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

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Karbauskaitė R., Dzemyda G.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 4
895-913
EN
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.
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Picture languages in automatic radiological palm interpretation

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Tadeusiewicz R., Ogiela M. R.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 2
305-312
EN
The paper presents a new technique for cognitive analysis and recognition of pathological wrist bone lesions. This method uses AI techniques and mathematical linguistics allowing us to automatically evaluate the structure of the said bones, based on palm radiological images. Possibilities of computer interpretation of selected images, based on the methodology of automatic medical image understanding, as introduced by the authors, were created owing to the introduction of an original relational description of individual palm bones. This description was built with the use of graph linguistic formalisms already applied in artificial intelligence. The research described in this paper demonstrates that for the needs of palm bone diagnostics, specialist linguistic tools such as expansive graph grammars and EDT-label graphs are particularly well suited. Defining a graph image language adjusted to the specific features of the scientific problem described here permitted a semantic description of correct palm bone structures. It also enabled the interpretation of images showing some in-born lesions, such as additional bones or acquired lesions such as their incorrect junctions resulting from injuries and synostoses.
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