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Intrinsic dimensionality detection criterion based on Locally Linear Embedding

Meng L., Breitkopf P.

Computer Science

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2018

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Vol. 19 (3)

345--356

EN

In this work, we revisit the Locally Linear Embedding (LLE) algorithm that is widely employed in dimensionality reduction. With a particular interest to the correspondences of the nearest neighbors in the original and embedded spaces, we observe that, when prescribing low-dimensional embedding spaces, LLE remains merely a weight-preserving rather than a neighborhood-preserving algorithm. Thus, we propose a \neighborhood-preserving ratio" criterion to estimate the minimal intrinsic dimensionality required for neighborhood preservation. We validate its efficiency on sets of synthetic data, including S-curve, Swiss roll, and a dataset of grayscale images.

2

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

Karbauskaitė R., Dzemyda G.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 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.

3

Semi-automatic human emotions recognition method based on I2D features

Lisowska A., Kotarski W., Kownacki A.

Journal of Medical Informatics & Technologies

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2005

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Vol. 9

215--222

EN

In the paper we present quite new approach to the problem of human emotion recognition with use of face images. We assume that basic emotions such as anger, disgust, fear, happiness, sadness, surprise are expressed by face mimic. Face images with the well defined emotions may be performed using the method based on geometrical wavelets (beamlets) in order to extract intrinsically two dimensional features, the most important ones from the Human Visual System point of view. Such an approach can be successfully applied in extraction process of the most important features that are responsible for recognition of basic elements of face (eyes, nose, lips, etc.). The listed elements of face have a little different location that depends on emotion expressed. It has been proved experimentally that it is possible using very small amount of information extracted from a face image, by the so-called beamlet extractor, to recognize emotion with high accuracy. Very promising results of experiments suggest that the method should be further investigated and improved.

4

Intrinsic Dimensional Selective Operator Based on Geometrical Wavelets

Lisowska A.

Journal of Applied Computer Science

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2005

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Vol. 13, nr 1

99-112

EN

The theory of geometrical wavelets is new and has found already many applications in different fields of digital image processing, though finding many others is still possible and justified. Although images are two dimensional objects they include areas which have different intrinsic (local) dimensionality. Ones of them are more important in the visual perception while the others are less important. The main problem lies in constructing good extractors, which can efficiently extract intrinsic two dimensional areas hidden in images (that is the more important ones). There are some well known nonlinear techniques which can do it relatively effectively. For example the one based on spectral methods, or especially on Volterra series or the one basing on tensors. In this paper there is presented the very novel approach of extracting of intrinsic two dimensional areas based on the theory of geometrical wavelets, especially beamlets. Basing on them the new intrinsic dimensional selective operator has been defined. As performed experiments have shown, giving quite satisfactory results, this approach may constitute serious competition for the well known methods used so far in the theory of intrinsic dimensional operators.

5

Automatic perception of significant image features based on psychology of vision

Lisowska A., Kotarski W.

Journal of Medical Informatics & Technologies

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2004

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Vol. 7

MIP31--40

EN

Recent investigations in neuropsychology and psychology of vision have proven that human eye does not get all the information from the surrounding world in the same degree. There are three classes of signals received by human brain. The more important one is the information about features such as corners, junctions, ends of lines, etc. Straight lines and edges are the second in the hierarchy of importance. And the last ones are textures they support the less important information about objects. Basing on these results, in image processing, theory of intrinsic dimensionality and related to it theory of feature extractors have been established. In the paper a survey of approaches that are used for construction of feature extractors based on intrinsic dimensionality have been presented. To carry out experiments the approach based on geometrical wavelets has been chosen and the software prepared by the first author has been used. Experiments presented in the paper have been performed on relatively complex images that had been faces' images. They confirmed that the information about the basic elements of faces (eyes, nose, lips, etc.) might be properly extracted from the face with the usage of the feature extractor. Moreover, the experiments have shown that in this way one could obtain the smallest possible amount of information, which was enough that human eyes yet have seen the face. Very promising results of experiments suggest that it is possible to use the proposed approach to face identification and recognition. Also some possible medical applications have been suggested.