<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data

Institute of Mathematics and Informatics, Vilnius University, Akademijos st. 4, 08663 Vilnius, Lithuania

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data

Published Online: Dec 30, 2015

Page range: 895 - 913

Received: Sep 11, 2014

DOI: https://doi.org/10.1515/amcs-2015-0064

Keywords
multidimensional data, intrinsic dimensionality, maximum likelihood estimator, manifold learning methods, image understanding

© 2015 Rasa Karbauskaitė et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Optimization of the Maximum Likelihood Estimator for Determining the Intrinsic Dimensionality of High–Dimensional Data

Published Online: Dec 30, 2015

Page range: 895 - 913

Received: Sep 11, 2014

DOI: https://doi.org/10.1515/amcs-2015-0064

Keywordsmultidimensional data, intrinsic dimensionality, maximum likelihood estimator, manifold learning methods, image understanding

© 2015 Rasa Karbauskaitė et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
multidimensional data, intrinsic dimensionality, maximum likelihood estimator, manifold learning methods, image understanding