{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T07:27:43Z","timestamp":1772695663494,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T00:00:00Z","timestamp":1730678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>We perform a sentence-level sentiment analysis study of different literary texts in English language. Each text is converted into a series in which the data points are the sentiment value of each sentence obtained using the sentiment analysis tool (VADER). By applying the Detrended Fluctuation Analysis (DFA) and the Higuchi Fractal Dimension (HFD) methods to these sentiment series, we find that they are monofractal with long-term correlations, which can be explained by the fact that the writing process has memory by construction, with a sentiment evolution that is self-similar. Furthermore, we discretize these series by applying a classification approach which transforms the series into a one on which each data point has only three possible values, corresponding to positive, neutral or negative sentiments. We map these three-states series to a Markov chain and investigate the transitions of sentiment from one sentence to the next, obtaining a state transition matrix for each book that provides information on the probability of transitioning between sentiments from one sentence to the next. This approach shows that there are biases towards increasing the probability of switching to neutral or positive sentences. The two approaches supplement each other, since the long-term correlation approach allows a global assessment of the sentiment of the book, while the state transition matrix approach provides local information about the sentiment evolution along the text.<\/jats:p>","DOI":"10.3390\/info15110698","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T10:57:20Z","timestamp":1730717840000},"page":"698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Correlations and Fractality in Sentence-Level Sentiment Analysis Based on VADER for Literary Texts"],"prefix":"10.3390","volume":"15","author":[{"given":"Ricardo","family":"Hern\u00e1ndez-P\u00e9rez","sequence":"first","affiliation":[{"name":"Escuela Superior de F\u00edsica y Matem\u00e1ticas, Instituto Polit\u00e9cnico Nacional, Edif. 9, 2o. Piso, UP Zacatenco, Mexico City 07738, Mexico"}]},{"given":"Pablo","family":"Lara-Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3079-3166","authenticated-orcid":false,"given":"Bibiana","family":"Obreg\u00f3n-Quintana","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8842-163X","authenticated-orcid":false,"given":"Larry S.","family":"Liebovitch","sequence":"additional","affiliation":[{"name":"Department of Physics, Queens College, City University of New York, New York, NY 11367, USA"},{"name":"Advanced Consortium on Cooperation, Conflict and Complexity (AC4), Climate School, Columbia University, New York, NY 10027, USA"}]},{"given":"Lev","family":"Guzm\u00e1n-Vargas","sequence":"additional","affiliation":[{"name":"Unidad Interdisciplinaria en Ingenier\u00eda y Tecnolog\u00edas Avanzadas, Instituto Polit\u00e9cnico Nacional, Av. IPN No. 2580, L. Ticom\u00e1n, Mexico City 07340, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s10902-009-9150-9","article-title":"Measuring the Happiness of Large-Scale Written Expression: Songs, Blogs, and Presidents","volume":"11","author":"Dodds","year":"2010","journal-title":"J. Happiness Stud."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dodds, P.S., Harris, K.D., Kloumann, I.M., Bliss, C.A., and Danforth, C.M. (2011). Temporal Patterns of Happiness and Information in a Global Social Network: Hedonometrics and Twitter. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0026752"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2936","DOI":"10.1016\/j.physa.2011.03.040","article-title":"Negative emotions boost user activity at BBC forum","volume":"390","author":"Chmiel","year":"2011","journal-title":"Physica A Stat. Mech. Its Appl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chmiel, A., Sienkiewicz, J., Thelwall, M., Paltoglou, G., Buckley, K., Kappas, A., and Ho\u0142yst, J.A. (2011). Collective Emotions Online and Their Influence on Community Life. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0022207"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5731","DOI":"10.1007\/s10462-022-10144-1","article-title":"A survey on sentiment analysis methods, applications, and challenges","volume":"55","author":"Wankhade","year":"2022","journal-title":"Artif. Intell. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1111\/j.1467-8640.2012.00456.x","article-title":"Emotions in text: Dimensional and categorical models","volume":"29","author":"Calvo","year":"2013","journal-title":"Comput. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jain, M., Jindal, R., and Jain, A. (2023). Building Domain-Specific Sentiment Lexicon Using Random Walk-Based Model on Common-Sense Semantic Network. International Conference on Innovative Computing and Communication, Springer.","DOI":"10.1007\/978-981-99-3010-4_17"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Cambria, E., Poria, S., Hazarika, D., and Kwok, K. (2018, January 2\u20137). SenticNet 5: Discovering conceptual primitives for sentiment analysis by means of context embeddings. Proceedings of the AAAI Conference on Artificial Intelligence, New Orleans, LA, USA.","DOI":"10.1609\/aaai.v32i1.11559"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MCI.2019.2954667","article-title":"How intense are you? Predicting intensities of emotions and sentiments using stacked ensemble [application notes]","volume":"15","author":"Akhtar","year":"2020","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s13278-021-00776-6","article-title":"A review on sentiment analysis and emotion detection from text","volume":"11","author":"Nandwani","year":"2021","journal-title":"Soc. Netw. Anal. Min."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.ins.2021.08.052","article-title":"A multi-dimensional relation model for dimensional sentiment analysis","volume":"579","author":"Xie","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s13278-022-01016-1","article-title":"Perceptible sentiment analysis of students\u2019 WhatsApp group chats in valence, arousal, and dominance space","volume":"13","author":"Roy","year":"2022","journal-title":"Soc. Netw. Anal. Min."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7445","DOI":"10.1007\/s11760-024-03406-8","article-title":"Enhanced speech emotion recognition using averaged valence arousal dominance mapping and deep neural networks","volume":"18","author":"Rizhinashvili","year":"2024","journal-title":"Signal Image Video Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"102412","DOI":"10.1016\/j.ipm.2020.102412","article-title":"SentiDraw: Using star ratings of reviews to develop domain specific sentiment lexicon for polarity determination","volume":"58","author":"Sharma","year":"2021","journal-title":"Inf. Process. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Baldwin, J., Brunsdon, T., Gaudoin, J., and Hirsch, L. (2024, May 27). Comparative Analysis of Lexicon-Based Sentiment Analysis Methods. Available online: https:\/\/ssrn.com\/abstract=4531226.","DOI":"10.2139\/ssrn.4531226"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2003","DOI":"10.1609\/icwsm.v18i1.31443","article-title":"sentibank: A Unified Resource of Sentiment Lexicons and Dictionaries","volume":"18","author":"Oh","year":"2024","journal-title":"Proc. Int. AAAI Conf. Web Soc. Media"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ophir, Y., and Walter, D. (2023). Computational Sentiment Analysis. Emotions in the Digital World: Exploring Affective Experience and Expression in Online Interactions, Oxford University Press.","DOI":"10.1093\/oso\/9780197520536.003.0007"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1162\/COLI_a_00049","article-title":"Lexicon-based methods for sentiment analysis","volume":"37","author":"Taboada","year":"2011","journal-title":"Comput. Linguist."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.dss.2016.11.001","article-title":"Adapting sentiment lexicons to domain-specific social media texts","volume":"94","author":"Deng","year":"2017","journal-title":"Decis. Support Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.procs.2017.10.101","article-title":"Developing resources for sentiment analysis of informal Arabic text in social media","volume":"117","author":"Itani","year":"2017","journal-title":"Procedia Comput. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Thelwall, M. (2017). The Heart and Soul of the Web? Sentiment Strength Detection in the Social Web with SentiStrength. Cyberemotions. Understanding Complex Systems, Springer.","DOI":"10.1007\/978-3-319-43639-5_7"},{"key":"ref_22","unstructured":"Sebastiani, F., and Esuli, A. (2006, January 22\u201328). Sentiwordnet: A publicly available lexical resource for opinion mining. Proceedings of the 5th International Conference on Language Resources and Evaluation, Genoa, Italy."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.asoc.2015.11.016","article-title":"SentiMI: Introducing point-wise mutual information with SentiWordNet to improve sentiment polarity detection","volume":"39","author":"Khan","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.3758\/s13428-012-0314-x","article-title":"Norms of valence, arousal, and dominance for 13,915 English lemmas","volume":"45","author":"Warriner","year":"2013","journal-title":"Behav. Res. Methods"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1145\/3489141","article-title":"Chinese EmoBank: Building Valence-Arousal Resources for Dimensional Sentiment Analysis","volume":"21","author":"Lee","year":"2022","journal-title":"ACM Trans. Asian Low-Resour. Lang. Inf. Process."},{"key":"ref_26","unstructured":"Bradley, M., and Lang, P.J. (1999). Affective Norms for English Words (ANEW): Instruction Manual and Affective Ratings, The Center for Research in Psychophysiology, University of Florida. Available online: https:\/\/pdodds.w3.uvm.edu\/teaching\/courses\/2009-08UVM-300\/docs\/others\/everything\/bradley1999a.pdf."},{"key":"ref_27","unstructured":"Nielsen, F.\u00c5. (2011). A new ANEW: Evaluation of a word list for sentiment analysis in microblogs. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1140\/epjds\/s13688-016-0085-1","article-title":"SentiBench\u2014A benchmark comparison of state-of-the-practice sentiment analysis methods","volume":"5","author":"Ribeiro","year":"2016","journal-title":"EPJ Data Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1609\/icwsm.v8i1.14550","article-title":"VADER: A Parsimonious Rule-Based Model for Sentiment Analysis of Social Media Text","volume":"8","author":"Hutto","year":"2014","journal-title":"Proc. Int. AAAI Conf. Web Soc. Media"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1140\/epjds3","article-title":"Positive words carry less information than negative words","volume":"1","author":"Garcia","year":"2012","journal-title":"EPJ Data Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Kloumann, I.M., Danforth, C.M., Harris, K.D., Bliss, C.A., and Dodds, P.S. (2012). Positivity of the English Language. PLoS ONE, 7.","DOI":"10.1371\/journal.pone.0029484"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yuri, B., and Pascale, F. (2024). Sentiment Analysis for Literary Texts: Hemingway as a Case-study. J. Data Min. Digit. Humanit., NLP4DH.","DOI":"10.46298\/jdmdh.13155"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Yeruva, V.K., Chandrashekar, M., Lee, Y., Rydberg-Cox, J., Blanton, V., and Oyler, N.A. (2020, January 12). Interpretation of sentiment analysis in aeschylus\u2019s Greek tragedy. Proceedings of the 4th Joint SIGHUM Workshop on Computational Linguistics for Cultural Heritage, Social Sciences, Humanities and Literature, Barcelona, Spain.","DOI":"10.1109\/BigData50022.2020.9378221"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Vinodini, S. (2023, January 14\u201315). Analyzing Sentiments in Paulo Coelho\u2019s Literary Works Using VADER Sentiment Analysis. Proceedings of the 2023 International Conference on Innovative Computing, Intelligent Communication and Smart Electrical Systems (ICSES), Chennai, India.","DOI":"10.1109\/ICSES60034.2023.10465319"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"031108","DOI":"10.1103\/PhysRevE.86.031108","article-title":"Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series","volume":"86","author":"Ausloos","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.physa.2014.07.063","article-title":"Scale and time dependence of serial correlations in word-length time series of written texts","volume":"414","author":"Rodriguez","year":"2014","journal-title":"Physica A Stat. Mech. Its Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7798","DOI":"10.3390\/e17117798","article-title":"Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis","volume":"17","author":"Liebovitch","year":"2015","journal-title":"Entropy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.ins.2015.10.023","article-title":"Quantifying origin and character of long-range correlations in narrative texts","volume":"331","author":"Kulig","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"113934","DOI":"10.1016\/j.chaos.2023.113934","article-title":"Semantic and sentiment trajectories of literary masterpieces","volume":"175","author":"Gromov","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1016\/j.chaos.2012.06.016","article-title":"Measuring complexity with multifractals in texts. Translation effects","volume":"45","author":"Ausloos","year":"2012","journal-title":"Chaos Solitons Fractals"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11071-022-07202-2","article-title":"Generalization of Higuchi\u2019s fractal dimension for multifractal analysis of time series with limited length","volume":"108","author":"Donner","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0167-2789(88)90081-4","article-title":"Approach to an irregular time series on the basis of the fractal theory","volume":"31","author":"Higuchi","year":"1988","journal-title":"Physica D Nonlinear Phenom."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1103\/PhysRevE.49.1685","article-title":"Mosaic organization of DNA nucleotides","volume":"49","author":"Peng","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3825","DOI":"10.1073\/pnas.1100760108","article-title":"Rethinking language: How probabilities shape the words we use","volume":"108","author":"Griffths","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1017\/S0269889706001074","article-title":"An Example of Statistical Investigation of the Text Eugene Onegin Concerning the Connection of Samples in Chains","volume":"19","author":"Markov","year":"2006","journal-title":"Sci. Context"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0378-3758(98)00249-3","article-title":"Self-affine time series: Measures of weak and strong persistence","volume":"80","author":"Malamud","year":"1999","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1103\/PhysRevLett.70.1343","article-title":"Long-range anti-correlations and non- Gaussian Behavior of the heartbeat","volume":"70","author":"Peng","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"4991","DOI":"10.1103\/PhysRevE.61.4991","article-title":"Integrated approach to the assessment of long range correlation in time series data","volume":"61","author":"Rangarajan","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/0167-2789(90)90039-R","article-title":"Relationship between the fractal dimension and the power law index for a time series: A numerical investigation","volume":"46","author":"Higuchi","year":"1990","journal-title":"Physica D Nonlinear Phenom."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"052901","DOI":"10.1103\/PhysRevE.67.052901","article-title":"Simple model of the aging effect in heart interbeat time series","volume":"67","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1063\/1.166141","article-title":"Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series","volume":"5","author":"Peng","year":"1995","journal-title":"Chaos"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/j.physa.2005.02.053","article-title":"Multifractal fluctuations in seismic interspike series","volume":"354","author":"Telesca","year":"2005","journal-title":"Physica A Stat. Mech. Its Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"5080","DOI":"10.1016\/j.physa.2008.04.023","article-title":"Comparison of detrending methods for fluctuation analysis","volume":"387","author":"Bashan","year":"2008","journal-title":"Physica A Stat. Mech. Its Appl."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Feder, J. (1988). Fractals, Springer.","DOI":"10.1007\/978-1-4899-2124-6"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2389","DOI":"10.1073\/pnas.1411678112","article-title":"Human language reveals a universal positivity bias","volume":"112","author":"Dodds","year":"2015","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Yang, T., Gu, C., and Yang, H. (2016). Long-range correlations in sentence series from a story of the stone. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0162423"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Bizzoni, Y., Moreira, P., Thomsen, M.R., and Nielbo, K.L. (2022, January 20). The fractality of sentiment arcs for literary quality assessment: The case of Nobel laureates. Proceedings of the 2nd International Workshop on Natural Language Processing for Digital Humanities, Taipei, Taiwan.","DOI":"10.18653\/v1\/2022.nlp4dh-1.5"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"9424","DOI":"10.1073\/pnas.0502613102","article-title":"Scaling and memory in volatility return intervals in financial markets","volume":"102","author":"Yamasaki","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_60","first-page":"68006","article-title":"Evolution in time and scales of the stability of heart interbeat rate","volume":"92","year":"2011","journal-title":"Europhys. Lett."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"38008","DOI":"10.1209\/0295-5075\/89\/38008","article-title":"Scaling properties of excursions in heartbeat dynamics","volume":"89","year":"2010","journal-title":"Europhys. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D graphics environment","volume":"9","author":"Hunter","year":"2007","journal-title":"Comput. Sci. Eng."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/11\/698\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:28:05Z","timestamp":1760113685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/15\/11\/698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,4]]},"references-count":62,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["info15110698"],"URL":"https:\/\/doi.org\/10.3390\/info15110698","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,4]]}}}