Multiple Ranking Research Articles

Consensus unsupervised feature ranking from multiple views

Feature ranking is a kind of feature selection process which ranks the features based on their relevances and importance with respect to the problem. This topic has been well studied in supervised classification area. However, very few works are done for unsupervised clustering under the condition that labels of all instances are unknown beforehand. Thus, feature ranking for unsupervised clustering is a challenging task due to the absence of labels of instances for guiding the computations of the relevances of features. This paper explores the feature ranking approach within the unsupervised clustering area. We propose a novel consensus unsupervised feature ranking approach, termed as unsupervised feature ranking from multiple views (FRMV). The FRMV method firstly obtains multiple rankings of all features from different views of the same data set and then aggregates all the obtained feature rankings into a single consensus one. Experimental results on several real data sets demonstrate that FRMV is often able to identify a better feature ranking when compared with that obtained by a single feature ranking approach.

Different ranking methods: potentialities and pitfalls for the case of European opinion poll

Prioritization and ranking of objects are primary needs in various substantive fields. It might be said that ranking and comparison are the first step in every risk assessment procedure, whatever the ‘risk’ is intended as: social, environmental, political or economic. Often objects to be ranked are valued by a multi-dimensional attribute which is usually transformed into a composite numerical score. In spite of conventional solutions, the author agrees with recent recommendations of performing multiple ranking, keeping indicators separated. Different innovative methods are analyzed and compared: Hasse diagrams method, POSAC and Nonlinear PCA. The first one stems directly from partial order theory, the second one may be seen as an approximation of Hasse representation in a two dimensional space, whilst the third one belongs to the wide set of non-linear multivariate techniques and it is particularly suitable in handling data of categorical type. Among them, the first two methods compare objects on the basis only on order property of data, whilst the last one simultaneously performs an optimal scale of qualitative attributes and a ranking of objects. The case study is based on the Eurobarometer survey carried out in 2002, at the request of the European Commission, which collects Europeans opinion about various political and social issues. The analysis is focused on users’ level of satisfaction about access easiness, cost, quality, information received and contracts of various services of general interest, such as telephone services, power (gas and electricity) providers, water and postal utilities, urban and rail transports. Separate indicators are set up for each facet of each service within different European regions. Eventually, the ranking of European regions is performed on the basis of the overall performance of services of general interest, as perceived by users. Selected methods lead to almost alike results, still with some differentiations due to different approaches used. As it frequently occurs, each method has its own advantages and pitfalls which are here explored and compared.

Response to Lo et al .

There is a constant tension between the findings of phylogenetic analyses and the expression of those findings in a classification. This is predominantly because the Linnean system was not designed to accommodate the multiple ranks necessary for groups with large numbers of clades. This problem is

Adaptive beamforming for multipath environments

Coherent multipaths present a significant challenge to most adaptive beamformers because they violate the common assumption of a rank-one plane wave or geometrically focused signal. When the multipath arrivals that characterize shallow water propagation are resolvable by the array’s aperture, the mismatch between the assumed and the true signal spatial structure causes signal suppression. If the amplitude and phase relationships among the various multipaths were known, they could, in principle, be included in a matched field beamforming approach. This is usually impractical due to inadequate knowledge of propagation parameters, especially bottom characteristics, and source/receiver motion. A generalization of the standard MVDR approach, called multirank MVDR, assumes only that the signal lies in a subspace of multiple rank rather than the usual rank-one assumption. An example of a subspace is a small fan of beams that cover the potential multipath directions. The signal may be rank one corresponding to fully coherent multipath or higher rank corresponding to incoherent or partially coherent multipath. The multirank approach is applied to the shallow water multipath problem and compared with the related technique of employing multiple linear constraints. Realistic simulations of alternative beamforming approaches for a large horizontal array are presented. [Work supported by ONR.]

Observability analysis for state estimation using Hachtel’s augmented matrix method

This paper presents algorithms of observability analysis for state estimation when Hachtel’s augmented matrix method is used in the formulation of state estimation. It is shown that the authors’ previously presented algorithms for determining observable islands and deciding multiple measurement placement for gain matrix are ready to be extended to Hachtel’s augmented matrix method, which is commonly used in power networks due to its robustness. Triangular factors updating with multiple rank is also presented, and the updated factors of Hachtel’s augmented matrix can be directly used by state estimator if the real data are used by observability analysis. The proposed algorithms have been tested on IEEE 14 bus and IEEE 118 systems. Numerical examples are provided to illustrate the details of the proposed algorithms. The simplicity and efficiency of proposed algorithms make possible their on-line application for current power networks.

Apples and oranges: Educational enrollment and attainment across countries in Latin America and the Caribbean

This paper uses household survey data to rank LAC countries’ performance in two areas: (i) getting children into school on time and keeping them there, and (ii) turning their contact with the educational system into years of schooling. It presents multiple rankings because most countries’ performance is not uniform across these dimensions. For instance, the Dominican Republic performs almost as well as the richest countries when it comes to keeping children in school, but as badly as the poorest few in terms of turning attendance into years of schooling. Further, the rankings, which are based on conventional and new measures of educational systems’ performance, are occasionally quite different from those obtained using more widely available administrative data.

A computational method for ranking L products of parameters

Research on multiple comparison ranking up to now has focused mainly on the comparison of preference in several objects (or items). This article presents a multiple comparison ranking procedure for comparing several scalar functions of parameters. A preference probability matrix for the procedure is introduced and its condition for warranting an optimal comparison ranking is studied. By using a Bayesian Monte Carlo method, we develop simulation-based procedure to estimate the matrix and obtain the optimal ranking via a row-sum scores method. The procedure is shown to be straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. Necessary theory and illustrative examples are provided.

Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices

Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue probability density functions (p.d.f's) are β-generalizations of the classical groups. Left open was the direct calculation of certain Jacobians. We provide the sought direct calculation. Furthermore, we show how a multiplicative rank 1 perturbation of the unitary Hessenberg matrices provides a joint eigenvalue p.d.f. generalizing the circular β-ensemble, and we show how this joint density is related to known interrelations between circular ensembles. Projecting the joint density onto the real line leads to the derivation of a random three-term recurrence for polynomials with zeros distributed according to the circular Jacobi β-ensemble.

Forest regeneration after disturbance: A modelling study for the Swiss Alps

To examine the speed of tree regeneration in lower subalpine forests (1300–1700 m a.s.l.) of the European Alps after blowdown events, we developed a spatially explicit simulation model. Calibrated with data from 10 years of observation on extensive blowdown areas in Switzerland, the model incorporates the interactions between the changing herb layer and the growth of Norway spruce ( Picea abies (L.) Karst.). The model consists of a vegetation model and a tree model: the vegetation model simulates spatial changes in the herb layer using a cellular automaton combined with a Markov transition matrix. Herb layer changes include the dispersal of tall herbs and raspberry ( Rubus idaeus) on different microsite types, the growth of pioneer tree species ( Sorbus aucuparia), the decay of fallen trunks, and their colonization by plants. The tree model simulates growth and demographic processes of spruce trees ( P. abies) with an individual-based approach, including seed dispersal, germination, establishment, growth and mortality as a function of herb layer properties. The model was evaluated through sensitivity analysis along with stepwise multiple rank regression. As a measure of the goodness of fit, we compared the model results with independent field data. The sensitivity analysis showed that seed availability, seedling survival and the presence of advance regeneration are the key processes for successful reforestation. The model reliably simulated the observed tree height distributions after 8 and 10 years ( R 2 between 0.81 and 0.93). Long-term simulations yielded initially sparse spruce regeneration, which is retarded by unfavourable microsite conditions. The results indicate that the recovery of the forest to protect against avalanches and landslides may not be achieved for several decades on blowdown sites with large distances to the nearest forest edge, and thus low seed supply. On sites where less than 10% of the surface was covered by logs and with higher seed supply, the protection against avalanches and landslides may be sufficient again about 50 years after a blowdown event.

Ranked Relations: Query Languages and Query Processing Methods for Multimedia

In this paper, we describe the notion of a ranked relation that incorporates to the relational data model the notion of rank, i.e. ordering among tuples or objects. The ordering of tuples may be based on a single rank information, or multiple ranks combined together. We show that such relations arise naturally in many applications, especially in applications that query outside sources and return ranked relations as answers to content based queries. We introduce an algebra for querying ranked relations and give examples of its use for various applications. We then prove various properties of the algebra with special emphasis on the preservation of the coherence property, which shows when different rank columns are guaranteed to induce the same ordering among tuples. We show how these properties can be used to produce approximate early returns. Finally, we give experimental results based on Internet search engines for our early returns method and show that our method provides meaningful and fast answers to the user.

Realizable (Average Stress, Average Strain) Pairs in a Plate with Holes

Here a complete characterization is given of the set of all possible (average stress, average strain) pairs that can exist in a plate containing a fixed volume fraction f of holes. Specifically, for a given average stress, the range of values the average strain takes as the microgeometry is varied (while keeping f fixed) is determined. It is shown that multiple rank laminate materials suffice to generate all possible values of the average strain. When the microgeometry is restricted to be a periodic array of holes, with only one hole per unit cell, the average strain takes a smaller range of values as the hole shape is varied. A certain necessary condition for optimality must be satisfied if the hole is such that the average strain is on the boundary of this range. Numerical results are obtained for the range in the limit where the holes are well separated and occupy a small volume fraction. Optimal hole shapes, associated with average strains on the boundary of the range of admissible values, are identif...

Exact Distributions of Multiple Comparisons Rank Statistics

Computation of exact p values of multiple comparisons rank statistics is often a very time-consuming task. In some cases approximations are available, but they are often unsatisfactory when samples are small or the number of ties is large. Some existing tables of exact critical values contain errors and are limited to small samples without ties and to Wilcoxon scores. Therefore, this article proposes a new algorithm to compute exact p values of generalized Steel statistics for one-way classification. This recursive algorithm builds up a generating function that represents the null distribution of the statistic. Several techniques are used to reduce computing time considerably. An improvement of an existing algorithm is given for computing exact p values, which is valid for a smaller class of statistics than the recursion. However, for this class of statistics, this algorithm outperforms the recursion. How to compute tight bounds on the p value when exact computation is too time-consuming is discussed. Also discussed is when to use which method (exact, bounds, normal approximation, or simulation) for computation of p values or critical values.

University Rankings in Japan

Japan has a highly diversified mass higher education system, consisting mainly of private institutions. In their highly developed and matured market, higher education institutions have been ranked in terms of selectivity for many years. However, the university rankings that began in the 1990s took a different approach, that is, showing multiple rankings in order to enrich the perspectives of university applicants. This article aims at tracing the development of university rankings in Japan and at explaining the link between rankings and the mature, but drastically changing, Japanese higher education market.

Land use history, plant rarity, and protected area adequacy in an intensively managed forest landscape

Assessment of biodiversity representation by protected areas mostly uses biological information to prioritise unrepresented features. Use of socio-economic factors (e.g. land use, ownership) is less prominent, even though they influence biodiversity distribution and reserve implementation. In regions with little protection, socio-economic factors may be more sensitive to prioritising risk among unprotected features: many biological priorities will exist but not all are threatened by land use. In an intensively managed region of New Brunswick, Canada, we conducted an ecosystem-based representation assessment and prioritised the unprotected elements with a combined biological and socio-economic ranking criteria. Biological data were the distribution and rarity of at-risk plants. Socio-economic data described land use intensity. Ecosystem units were fine-scale polygons resolved across topographical and edaphic gradients. We asked: 1) how adequately are units with rare plant hotspots protected? and 2) what are the relative risks to unprotected units from land use? Nineteen of twenty-eight ecosystems were preserved inadequately. Based on the combined ranking procedure, however, not all were equally at-risk. High risk units with rare plant hotspots were fertile, of gentle slopes or bottomlands, privately owned, and agriculture-dominated. Rare plants were concentrated in highly isolated forest remnants. Low risk units were infertile, poorly drained or topographically rugged, and owned by government or the forest industry; some contained rare plants but were well protected. Several unprotected and disturbed units were not ranked highly due to biological data base inconsistencies, and due to the weighting of the ranking criteria itself. Such problems, common to representation analyses, were highlighted by our use of multiple ranking criteria; affected units will require supplemental risk assessment. Our results indicate that high risk ecosystems will be difficult to protect because of habitat conversion and mostly private ownership. At the same time, socio-economic impacts, driven by forestry, appear to be shifting away from ecosystems now considered high priority. Tracking shifts in socio-economic pressure may anticipate future biodiversity impacts indiscernible using assessments based on species presently at-risk.

FIELD VALIDATION AND SENSITIVITY ANALYSIS OF A MECHANISTIC MODEL FOR TREE SEED DISPERSAL BY WIND

We present a temporally and spatially explicit mechanistic model of tree seed dispersal by wind, incorporating full stochasticity based on natural variation. The model simulates the dispersal of each individual seed by integrating the temporal effects of climatic conditions on the rate of seed release, and the spatial effects of wind direction and horizontal and vertical velocities, the terminal velocity of seeds (i.e., the constant descent velocity in calm air), and the height of seed release, partitioned into tree height and the distribution of seeds with tree height. The model was tested for two Pinus halepensis stands within the Mediterranean region of Israel, in which seed dispersal has been extensively monitored by seed traps. The predicted dispersal curve verified expectations of a positively skewed leptokurtic distribution and of peak location at some distance from a point source and at zero distance from an area source. Long-distance dispersal events occurred with very low frequency, but given the large seed crop in P. halepensis, even a small fraction should result in a considerable number of seeds dispersed far from their source. The model reliably simulates the observed dispersal pattern in a spatial resolution of 1 m2 (R2 between 60% and 90%), as revealed from comparisons of the predicted and observed proportions of seed dispersed to seed traps. A sensitivity analysis using Latin hypercube sampling along with stepwise multiple rank regression showed that the effects of the horizontal and vertical wind velocities on the dispersal distance override those of the biotic factors. This suggests that the synchronization of seed release with favorable winds is the most effective plant-controlled mechanism to increase the distance of dispersal in wind-dispersed species such as P. halepensis.

Categorizing risks for risk ranking.

Any practical process of risk ranking must group hazards into a manageable number of categories. Defining such categories requires value choices that can have important implications for the rankings that result. Most risk-management organizations will find it useful to begin defining categories in terms of environmental loadings or initiating events. However, the resulting categories typically need to be modified in light of other considerations. Risk-ranking projects can benefit from considering several alternative categorization strategies and drawing upon elements of each in developing their final categorization of risks. In principle, conducting multiple ranking exercises by using different categorizations could be interesting and useful. In practice, agencies are unlikely to have either the resources or patience to do this, but other groups in society might. Done well, such additional independent rankings could add valuable inputs to democratic risk-management decision making.

A Branch and Bound Algorithm for Solving Low Rank Linear Multiplicative and Fractional Programming Problems

This paper is concerned with a practical algorithm for solving low rank linear multiplicative programming problems and low rank linear fractional programming problems. The former is the minimization of the sum of the product of two linear functions while the latter is the minimization of the sum of linear fractional functions over a polytope. Both of these problems are nonconvex minimization problems with a lot of practical applications. We will show that these problems can be solved in an efficient manner by adapting a branch and bound algorithm proposed by Androulakis–Maranas–Floudas for nonconvex problems containing products of two variables. Computational experiments show that this algorithm performs much better than other reported algorithms for these class of problems.

A novel peak-hopping stepwise feature selection method with application to Raman spectroscopy

A new stepwise approach to variable selection for spectroscopy that includes chemical information and attempts to test several spectral regions producing high ranking coefficients has been developed to improve on currently available methods. Existing selection techniques can, in general, be placed into two groups: the first, time-consuming optimization approaches that ignore available information about sample chemistry and require considerable expertise to arrive at appropriate solutions (e.g. genetic algorithms), and the second, stepwise procedures that tend to select many variables in the same area containing redundant information. The algorithm described here is a fast stepwise procedure that uses multiple ranking chains to identify several spectral regions correlated with known sample properties. The multiple-chain approach allows the generation of a final ranking vector that moves quickly away from the initial selection point, testing several areas exhibiting correlation between spectra and composition early in the stepping procedure. Quantitative evidence of the success of this approach as applied to Raman spectroscopy is given in terms of processing speed, number of selected variables, and prediction error in comparison with other selection methods. In this respect, the procedure described here may be considered as a significant evolutionary step in variable selection algorithms.

Extension of Spearman's Footrule to Multiple Rankings

Spearman's footrule measure of the relationship between two rankings is recast as a chance-corrected measure of agreement, extended to encompass multiple rankings, and generalized to include tied ranks.

Robust LQG controller design for lightly damped uncertain linear systems

In this note, we consider lightly damped uncertain linear systems with natural frequency variations. This type of uncertainty has multiple uncertain parameters with multiple rank structure. It is well known that the conventional LQG or LQG/LTR methods can not be applied to such system bccause of the instability and the design conservatism. To overcome such shortcomings, we propose a systematic method to design robust LQG controllers. The proposed method requires only the LQG tuning parameters and the structure information of uncertainty. It will be shown that our approach can be effectively applied to flexible structure control design problems.