Páros összehasonlításon alapuló pontozási eljárások monotonitása: önkonzisztencia és önkonzisztens monotonitás. Adalékok a pontozási eljárások axiomatikus tárgyalásához = Monotonicity of paired comparison-based ranking methods: self-consistency and self-consistent monotonicity. Contributions to an axiomatic analysis of scoring methods

A cikk a páros összehasonlításokon alapuló pontozási eljárásokat tárgyalja axiomatikus megközelítésben. A szakirodalomban számos értékelő függvényt javasoltak erre a célra, néhány karakterizációs eredmény is ismert. Ennek ellenére a megfelelő módszer kiválasztása nem egy-szerű feladat, a különböző tulajdonságok bevezetése elsősorban ebben nyújthat segítséget. Itt az összehasonlított objektumok teljesítményén érvényesülő monotonitást tárgyaljuk az önkonzisztencia és önkonzisztens monotonitás axiómákból kiindulva. Bemutatásra kerülnek lehetséges gyengítéseik és kiterjesztéseik, illetve egy, az irreleváns összehasonlításoktól való függetlenséggel kapcsolatos lehetetlenségi tétel is. A tulajdonságok teljesülését három eljárásra, a klasszikus pontszám eljárásra, az ezt továbbfejlesztő általánosított sorösszegre és a legkisebb négyzetek módszerére vizsgáljuk meg, melyek mindegyike egy lineáris egyenletrendszer megoldásaként számítható. A kapott eredmények új szempontokkal gazdagítják a pontozási eljárás megválasztásának kérdését. _____ The paper provides an axiomatic analysis of some scoring procedures based on paired comparisons. Several methods have been proposed for these generalized tournaments, some of them have been also characterized by a set of properties. The choice of an appropriate method is supported by a discussion of their theoretical properties. In the paper we focus on the connections of self-consistency and self-consistent-monotonicity, two axioms based on the comparisons of object's performance. The contradiction of self-consistency and independence of irrel-evant matches is revealed, as well as some possible reductions and extensions of these properties. Their satisfiability is examined through three scoring procedures, the score, generalised row sum and least squares methods, each of them is calculated as a solution of a system of linear equations. Our results contribute to the problem of finding a proper paired comparison based scoring method.

Svájci rendszerű sakk csapatversenyek rangsorolása (Ranking in Swiss system chess team tournaments)

A cikk a páros összehasonlításokon alapuló pontozási eljárásokat alkalmazza svájci rendszerű sakk csapatversenyek eredményének meghatározására. Bemutatjuk a nem körmérkőzéses esetben felmerülő kérdéseket, az egyéni és csapatversenyek jellemzőit, valamint a hivatalos lexikografikus rendezések hibáit. Axiomatikus alapokon rangsorolási problémaként modellezzük a bajnokságokat, definícióinkat összekapcsoljuk a pontszám, az általánosított sorösszeg és a legkisebb négyzetek módszerének tulajdonságaival. A javasolt eljárást két sakkcsapat Európa-bajnokság részletes elemzésével illusztráljuk. A végső rangsorok összehasonlítását távolságfüggvények segítségével végezzük el, majd a sokdimenziós skálázás révén ábrázoljuk azokat. A hivatalos sorrendtől való eltérés okait a legkisebb négyzetek módszerének dekompozíciójával tárjuk fel. A sorrendeket három szempont, az előrejelző képesség, a mintailleszkedés és a robusztusság alapján értékeljük, és a legkisebb négyzetek módszerének alkalmas eredménymátrixszal történő használata mellett érvelünk. ____ The paper uses paired comparison-based scoring procedures in order to determine the result of Swiss system chess team tournaments. We present the main challenges of ranking in these tournaments, the features of individual and team competitions as well as the failures of official lexicographical orders. The tournament is represented as a ranking problem, our model is discussed with respect to the properties of the score, generalised row sum and least squares methods. The proposed method is illustrated with a detailed analysis of the two recent chess team European championships. Final rankings are compared through their distances and visualized by multidimensional scaling (MDS). Differences to official ranking are revealed due to the decomposition of least squares method. Rankings are evaluated by prediction accuracy, retrodictive performance, and stability. The paper argues for the use of least squares method with an appropriate generalised results matrix favouring match points.

Fogalmak, módszerek. Páros összehasonlításokon alapuló rangsorolási módszerek (Ranking methods based on paired comparisons)

A páronként összehasonlított alternatívák rangsorolásának problémája egyaránt felmerül a szavazáselmélet, a statisztika, a tudománymetria, a pszichológia és a sport területén. A nemzetközi szakirodalom alapján részletesen áttekintjük a megoldási lehetőségeket, bemutatjuk a gyakorlati alkalmazások során fellépő kérdések kezelésének, a valós adatoknak megfelelő matematikai környezet felépítésének módjait. Kiemelten tárgyaljuk a páros összehasonlítási mátrix megadását, az egyes pontozási eljárásokat és azok kapcsolatát. A tanulmány elméleti szempontból vizsgálja a Perron-Frobenius tételen alapuló invariáns, fair bets, PageRank, valamint az irányított gráfok csúcsainak rangsorolásra javasolt internal slackening és pozíciós erő módszereket. A közülük történő választáshoz az axiomatikus megközelítést ajánljuk, ennek keretében bemutatjuk az invariáns és a fair bets eljárások karakterizációját, és kitérünk a módszerek vitatható tulajdonságaira. _____ The ranking of the alternatives or selecting the best one are fundamental issues of social choice theory, statistics, psychology and sport. Different solution concepts, and various mathematical models of applications are reviewed based on the international literature. We are focusing on the de¯nition of paired comparison matrix, on main scoring procedures and their relation. The paper gives a theoretical analysis of the invariant, fair bets and PageRank methods, which are founded on Perron-Frobenius theorem, as well as the internal slackening and positional power procedures used for ranking the nodes of a directed graph. An axiomatic approach is proposed for the choice of an appropriate method. Besides some known characterizations for the invariant and fair bets methods, we also discuss the violation of some properties, meaning their main weakness.

Ranking in Swiss system chess team tournaments

The paper uses paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the main challenges of ranking in Swiss system, the features of individual and team competitions as well as the failures of official lexicographical orders. The tournament is represented as a ranking problem, our model is discussed with respect to the properties of the score, generalized row sum and least squares methods. The proposed procedure is illustrated with a detailed analysis of the two recent chess team European championships. Final rankings are compared by their distances and visualized with multidimensional scaling (MDS). Differences to official ranking are revealed by the decomposition of least squares method. Rankings are evaluated by prediction accuracy, retrodictive performance, and stability. The paper argues for the use of least squares method with a results matrix favoring match points.

Select, Link and Rank: Diversified Query Expansion and Entity Ranking using Wikipedia

A search query, being a very concise grounding of user intent, could potentially have many possible interpretations. Search engines hedge their bets by diversifying top results to cover multiple such possibilities so that the user is likely to be satisfied, whatever be her intended interpretation. Diversified Query Expansion is the problem of diversifying query expansion suggestions, so that the user can specialize the query to better suit her intent, even before perusing search results. We propose a method, Select-Link-Rank, that exploits semantic information from Wikipedia to generate diversified query expansions. SLR does collective processing of terms and Wikipedia entities in an integrated framework, simultaneously diversifying query expansions and entity recommendations. SLR starts with selecting informative terms from search results of the initial query, links them to Wikipedia entities, performs a diversity-conscious entity scoring and transfers such scoring to the term space to arrive at query expansion suggestions. Through an extensive empirical analysis and user study, we show that our method outperforms the state-of-the-art diversified query expansion and diversified entity recommendation techniques.

Generating Discriminative Objective Proposals via Submodular Ranking

Object recognition has long been a core problem in computer vision. To improve object spatial support and speed up object localization for object recognition, generating high-quality category-independent object proposals as the input for object recognition system has drawn attention recently. Given an image, we generate a limited number of high-quality and category-independent object proposals in advance and used as inputs for many computer vision tasks. We present an efficient dictionary-based model for image classification task. We further extend the work to a discriminative dictionary learning method for tensor sparse coding. In the first part, a multi-scale greedy-based object proposal generation approach is presented. Based on the multi-scale nature of objects in images, our approach is built on top of a hierarchical segmentation. We first identify the representative and diverse exemplar clusters within each scale. Object proposals are obtained by selecting a subset from the multi-scale segment pool via maximizing a submodular objective function, which consists of a weighted coverage term, a single-scale diversity term and a multi-scale reward term. The weighted coverage term forces the selected set of object proposals to be representative and compact; the single-scale diversity term encourages choosing segments from different exemplar clusters so that they will cover as many object patterns as possible; the multi-scale reward term encourages the selected proposals to be discriminative and selected from multiple layers generated by the hierarchical image segmentation. The experimental results on the Berkeley Segmentation Dataset and PASCAL VOC2012 segmentation dataset demonstrate the accuracy and efficiency of our object proposal model. Additionally, we validate our object proposals in simultaneous segmentation and detection and outperform the state-of-art performance. To classify the object in the image, we design a discriminative, structural low-rank framework for image classification. We use a supervised learning method to construct a discriminative and reconstructive dictionary. By introducing an ideal regularization term, we perform low-rank matrix recovery for contaminated training data from all categories simultaneously without losing structural information. A discriminative low-rank representation for images with respect to the constructed dictionary is obtained. With semantic structure information and strong identification capability, this representation is good for classification tasks even using a simple linear multi-classifier.

Ranking of fibre-reinforced composite plate surface finish quality by wavelet texture analysis

In the automotive and other industries, the visual appearance of external surfaces is a key factor in perceived product quality. Traditionally, the quality of an automotive surface finish has been judged by expert human auditors. A set of 17 fibre-reinforced composite plates was previously manufactured to have a range of surface finish qualities and these plates were ranked by three expert observers and also optically digitally imaged. Following validation of the previous rankings, the wavelet texture analysis (WTA) technique was applied to the digital photographs to derive an instrumental measure of surface finish quality based on the panel images. The rank correlation between the human expert surface finish quality ratings and those from the W TA image analysis process was found to be positive, large and statistically significant. This finding indicates that WTA could form the basis of an inexpensive and practical instrumental method for the ranking of fibre-reinforced composite surface finish quality.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.