Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data
One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a...
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| Format: | Article |
| Language: | English |
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Sciendo
2015-12-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/amcs-2015-0064 |
| _version_ | 1818715988748664832 |
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| author | Karbauskaitė Rasa Dzemyda Gintautas |
| author_facet | Karbauskaitė Rasa Dzemyda Gintautas |
| author_sort | Karbauskaitė Rasa |
| collection | DOAJ |
| description | One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis, because it is possible to reduce the dimensionality of the data without losing much information. In this paper, the maximum likelihood estimator (MLE) of the intrinsic dimensionality is explored experimentally. In contrast to the previous works, the radius of a hypersphere, which covers neighbours of the analysed points, is fixed instead of the number of the nearest neighbours in the MLE. A way of choosing the radius in this method is proposed. We explore which metric—Euclidean or geodesic—must be evaluated in the MLE algorithm in order to get the true estimate of the intrinsic dimensionality. The MLE method is examined using a number of artificial and real (images) data sets. |
| first_indexed | 2024-12-17T19:12:07Z |
| format | Article |
| id | doaj.art-6e418434a13c46acb7ff79eae5a8be71 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-17T19:12:07Z |
| publishDate | 2015-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-6e418434a13c46acb7ff79eae5a8be712022-12-21T21:35:51ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922015-12-0125489591310.1515/amcs-2015-0064amcs-2015-0064Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional DataKarbauskaitė Rasa0Dzemyda Gintautas1Institute of Mathematics and Informatics, Vilnius University, Akademijos st. 4, 08663 Vilnius, LithuaniaInstitute of Mathematics and Informatics, Vilnius University, Akademijos st. 4, 08663 Vilnius, LithuaniaOne of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis, because it is possible to reduce the dimensionality of the data without losing much information. In this paper, the maximum likelihood estimator (MLE) of the intrinsic dimensionality is explored experimentally. In contrast to the previous works, the radius of a hypersphere, which covers neighbours of the analysed points, is fixed instead of the number of the nearest neighbours in the MLE. A way of choosing the radius in this method is proposed. We explore which metric—Euclidean or geodesic—must be evaluated in the MLE algorithm in order to get the true estimate of the intrinsic dimensionality. The MLE method is examined using a number of artificial and real (images) data sets.https://doi.org/10.1515/amcs-2015-0064multidimensional dataintrinsic dimensionalitymaximum likelihood estimatormanifold learning methodsimage understanding |
| spellingShingle | Karbauskaitė Rasa Dzemyda Gintautas Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data International Journal of Applied Mathematics and Computer Science multidimensional data intrinsic dimensionality maximum likelihood estimator manifold learning methods image understanding |
| title | Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data |
| title_full | Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data |
| title_fullStr | Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data |
| title_full_unstemmed | Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data |
| title_short | Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data |
| title_sort | optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high dimensional data |
| topic | multidimensional data intrinsic dimensionality maximum likelihood estimator manifold learning methods image understanding |
| url | https://doi.org/10.1515/amcs-2015-0064 |
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