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Journal articles on the topic 'Dimensionality'

To see the other types of publications on this topic, follow the link: Dimensionality.

Author: Grafiati

Published: 4 June 2021

Last updated: 13 April 2024

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1

Nandakumar, Ratna. "Traditional Dimensionality Versus Essential Dimensionality." Journal of Educational Measurement 28, no. 2 (June 1991): 99–117. http://dx.doi.org/10.1111/j.1745-3984.1991.tb00347.x.

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2

Warfield, J. N., and A. N. Christakis. "Dimensionality." Systems Research 4, no. 2 (June 1987): 127–37. http://dx.doi.org/10.1002/sres.3850040207.

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3

Li, Hongda, Jian Cui, Xinle Zhang, Yongqi Han, and Liying Cao. "Dimensionality Reduction and Classification of Hyperspectral Remote Sensing Image Feature Extraction." Remote Sensing 14, no. 18 (September 13, 2022): 4579. http://dx.doi.org/10.3390/rs14184579.

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Terrain classification is an important research direction in the field of remote sensing. Hyperspectral remote sensing image data contain a large amount of rich ground object information. However, such data have the characteristics of high spatial dimensions of features, strong data correlation, high data redundancy, and long operation time, which lead to difficulty in image data classification. A data dimensionality reduction algorithm can transform the data into low-dimensional data with strong features and then classify the dimensionally reduced data. However, most classification methods cannot effectively extract dimensionality-reduced data features. In this paper, different dimensionality reduction and machine learning supervised classification algorithms are explored to determine a suitable combination method of dimensionality reduction and classification for hyperspectral images. Soft and hard classification methods are adopted to achieve the classification of pixels according to diversity. The results show that the data after dimensionality reduction retain the data features with high overall feature correlation, and the data dimension is drastically reduced. The dimensionality reduction method of unified manifold approximation and projection and the classification method of support vector machine achieve the best terrain classification with 99.57% classification accuracy. High-precision fitting of neural networks for soft classification of hyperspectral images with a model fitting correlation coefficient (R2) of up to 0.979 solves the problem of mixed pixel decomposition.

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4

Schwartz, M. A., and C. S. Chen. "Deconstructing Dimensionality." Science 339, no. 6118 (January 24, 2013): 402–4. http://dx.doi.org/10.1126/science.1233814.

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5

Verberck, Bart. "Dimensionality matters." Nature Physics 12, no. 4 (April 2016): 287. http://dx.doi.org/10.1038/nphys3726.

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6

Wojcieszak, Magdalena E. "Three Dimensionality." Television & New Media 10, no. 6 (September 2009): 459–81. http://dx.doi.org/10.1177/1527476409343798.

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7

Sharma, Sunil. "The Dimensionality." Volume 5 - 2020, Issue 9 - September 5, no. 9 (September 17, 2020): 166–69. http://dx.doi.org/10.38124/ijisrt20sep168.

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This thesis is all about dimensions and the law of Visual, Physical and Time (V,P,T) dimension which succeed to discovered more than 9 dimension (with examples) which includes current three spatial dimensions as well. General idea of the law is to show that the Dimensions are categorized by phases not by sequences, and Visual, Physical, and Time are the phases the contains their own specific dimensions e.g. Initial Dimensions like Length, Mass and Infinite Time, respectively. Although this paper covers some of the major topics which are (i) Non-Existence of 4th dimension, (ii) Understanding the law of VPT Dimension (iii) Types (iv) Phases (v) Rules of Representation (vi) General term and Numerical term, (vii) Human Dimension, and some uses. This research can be used in various fields like physics, cosmology studies, mathematics, architecture, etc. which generates massive impact on science development. The topics which are not entertain in this paper are Dimensional formula, some theories claim higher dimensions and higher dimensions like 5th 6th and so on

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8

Pestov, Vladimir. "Intrinsic dimensionality." SIGSPATIAL Special 2, no. 2 (July 2010): 8–11. http://dx.doi.org/10.1145/1862413.1862416.

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9

Goren, Paul. "Dimensionality Redux." Political Research Quarterly 61, no. 1 (March 2008): 162–64. http://dx.doi.org/10.1177/1065912907308653.

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10

Shelah, Saharon. "Multi-dimensionality." Israel Journal of Mathematics 74, no. 2-3 (October 1991): 281–88. http://dx.doi.org/10.1007/bf02775792.

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11

Albeverio, Sergio, Iryna Garko, Muslem Ibragim, and Grygoriy Torbin. "Non-normal numbers: Full Hausdorff dimensionality vs zero dimensionality." Bulletin des Sciences Mathématiques 141, no. 2 (March 2017): 1–19. http://dx.doi.org/10.1016/j.bulsci.2016.04.001.

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12

Brunet, Olivier. "Orthogonality and Dimensionality." Axioms 2, no. 4 (December 13, 2013): 477–89. http://dx.doi.org/10.3390/axioms2040477.

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13

Sidharth, B. G. "Scale dependent dimensionality." Chaos, Solitons & Fractals 12, no. 7 (June 2001): 1369–70. http://dx.doi.org/10.1016/s0960-0779(00)00095-3.

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14

Sidharth, B. G. "Dimensionality and fractals." Chaos, Solitons & Fractals 14, no. 6 (October 2002): 831–38. http://dx.doi.org/10.1016/s0960-0779(02)00028-0.

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15

Kitchen, Philip J. "Diversity, Dimensionality, Distinctiveness." Journal of Marketing Communications 24, no. 1 (December 8, 2017): 1–2. http://dx.doi.org/10.1080/13527266.2018.1409948.

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16

Kapsou, Margarita, Georgia Panayiotou, Constantinos M. Kokkinos, and Andreas G. Demetriou. "Dimensionality of Coping." Journal of Health Psychology 15, no. 2 (March 2010): 215–29. http://dx.doi.org/10.1177/1359105309346516.

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17

Aihara, Jun-ichi. "Dimensionality of Aromaticity." Bulletin of the Chemical Society of Japan 81, no. 2 (February 15, 2008): 241–47. http://dx.doi.org/10.1246/bcsj.81.241.

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18

Rovny, Jan, and Erica E. Edwards. "Struggle over Dimensionality." East European Politics and Societies: and Cultures 26, no. 1 (January 18, 2012): 56–74. http://dx.doi.org/10.1177/0888325410387635.

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This article analyzes the impact of party strategies on the issue structure, and consequently the dimensional structure, of party systems across Europe. Conceptualizing political competition in two dimensions (economic left-right and social traditionalism versus liberalism), the authors demonstrate that political parties in both Eastern and Western Europe contest the issue composition of political space. The authors argue that large, mainstream parties are invested in the dimensional status quo, preferring to compete on the primary dimension by emphasizing economic issues. Systematically disadvantaged niche parties, conversely, prefer to compete along a secondary dimension by stressing social issues. Adopting such a strategy enables niche parties to divert voter attention and challenge the structure of conflict between the major partisan competitors. The authors test these propositions using the 2006 iteration of the Chapel Hill Expert Surveys on Party Positions. Findings indicate that while the structure of political conflict in Eastern versus Western Europe could not be more different, the logic with which parties compete in their respective systems is the same. The authors conclude that political competition is primarily a struggle over dimensionality; it does not merely occur along issue dimensions but also over their content.

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19

Marchette, David J., and Wendy L. Poston. "Local dimensionality reduction." Computational Statistics 14, no. 4 (September 12, 1999): 469–89. http://dx.doi.org/10.1007/s001800050026.

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20

Bajorski, Peter. "Second Moment Linear Dimensionality as an Alternative to Virtual Dimensionality." IEEE Transactions on Geoscience and Remote Sensing 49, no. 2 (February 2011): 672–78. http://dx.doi.org/10.1109/tgrs.2010.2057434.

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21

Cheng, Long, Chenyu You, and Yani Guan. "Random Projections for Non-linear Dimensionality Reduction." International Journal of Machine Learning and Computing 6, no. 4 (August 2016): 220–25. http://dx.doi.org/10.18178/ijmlc.2016.6.4.601.

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22

Shen, Zilin. "Comparison and Evaluation of Classical Dimensionality Reduction Methods." Highlights in Science, Engineering and Technology 70 (November 15, 2023): 411–18. http://dx.doi.org/10.54097/hset.v70i.13890.

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As one of the tasks of unsupervised learning, data dimensionality reduction is faced with the problem of a lack of evaluation methods. Based on this, three classical dimensionality reduction methods such as PCA, t-SNE and UMAP were selected as the research object in this paper. This article selected 5 three-classification datasets and used the three methods mentioned above to perform dimensionality reduction. This paper plotted 3D scatter graphs after dimensionality reduction to analyze the differentiation effect of the data on different categories of the target variable. Then the data after dimensionality reduction was classified using random forest model and the classification accuracy was obtained. According to the 3D scatter plots and the accuracy of random forest, it is found that PCA has a good dimensionality reduction effect on most of the selected datasets, and t-SNE has a relatively stable dimensionality reduction effect. In contrast, UMAP has good dimensionality reduction performance in some individual datasets but lacks stability. Overall, this paper proposes a dimensionality reduction evaluation method that combines scatter-plot visualization results and classification models, which can effectively predict the performances of the dimensionality reduction methods for a variety of datasets, thereby promoting the comparison and selection of dimensionality reduction methods in the field of unsupervised learning.

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23

Жихарев, Л., and L. Zhikharev. "Fractal Dimensionalities." Geometry & Graphics 6, no. 3 (November 14, 2018): 33–48. http://dx.doi.org/10.12737/article_5bc45918192362.77856682.

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One of the most important characteristics of a fractal is its dimensionality. In general, there are several options for mathematical definition of this value, but usually under the object dimensionality is understood the degree of space filling by it. It is necessary to distinguish the dimensionality of space and the dimension of multitude. Segment, square and cube are objects with dimensionality 1, 2 and 3, which can be in respective spaces: on a straight line, plane or in a 3D space. Fractals can have a fractional dimensionality. By definition, proposed by Bernois Mandelbrot, this fractional dimensionality should be less than the fractal’s topological dimension. Abram Samoilovich Bezikovich (1891–1970) was the author of first mathematical conclusions based on Felix Hausdorff (1868–1942) arguments and allowing determine the fractional dimensionality of multitudes. Bezikovich – Hausdorff dimensionality is determined through the multitude covering by unity elements. In practice, it is more convenient to use Minkowsky dimensionality for determining the fractional dimensionalities of fractals. There are also numerical methods for Minkowsky dimensionality calculation. In this study various approaches for fractional dimensionality determining are tested, dimensionalities of new fractals are defined. A broader view on the concept of dimensionality is proposed, its dependence on fractal parameters and interpretation of fractal sets’ structure are determined. An attempt for generalization of experimental dependences and determination of general regularities for fractals structure influence on their dimensionality is realized. For visualization of three-dimensional geometrical constructions, and plain evidence of empirical hypotheses were used computer models developed in the software for three-dimensional modeling (COMPASS, Inventor and SolidWorks), calculations were carried out in mathematical packages such as Wolfram Mathematica.

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24

Lehky, Sidney R., Roozbeh Kiani, Hossein Esteky, and Keiji Tanaka. "Dimensionality of Object Representations in Monkey Inferotemporal Cortex." Neural Computation 26, no. 10 (October 2014): 2135–62. http://dx.doi.org/10.1162/neco_a_00648.

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We have calculated the intrinsic dimensionality of visual object representations in anterior inferotemporal (AIT) cortex, based on responses of a large sample of cells stimulated with photographs of diverse objects. Because dimensionality was dependent on data set size, we determined asymptotic dimensionality as both the number of neurons and number of stimulus image approached infinity. Our final dimensionality estimate was 93 (SD: [Formula: see text] 11), indicating that there is basis set of approximately 100 independent features that characterize the dimensions of neural object space. We believe this is the first estimate of the dimensionality of neural visual representations based on single-cell neurophysiological data. The dimensionality of AIT object representations was much lower than the dimensionality of the stimuli. We suggest that there may be a gradual reduction in the dimensionality of object representations in neural populations going from retina to inferotemporal cortex as receptive fields become increasingly complex.

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25

Calderón, Dolores. "One-Dimensionality and Whiteness." Policy Futures in Education 4, no. 1 (March 2006): 73–82. http://dx.doi.org/10.2304/pfie.2006.4.1.73.

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26

Hansen, William. "Myth and One-Dimensionality." Humanities 6, no. 4 (December 14, 2017): 99. http://dx.doi.org/10.3390/h6040099.

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27

Sun, Yu-Yin, Michael Ng, and Zhi-Hua Zhou. "Multi-Instance Dimensionality Reduction." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 3, 2010): 587–92. http://dx.doi.org/10.1609/aaai.v24i1.7700.

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Multi-instance learning deals with problems that treat bags of instances as training examples. In single-instance learning problems, dimensionality reduction is an essential step for high-dimensional data analysis and has been studied for years. The curse of dimensionality also exists in multiinstance learning tasks, yet this difficult task has not been studied before. Direct application of existing single-instance dimensionality reduction objectives to multi-instance learning tasks may not work well since it ignores the characteristic of multi-instance learning that the labels of bags are known while the labels of instances are unknown. In this paper, we propose an effective model and develop an efficient algorithm to solve the multi-instance dimensionality reduction problem. We formulate the objective as an optimization problem by considering orthonormality and sparsity constraints in the projection matrix for dimensionality reduction, and then solve it by the gradient descent along the tangent space of the orthonormal matrices. We also propose an approximation for improving the efficiency. Experimental results validate the effectiveness of the proposed method.

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28

Danesi, Marcel. "The dimensionality of metaphor." Sign Systems Studies 27 (December 31, 1999): 60–87. http://dx.doi.org/10.12697/sss.1999.27.04.

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29

Marcuse, Peter. "Marcuse’s Concept of Dimensionality." Radical Philosophy Review 20, no. 1 (2017): 31–47. http://dx.doi.org/10.5840/radphilrev201741869.

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30

金聖京. "Dimensionality of Japanese Noun." Journal of Japanese Culture ll, no. 35 (November 2007): 23–34. http://dx.doi.org/10.21481/jbunka..35.200711.23.

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31

Koren, Y., and L. Carmel. "Robust linear dimensionality reduction." IEEE Transactions on Visualization and Computer Graphics 10, no. 4 (July 2004): 459–70. http://dx.doi.org/10.1109/tvcg.2004.17.

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32

Ouma, Christopher EW. "Literacy and three-dimensionality." Scrutiny2 17, no. 2 (September 2012): 138–43. http://dx.doi.org/10.1080/18125441.2012.747770.

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33

Wu, Qihan, Aenne Brielmann, Mika Simoncelli, and Denis Pelli. "The dimensionality of beauty." Journal of Vision 18, no. 10 (September 1, 2018): 1326. http://dx.doi.org/10.1167/18.10.1326.

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34

Schmelkin, Liora P. "Dimensionality of disability labels." Rehabilitation Psychology 30, no. 4 (1985): 221–33. http://dx.doi.org/10.1037/0090-5550.30.4.221.

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35

Zhai, Yiteng, Yew-Soon Ong, and Ivor W. Tsang. "The Emerging "Big Dimensionality"." IEEE Computational Intelligence Magazine 9, no. 3 (August 2014): 14–26. http://dx.doi.org/10.1109/mci.2014.2326099.

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36

Walker, Cindy M., Razia Azen, and Thomas Schmitt. "Statistical Versus Substantive Dimensionality." Educational and Psychological Measurement 66, no. 5 (October 2006): 721–38. http://dx.doi.org/10.1177/0013164405285907.

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37

Doxas, I., S. Dennis, and W. L. Oliver. "The dimensionality of discourse." Proceedings of the National Academy of Sciences 107, no. 11 (March 1, 2010): 4866–71. http://dx.doi.org/10.1073/pnas.0908315107.

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38

Patel, Niketu P., Elie Sarraf, and Mitchell H. Tsai. "The Curse of Dimensionality." Anesthesiology 129, no. 3 (September 1, 2018): 614–15. http://dx.doi.org/10.1097/aln.0000000000002350.

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39

Lotlikar, R., and R. Kothari. "Fractional-step dimensionality reduction." IEEE Transactions on Pattern Analysis and Machine Intelligence 22, no. 6 (June 2000): 623–27. http://dx.doi.org/10.1109/34.862200.

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40

Amitrano, C. "Fractal dimensionality for theηmodel." Physical Review A 39, no. 12 (June 1, 1989): 6618–20. http://dx.doi.org/10.1103/physreva.39.6618.

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41

Schmelkin, Liora P. "Dimensionality of disability labels." Rehabilitation Psychology 30, no. 4 (1985): 221–33. http://dx.doi.org/10.1037/h0091032.

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42

Cieplak, Marek, and Andrzej Majhofer. "Spectral dimensionality and hyperscaling." Physical Review B 34, no. 7 (October 1, 1986): 4892–93. http://dx.doi.org/10.1103/physrevb.34.4892.

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43

Li, Lu. "Probe for electronic dimensionality." Nature Physics 6, no. 1 (January 2010): 7–8. http://dx.doi.org/10.1038/nphys1492.

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44

Heckel, Reinhard, Michael Tschannen, and Helmut Bölcskei. "Dimensionality-reduced subspace clustering." Information and Inference: A Journal of the IMA 6, no. 3 (March 14, 2017): 246–83. http://dx.doi.org/10.1093/imaiai/iaw021.

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45

Bader, S. D. "Magnetism in low dimensionality." Surface Science 500, no. 1-3 (March 2002): 172–88. http://dx.doi.org/10.1016/s0039-6028(01)01625-9.

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46

Bele, Irene Velsvik. "Dimensionality in Voice Quality." Journal of Voice 21, no. 3 (May 2007): 257–72. http://dx.doi.org/10.1016/j.jvoice.2005.12.001.

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47

Gottlieb, Lee-Ad, Aryeh Kontorovich, and Robert Krauthgamer. "Adaptive metric dimensionality reduction." Theoretical Computer Science 620 (March 2016): 105–18. http://dx.doi.org/10.1016/j.tcs.2015.10.040.

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48

Pang, Rich, Benjamin J. Lansdell, and Adrienne L. Fairhall. "Dimensionality reduction in neuroscience." Current Biology 26, no. 14 (July 2016): R656—R660. http://dx.doi.org/10.1016/j.cub.2016.05.029.

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49

Kaatz, Forrest H., and Adhemar Bultheel. "Dimensionality of hypercube clusters." Journal of Mathematical Chemistry 54, no. 1 (August 25, 2015): 33–43. http://dx.doi.org/10.1007/s10910-015-0546-y.

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50

Strahringer, Selma. "Dimensionality of ordinal structures." Discrete Mathematics 144, no. 1-3 (September 1995): 97–117. http://dx.doi.org/10.1016/0012-365x(94)00289-u.

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