Combinatorial compression algorithms for ordered record sequences

The problem of efficient use and storage of data in memory is considered. Three compression algorithms for ordered sequences of records are proposed, which are essentially faster than the statistical algorithms. The running time of the proposed algorithms is linear in the number of records.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 121–128, November–December, 1991.     

Ordinal regression with explainable distance metric learning based on ordered sequences

Machine Learning - The purpose of this paper is to introduce a new distance metric learning algorithm for ordinal regression. Ordinal regression addresses the problem of predicting classes for...     

Similarity-based test case prioritization using ordered sequences of program entities

Test suites often grow very large over many releases, such that it is impractical to re-execute all test cases within limited resources. Test case prioritization rearranges test cases to improve the effectiveness of testing. Code coverage has been widely used as criteria in test case prioritization. However, the simple way may not reveal some bugs, such that the fault detection rate decreases. In this paper, we use the ordered sequences of program entities to improve the effectiveness of test case prioritization. The execution frequency profiles of test cases are collected and transformed into the ordered sequences. We propose several novel similarity-based test case prioritization techniques based on the edit distances of ordered sequences. An empirical study of five open source programs was conducted. The experimental results show that our techniques can significantly increase the fault detection rate and be effective in detecting faults in loops. Moreover, our techniques are more cost-effective than the existing techniques.     

Optimal interval enclosing of certain sets of matrices,with application to monotone enclosing of square roots

In this paper, two kinds of partial ordering for symmetric matrices are related to each other, namely, the natural partial ordering ≤ generated by the coneK of elementwise nonnegative matrices, and the definite partial ordering \( \leqslant \cdot\) generated by the coneK _D of nonnegative definite matrices. The main result of this paper shows how a matrix interval in the sense of the definite partial ordering can be enclosed between optimal bounds with respect to the natural partial ordering. By means of this result, it is possible to compute a numerically practicable inclusion based on the natural partial ordering from a given inclusion of some matrix with the definite partial ordering. In this way, an always and moreover quadratically convergent method of elementwise enclosing the square root of a positive definite, symmetric matrix can be constructed.     

Finding minimal enclosing boxes

The problem of finding minimal volume boxes circumscribing a given set of three-dimensional points is investigated. It is shown that it is not necessary for a minimum volume box to have any sides flush with a face of the convex hull of the set of points, which makes a naive search problematic. Nevertheless, it is proven that at least two adjacent box sides are flush with edges of the hull, and this characterization enables anO(n ³) algorithm to find all minimal boxes for a set ofn points.     

领域自适应的最小包含球设计方法

支持向量域描述(SVDD)算法适用于异常点检测,但对于不同领域样本组的整体快速识别则力不从心.为此,基于SVDD算法提出一种基于最小包含球的领域自适应算法(MEB-DA),并将其发展为基于中心约束型最小包含球的领域自适应法(CCMEB-DA),以满足大样本数据的快速计算.该算法通过计算各自数据组的包含球球心对不同领域数据进行整体校正和相似度识别,具有较好的便捷性和自适应性.将所提出的算法应用于无限保真(WIFI)数据的室内定位和人脸识别检测,均取得了较好的效果,从而验证了所提出算法的有效性和快速性.     

On the smallest enclosing information disk

We present a generalization of Welzl's smallest enclosing disk algorithm [E. Welzl, Smallest enclosing disks (balls and ellipsoids), in: New Results and New Trends in Computer Science, in: Lecture Notes in Computer Science, vol. 555, Springer, 1991, pp. 359-370] for point sets lying in information-geometric spaces. Given a set of points equipped with a Bregman divergence as a (dis)similarity measure, we investigate the problem of finding its unique (circum)center defined as the point minimizing the maximum divergence to the point set. As an application, we show how to solve a statistical model estimation problem by computing the center of a finite set of univariate normal distributions.     

Fast computation of smallest enclosing circle with center on a query line segment

Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is constrained to lie on a query line segment. Our algorithm preprocesses a given set of n points P={p₁,p₂,…,pn} such that for any query line or line segment L, it efficiently locates a point c on L that minimizes the maximum distance among the points in P from c. Roy et al. [S. Roy, A. Karmakar, S. Das, S.C. Nandy, Constrained minimum enclosing circle with center on a query line segment, in: Proc. of the 31st Mathematical Foundation of Computer Science, 2006, pp. 765-776] have proposed an algorithm that solves the query problem in O(log²n) time using O(nlogn) preprocessing time and O(n) space. Our algorithm improves the query time to O(logn); but the preprocessing time and space complexities are both O(n²).     

Camera calibration with enclosing ellipses by an extended application of generalized eigenvalue decomposition

Conics-based calibration has been widely inves- tigated in the past several years. The primary method is to utilize the generalized eigenvalue decomposition (GED) of conics. In this paper, we extend the GED method to deal with a general case: two enclosing ellipses. We construct a link between enclosing ellipses and confocal conics. The homography is, thus, decomposed to three components, each of which corresponds to a clear geometrical meaning. Other general conics cases including separate case, intersecting case and hyperbolas case are also discussed. Experiments with simulated and real data demonstrate the good performance of our camera calibration algorithms.     

Equilibria in games with ordered outcomes

The existence of equilibria is proved in mixed extensions of games with ordered outcomes, and methods for finding these equilibria are given.Translated from Kibernetika, No. 5, pp. 98–104, September–October, 1989.     

A fast deterministic smallest enclosing disk approximation algorithm

We describe a simple and fast -time algorithm for finding a (1+?)-approximation of the smallest enclosing disk of a planar set of n points or disks. Experimental results of a readily available implementation are presented.     

Scheduling problems with partially ordered jobs

Scheduling problems with given precedence constraints (with partially ordered jobs) are considered. A review of the results obtained in this area by the members of Minsk Scheduling Theory school created by V.S. Tanaev is done.     

Logic modeling with partially ordered preferences

Logic modeling is the use of formal logic as a modeling tool for problems of interest to management science. Based on a review of the logic of preference literature this paper presents five axioms for reasoning about a decision maker's preferences. A semantics of situations is adopted for the symbols used. Both logical deduction and a modification of dynamic programming are proposed for the problem of selecting preferred states of affairs over time. Finally, a sketch of an implementation in Prolog is presented.     

Sequential decision making with partially ordered preferences

This paper presents new insights and novel algorithms for strategy selection in sequential decision making with partially ordered preferences; that is, where some strategies may be incomparable with respect to expected utility. We assume that incomparability amongst strategies is caused by indeterminacy/imprecision in probability values. We investigate six criteria for consequentialist strategy selection: Γ-Maximin, Γ-Maximax, Γ-Maximix, Interval Dominance, Maximality and E-admissibility. We focus on the popular decision tree and influence diagram representations. Algorithms resort to linear/multilinear programming; we describe implementation and experiments.     

Variance measures with ordered weighted aggregation operators

The variance is a statistical measure widely used in many real-life application areas. This article makes an extensive investigation on variance measure in the case when the uncertainty is not of a probabilistic nature. It generalizes the notion of variance as well as the theory of ordered weighted aggregation operators. First, we extend the idea of representative value/expected value of a decision maker and develop some new deviation measures based on ordered weighted geometric (OWG) average and ordered weighted harmonic average (OWHA) operators. These measures are developed with the consideration that decision maker can represent his/her attitudinal expected value by using any one of the ordered weighted aggregation (OWA) operators. Further, this study proposes some deviation measures by using the generalized-OWA (GOWA) and Quasi-OWA as an expected value of decision maker and discusses their particular cases. Second, a number of generalized deviation measures are introduced by taking the generalized arithmetic mean and quasi-arithmetic means for aggregation of the individual dispersion. This approach provides an ability to the user for considering the deviation under different realistic-scenario. These measures lead to many interesting particular and limiting cases and enrich the use of ordered weighted aggregation operators in the variance.