The problem of the missing values (blanks) recovering in real data is well-known. Usually, the recovery of the lost measurement results of object characteristics (features) is under investigation. ...This article considers the case when the experimental data are immediately presented by paired comparisons and some of them have been lost. Since the matrix of measurements of object features is initially not presented, it requires the development of a special approach to the recovery of such missing values. The proposed approach can be implemented to compare different structured objects in image analysis, machine learning, etc.
The Kemeny median is the well-known method to get a coordinated decision for a group opinion. This ranking is known as the least different from experts’ individual orderings of alternatives. If ...rankings are immersed in a metric space like points, the median should be the mean ranking from the mathematical point of view. As a result, the correct median should be the center of the set of rankings as points in a metric space. Based on this idea, new types of the median are denoted as the Kemeny metric median and the Kemeny weighted median as another type of the metric one. A new procedure is developed for the linear combination of experts’ rankings to build the weighted median. As it is showed, the locally optimal algorithm can be used as the basis to build all types of Kemeny medians.
A coordinated ranking as an opinion of an expert group can be represented by the well-known Kemeny’s median. Such a decision is a least different from other rankings, and is free of some ...contradictions of the majority rule problem. As a mathematical principle, the Kemeny’s median gives a decision in any case, in particular, for conflicting experts or groups. In practice, competing opinions are usually identified, and special procedures are used to achieve the required level of consensus. One known approach consists in assigning weights to expert opinions. In this paper, the correct mathematical basis is formulated for new types on the Kemeny’s median, like metric and weighted ones. The problem to find the median for a linear combination of expert rankings is investigated based on the well-known locally optimal Kemeny’s algorithm. It is proposed to investigate the rank aggregation problem based on new types of the median.
A DENOISING OF BIOMEDICAL IMAGES Thanh, D. N. H.; Dvoenko, S. D.
International archives of the photogrammetry, remote sensing and spatial information sciences.,
05/2015, Volume:
XL-5/W6, Issue:
5
Journal Article, Conference Proceeding
Peer reviewed
Open access
Today imaging science has an important development and has many applications in different fields of life. The researched object of imaging science is digital image that can be created by many digital ...devices. Biomedical image is one of types of digital images. One of the limits of using digital devices to create digital images is noise. Noise reduces the image quality. It appears in almost types of images, including biomedical images too. The type of noise in this case can be considered as combination of Gaussian and Poisson noises. In this paper we propose method to remove noise by using total variation. Our method is developed with the goal to combine two famous models: ROF for removing Gaussian noise and modified ROF for removing Poisson noise. As a result, our proposed method can be also applied to remove Gaussian or Poisson noise separately. The proposed method can be applied in two cases: with given parameters (generated noise for artificial images) or automatically evaluated parameters (unknown noise for real images).
Recently, raw experimental data in machine learning often appear as direct comparisons between objects (featureless data). Different ways to evaluate difference or similarity of a pair of objects in ...image and data mining, image analysis, bioinformatics, etc., are usually used in practice. Nevertheless, such comparisons often are not distances or correlations (scalar products) like a correct function defined on a limited set of elements in machine learning. This problem is denoted as metric violations in ill-posed matrices. Therefore, it needs to recover violated metrics and provide optimal conditionality of corresponding matrices of pairwise comparisons for distances and similarities. This is the correct basis for using of modern machine learning algorithms.
There are many modern devices are used to create digital images. These devices use optical effects to create images. Therefore, the image quality depends on quality of optical sensors. Because of the ...limits of technology, these sensors cannot reconstruct the images perfectly, and always include some defects. One from these defects is noise. The noise reduces image quality and result of image processing. The image noises can be classified into some types: Gaussian noise, Poisson noise, speckle noise and so on. Depending on particular noises, we have efficient methods to remove them. There is no existing a universal method to remove all noises effectively. In this paper, we proposed a method to remove a noise that is popular in biomedicine. This noise can be considered as a combination of Gaussian and Poisson noises. Our method is based on the total variation of an image intensity (brightness) function.
The problem to recognize objects that form an array of interrelated data is investigated. In the problem of machine learning, the array components belong to some class of a finite set. In this paper ...the interrelationship of array elements is presented by its adjacency graph. An efficient noniterative recognition algorithm for restoring an a posteriori marginal distributions of hidden classes for array elements is developed for a treelike adjacency graph. This algorithm modifies for each array element the hidden class distribution obtained as a result of learning for independent objects. Usually arbitrary graphs for real data contain cycles, for example, the rectangular adjacency lattice of points for 2D raster images or 3D seismic data. The treelike approximation of such graphs inevitably strongly distorts the interrelations between array elements. In the present paper, the reduced set of interrelations between array elements is balanced by an extended set of acyclic graphs themselves. By the example of the segmentation problem for texture raster images, we investigate a set of acyclic graphs and present the experimental results.
The ability of a denoising procedure to preserve fine image structures when suppressing unwanted noise has crucial importance for an accurate and effective medical diagnosis. We introduce here a new ...procedure of edge-preserving denoising for medical images, that combines the flexibility in prior assumptions, and computational effectiveness of parametric multi-quadratic dynamic programming with the increased accuracy of a tree-like representation of a discrete lattice based on the full set of possible adjacency graphs of image elements. Proposed procedure can effectively remove an additive white Gaussian noise with high quality. We provide experimental results in image denoising as well as comparison with related methods.
The bi-partial criterion for clustering problem consists of two parts, where the first one takes into account intra-cluster relations, and the second - inter-cluster ones. In the case of k-means ...algorithm, such bi-partial criterion combines intra-cluster dispersion with inter-cluster similarity, to be jointly minimized. The first part only of such objective function provides the "standard" quality of clustering based on distances between objects (the well-known classical k-means). To improve the clustering quality based on the bi-partial objective function, we develop the permutable version of k-means algorithm. This paper shows that the permutable k-means appears to be a new type of a clustering procedure.
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