# online read us now

Paper details

Number 4 - December 2015

Volume 25 - 2015

**Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data**

Rasa Karbauskaitė, Gintautas Dzemyda

**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.

**Keywords**

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