forWebPersonalizationand Recommender Systems AAAI Technical Report WS-12-09D Jannach S S Anand B Mobasher and A Kobsa Eds pp48ndash52 The AAAI Press Menlo Park Calif USA 2012

[24] D McNamara Y Ozuru A Greasser and M LouwerseldquoValidating coh-metrixrdquo in Proceedings of the 28th AnnualConference of the cognitive Science Society R Sun and NMiyake Eds Erlbaum Mahwah NJ USA 2006

[25] A V Samsonovich and G A Ascoli ldquoComputing semantics ofpreference with a semantic cognitive map of natural language

application to mood sensing from textrdquo in MultidisciplinaryWorkshop on Advances in Preference Handling Papers from the2008 AAAI Workshop AAAI Technical Report WS-08-09 JChomicki V Conitzer U Junker and P Perny Eds pp 91ndash96AAAI Press Menlo Park Calif USA July 2008

[26] R Moraes J F Valiati and W P G Neto ldquoDocument-level sentiment classification an empirical comparison betweenSVM and ANNrdquo Expert Systems with Applications vol 40 no2 pp 621ndash633 2013

[27] W Shakespeare A Loverrsquos Complaint The Electronic TextCenter University of Virginia 16092006

[28] A V Samsonovich and C P Sherrill ldquoComparative study ofself-organizing semantic cognitive maps derived from naturallanguagerdquo in Proceedings of the 29th Annual Cognitive ScienceSociety D S McNamara and J G Trafton Eds p 1848Cognitive Science Society Austin Tex USA 2007

[29] I Kant Critique of Pure Reason vol A 51B 75 Norman KempSmith St Martins NY USA 17811965

[30] G A Ascoli and A V Samsonovich ldquoScience of the consciousmindrdquoThe Biological Bulletin vol 215 no 3 pp 204ndash215 2008

[31] A Wierzbicka Semantics Primes and Universals Oxford Uni-versity Press 1996

[32] C Goddard and A Wierzbicka ldquoSemantics and cognitionrdquoWiley Interdisciplinary Reviews Cognitive Science vol 2 no 2pp 125ndash135 2011

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



general sense as discussed below weak semantic cognitivemaps may capture other binary semantic relations as wellincluding hypernymy-hyponymy holonymy-meronymy tro-ponymy causality and dependence

While the understanding of dissimilarity as the basis ofantonymy is widespread many examples of the dictionaryantonym pairs used in our analysis suggest that dissimilarityand antonymy are distinct notions Most unrelated wordsmay be considered dissimilar (eg ldquoapplerdquo and ldquoinequalityrdquo)yet do not constitute antonym pairs In contrast antonympairs include words that are related to each other and in acertain sense are similar to each other in their meaning andusage for example king and queen major and minor andascent and descent It appears that most antonym pairs (atleast in the dictionaries that we used) are consistent with thenotion of ldquooppositerdquo rather than ldquodissimilarrdquo

More generally the method of weak semantic map-ping is essentially different from most vector-space-basedapproaches including LSA LDA MDS and ConceptNet [1ndash4] primarily because there is no a priori attribution of seman-tic features to representations in the constructive definitionof the map Only relations but not semantic features aregiven as input As a result semantic dimensions of the mapthat are not predefined to emerge naturally starting froma randomly generated initial distribution of words in anabstract space with no a priori given semantics and followingthe strategy to pull synonyms together and antonyms apart[10 11] (see Section 2 Methods) In contrast to LSA principalcomponent analysis is used here to reveal the main emergentsemantic dimensions at the final stage only The advan-tage of the antonymy-based weak semantic cognitive mapcompared to ldquostrongrdquo maps based on dissimilarity metricsis that its dimensions have clearly identifiable semantics(naturally given by the corresponding pairs of antonyms) thatare domain-independent For example the notion of ldquogoodversus badrdquo that corresponds to the first principal componentapplies to all domains of human knowledge

Interestingly semantics of the emergent dimensions ofantonym-based weak semantic cognitive maps are closelyrelated to those of another broad category of ldquodimensionalmodelsrdquo of affects [12] that attempt to capture humanemotions feelings affects appraisals sentiments and atti-tudes Examples range from original classical models suchas Osgoodrsquos semantic differential [13] Russellrsquos circumplex[14] and Plutchikrsquos wheel [15] to many more recent deriva-tive integrated frameworks like PAD (pleasure arousaland dominance) [16] ANEW (Affective Norms for EnglishWords) [17] EPA (evaluation potency and arousal) [18] anda recent 3D model linking emotions to main neurotrans-mitters [19] These dimensional models are usually derivedfrom human experimental studies involving psychometricsor introspective judgment evaluated on the Likert scale [20]While these models provide the most common bases foropinionmining or sentiment analysis [21] the weak semanticmap is more complete in the sense that (i) it assigns valuesto all words not only to emotionally meaningful words (ii)it measures semantics associated with all antonym pairs notonly emotionally meaningful antonym pairs and thereforeis applicable to all domains of knowledge and (iii) its

dimensions are orthogonal and independent of each otherThe combination of these featuresmakesweak semanticmapsextremely valuable for numerous applications

It is surprising that the well-known dimensions of thesemantic differential PAD EPA and related models canbe recognized in the main principal components (PC) ofthe above cited weak semantic map where PC1 is relatedto valence PC2 to arousal and PC3 to dominance [11](This correspondence is approximate because the principalcomponents have zero correlations with each other whilethe variables of eg ANEW are strongly correlated) Forexample ldquoloverdquo and ldquojoyrdquo have top values of valence in theaffective database ANEW and also top values of PC1 of weaksemantic cognitive mapWords like ldquoangerrdquo and ldquoexcitementrdquohave top values of arousal in the affective database ANEWand also top values of PC2 in weak semantic cognitive mapThis correspondence is consistent in weak semantic mapsconstructed based on different corpora in several majorlanguages [11] The observation is unexpected because theweak semantic map is not derived from any semantic featuresof words given a priori and is not explicitly related toemotions and feelings by its construction In fact any pair ofantonyms defines a map dimension including antonym pairsthat are not associated with affects for example ldquoabstract-specificrdquo It is also surprising that the weak semantic map islow-dimensional the number of PCs that account for 95of the variance of the multidimensional distribution typicallyvaries from 4 to 6 depending on the corpus [11]

How complete is the weak semantic map narrowlydefined only by antonym pairs Certainly at least somesemantic differences cannot be captured by antonymy rela-tions because not all concepts have antonyms (eg thenumber 921714083) Here we address a different questionwhether all universal semantic dimensions can be capturedby antonymy relations For example it may seem obvious thatcausality cannot be captured by antonymyHowever the issueis nontrivial as there are many examples of causally relatedantonyms (eg attack-defend begin-end send-receive andeven cause-effect) Thus two logical possibilities stand

(1) Antonym-based semantic maps separate representa-tions along all semantic dimensions that make sensefor all domains of knowledge Thus if there is asemantic characteristic 119883 that makes sense for alldomains of knowledge such that some concepts canbe characterized as having more 119883 than others thenthere is a direction on the narrow weak semantic mapalong which those concepts are separated based ontheir value of X

(2) The alternative there is at least one general seman-tic characteristic 119883 defined for all domains that isignored by the antonym-based weak semantic mapIn other words the variance in 119883 measured acrossall concepts is not accounted by the map coordinatesof concepts and vice versa no significant part of thevariance of the map can be accounted by X

Here we argue for (2) quantifying the notion of ldquoabstract-nessrdquo (or ontological generality) as an example of 119883 Our



minus2

minus15

minus1

minus05

0

05

1

15

2

PC1 valence

PC2

arou

sal

Good

Bad

Calm

Exciting

Screw

Tired

Action

WithdrawalObject




2 Methods




119867(x) = minus12

119873

sum

119894119895 =1

119882119894119895x119894sdot x119895+1

4

119873

sum

119894 =1

1003816100381610038161003816x1198941003816100381610038161003816

4 x isin R119873 otimesR119863 (1)








1000

2000

3000

4000

5000

6000

7000

8000

9000


Wor

d co

unts









= argminR119899

[

[

119899

sum

119894119895 =1

119882119894119895(119909119894minus 119909119895minus 1)2

+ 120583

119899

sum

119894 =1

1199092

119894]

]

(2)





3 Results





minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

3


PC1

val

ence

PC2

arou

sal

minus4

minus2

0

2

4

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)




2119877 119877

2119877 119877

2








minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)








1 11 12 13 14 15

02

03

04

05

06

07

Vale

nce 1

2 3

4

56

7

8

9

1011

1213


(a)

1 11 12 13 14 15

01

015

02

Aro

usal

1

2

3

4

56

7

8

9

10

11

12

13


(b)

Valence

01

015

02

Aro

usal

02 04 06 08

1

2

3

4

56

7

8

9

10

11

12

13

(c)


minus002

0

002

004Ri

chne

ss

Freedom

1

2

3

4

5

6

7

8

9

10

11

1213

(d)




















4 Discussion















Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





minus2

minus15

minus1

minus05

0

05

1

15

2

PC1 valence

PC2

arou

sal

Good

Bad

Calm

Exciting

Screw

Tired

Action

WithdrawalObject




2 Methods




119867(x) = minus12

119873

sum

119894119895 =1

119882119894119895x119894sdot x119895+1

4

119873

sum

119894 =1

1003816100381610038161003816x1198941003816100381610038161003816

4 x isin R119873 otimesR119863 (1)








1000

2000

3000

4000

5000

6000

7000

8000

9000


Wor

d co

unts









= argminR119899

[

[

119899

sum

119894119895 =1

119882119894119895(119909119894minus 119909119895minus 1)2

+ 120583

119899

sum

119894 =1

1199092

119894]

]

(2)





3 Results





minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

3


PC1

val

ence

PC2

arou

sal

minus4

minus2

0

2

4

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)




2119877 119877

2119877 119877

2








minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)








1 11 12 13 14 15

02

03

04

05

06

07

Vale

nce 1

2 3

4

56

7

8

9

1011

1213


(a)

1 11 12 13 14 15

01

015

02

Aro

usal

1

2

3

4

56

7

8

9

10

11

12

13


(b)

Valence

01

015

02

Aro

usal

02 04 06 08

1

2

3

4

56

7

8

9

10

11

12

13

(c)


minus002

0

002

004Ri

chne

ss

Freedom

1

2

3

4

5

6

7

8

9

10

11

1213

(d)




















4 Discussion















Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





1000

2000

3000

4000

5000

6000

7000

8000

9000


Wor

d co

unts









= argminR119899

[

[

119899

sum

119894119895 =1

119882119894119895(119909119894minus 119909119895minus 1)2

+ 120583

119899

sum

119894 =1

1199092

119894]

]

(2)





3 Results





minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

3


PC1

val

ence

PC2

arou

sal

minus4

minus2

0

2

4

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)




2119877 119877

2119877 119877

2








minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan

ce


(a)

minus5 0 5minus3

minus2

minus1

0

1

2

3

minus2

minus1

0

1

2

minus2

minus1

0

1

2


PC1

val

ence

PC2

arou

sal

PC3

free

dom

dom

inan


(b)








1 11 12 13 14 15

02

03

04

05

06

07

Vale

nce 1

2 3

4

56

7

8

9

1011

1213


(a)

1 11 12 13 14 15

01

015

02

Aro

usal

1

2

3

4

56

7

8

9

10

11

12

13


(b)

Valence

01

015

02

Aro

usal

02 04 06 08

1

2

3

4

56

7

8

9

10

11

12

13

(c)


minus002

0

002

004Ri

chne

ss

Freedom

1

2

3

4

5

6

7

8

9

10

11

1213

(d)




















4 Discussion















Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




minus5 0 5minus3

minus2

minus1

0

1

2

3

minus3

minus2

minus1

0

1

2

3


PC1

val

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Advances in

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Volume 2014












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Advances in

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Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




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Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











4 Discussion















Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in














Acknowledgments


References










































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










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Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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