Partial Order Ranking Research Articles

Ranking Karnataka Districts by the Multidimensional Poverty Index (MPI) and by Applying Simple Elements of Partial Order Theory

This study focuses on the Multidimensional Poverty Index (MPI) ranking. The standard ranking process of the MPI produces a single total (linear) rank of units by simply ordering them from the best to the worst (or the inverse) as a function of their MPI score. However, units are not necessarily comparable regarding all 10 indicators simultaneously on which the MPI is based. We use the 2012/13 India District Level Household Survey wave four with a special focus on the State of Karnataka. By using partial order theory (i.e. the Hasse Diagram technique and the software package PyHasse), we found that, in Karnataka, the number of incomparabilities greatly exceeds the number of comparabilities. This indicates that the aggregation process leading to the MPI hides the individual role of indicators. We utilized a number of tools in partial order theory to analyze the comparabilities and incomparabilities. This included local partial order, antichain, and average height analysis. In contrast with the standard MPI ranking, partial order theory provides average height which does not only account for comparable districts, but also considers to what extent incomparable districts influence the position of a district in the ranking. We found that the results of partial order ranking deviate considerably from those of the MPI ranking. Given the extent of incomparabilities, for most of our sample, the MPI ranking does not provide an adequate ranking. The Hasse Diagram technique, can therefore be seen as a synthetic ranking tool or a robustness tool that complements the standard ranking process of the MPI.

Boosting with structural sparsity: A differential inclusion approach

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative regularization path with structural sparsity where the parameter is sparse under some linear transforms, based on variable splitting and the Linearized Bregman Iteration. Hence it is called Split LBI . Despite its simplicity, Split LBI outperforms the popular generalized Lasso in both theory and experiments. A theory of path consistency is presented that equipped with a proper early stopping, Split LBI may achieve model selection consistency under a family of Irrepresentable Conditions which can be weaker than the necessary and sufficient condition for generalized Lasso. Furthermore, some ℓ 2 error bounds are also given at the minimax optimal rates. The utility and benefit of the algorithm are illustrated by several applications including image denoising, partial order ranking of sport teams, and world university grouping with crowdsourced ranking data.

Analysis of membrane bioreactor performance for wastewater treatment using ranking methods

ABSTRACTThe research compares four types of different designs of membrane bioreactors: (1) with 295-mm draft tube and without plastic carriers; (2) plastic carriers and 295-mm draft tube; (3) plastic carriers and 235-mm draft tube with two meshes around the bottom and top of a draft tube; and (4) plastic carriers without a draft tube. The feed for the reactors was artificial wastewater made from domestic wastewater and chicken manure, and membrane test data were based on a hollow fiber membrane module under ambient desert conditions. Process operation type D is the optimal choice. Mathematical analysis using total ranking methods, multi-indicator decision-making, and Hasse diagram support this choice. Concerning analysis by the different tools, inconsistencies between the rankings are noticed. Partial order ranking, as a method without any pre-assumptions concerning the possible relation between the single parameters, proves to be an elegant ranking method.

Application of partial order ranking to identify enhancement potentials for the provision of selected ecosystem services by different land use strategies

Conventional agricultural practices have often been associated with negative externalities, such as land degradation, pollution of soil and water resources, loss of biodiversity, and decreased provision of ecosystem services (ES). In response to these negative effects, the number of indicator-based attempts to assess ES provided by land use systems has increased. However, decisions regarding the importance of the different ES are usually made subjectively. Following an objective approach through the use of a partial order ranking method, this study aimed to assess several non-provisioning ES supplied by alley cropping system (ACS) in comparison with conventional agriculture (CA). The main objective of the study was to verify the applicability of partial order ranking to an ecologically-based assessment, focusing on soil, water, and biodiversity indicators. Results from 40 hypothetical scenarios representing various site conditions of agricultural fields in Germany were calculated using the Ecosystem Services Assessment Tool for Agroforestry (ESAT-A), a toolbox designed to assess selected ES of ACS following an empirical approach. The results were ranked using partial order and were visualized by a Hasse diagram. The findings depict partial order ranking as a promising technique to support decision making in order to find priority scenarios and indicators where the provision of ES can be enhanced by establishing ACS. The minimal scenarios under CA identified with simultaneously low values of all indicators were perceived as target scenarios for establishing ACS. The values of the indicators for the current land use system need to be taken into account in order to avoid scenarios where high tradeoff was suggested. Additionally, this approach can be extended and utilized at the field level to aid farmer decisions on which land use strategy is the most suitable alternative to increase the provision of ES.

A Choice Index: Insuring Weather and Disaster Risk

Index triggers have enabled the extension of insurance to disaster risks by providing a simple mechanism to determine insurance payment. Disaster risks are notoriously difficult to insure against due to the covariant nature of risks, moral hazard and adverse selection. Index based risk transfer minimizes these obstacles by not fully insuring the risk. However, such incompleteness generates basis risk, that is the risk that claims do not match losses. This paper analyzes the upside basis risk (receiving a claim without a loss) and downside basis risk (having a loss but no claim) to determine a partial order ranking of indices for any risk averse individual. The partial ranking allows the selection of an index that is optimal for any individual with unknown risk aversion. Results demonstrate that correlation and covariance can provide incorrect comparisons between indices.

Partial order methodology: a valuable tool in chemometrics

Often from multi‐indicator system (MIS), a composite indicator is derived by applying weighted sums of the single indicators. The eventual ranking being based on composite indicator yields a total (linear) ranking. In contrast, partial order ranking constitutes an alternative approach where assumptions about linearity or distribution of the indicators are not needed and indicators are in general used without quantification of mutual preferences. The present paper describes analyses of MIS based on a series of partial order techniques as offered by the PyHasse software. The paper describes how important information on an MIS can be obtained without lengthy and often controversial and possible subjective discussions about indicator weights and thus avoiding both covering up valuable information contained in the single indicators as well as unwanted compensation effects. The application of partial order for obtaining chemometric information is illustrated by a study of 12 chloro‐organic pesticides. All calculation has been carried out applying the experimental software PyHasse. Copyright © 2013 John Wiley & Sons, Ltd.

On the ranking of chemicals based on their PBT characteristics: Comparison of different ranking methodologies using selected POPs as an illustrative example

Knowledge of the environmental behavior of chemicals is a fundamental part of the risk assessment process. The present paper discusses various methods of ranking of a series of persistent organic pollutants (POPs) according to the persistence, bioaccumulation and toxicity (PBT) characteristics. Traditionally ranking has been done as an absolute (total) ranking applying various multicriteria data analysis methods like simple additive ranking (SAR) or various utility functions (UFs) based rankings. An attractive alternative to these ranking methodologies appears to be partial order ranking (POR). The present paper compares different ranking methods like SAR, UF and POR. Significant discrepancies between the rankings are noted and it is concluded that partial order ranking, as a method without any pre-assumptions concerning possible relation between the single parameters, appears as the most attractive ranking methodology. In addition to the initial ranking partial order methodology offers a wide variety of analytical tools to elucidate the interplay between the objects to be ranked and the ranking parameters. In the present study is included an analysis of the relative importance of the single P, B and T parameters.

Can the National Classification System for Contaminated Sites be used to rank sites?

In this paper, the ability of the National Classification System for Contaminated Sites (NCSCS) to rank contaminated sites has been investigated by comparing NCSCS score ranks to preliminary quantitative risk assessment (PQRA) result ranks. A recently published hierarchical partial order ranking procedure was applied to hazard quotients from PQRAs to generate ranks. Using data from 20 federal contaminated sites, the study showed that sites with low and high NCSCS score ranks correspond reasonably with low and high PQRA results ranks though there is scatter amongst the data in mid-ranges. Although the output from both the NCSCS and PQRAs have significant uncertainties, the study concludes that indeed the NCSCS can be used to rank sites. A figure is provided indicating the probability that a site with a higher NCSCS score will have a higher rank, as per PQRA.

How to Guide and Assess Risk Reduction using Risk Characterization Indicators

Problem statement: The risk level predictions in risk assessment often suffer from uncertainties and may, thus, overlook some adverse effects. This problem can be reduced by using risk reduction strategies that continuously guide activities toward lowest possible risk. Approach: This study suggested a method to guide and assess such risk reduction strategies using multi-indicator risk characterization. It was a challenge for the method to secure robustness against unavoidable high uncertainty and to secure flexibility that embraced multiple indicators for different aspects governing the risk level. This methodology was to protect real existing targets, denoted Protection Units (PU), against adverse effects and applied knowledge about all PUs, or a representative fraction of those. A set of risk indicators described different aspects of the risk level for each PU. A scenario in this context contained the set of PUs, each having their risk level described by the set of different risk indicator values. Results: The result was a multi-criterion solution that was analyzed using partial order ranking, where ambiguities between single criteria prediction of risk level as either higher or lower were analyzed and mapped. Conclusion/Recommendations: Risk level hotspots, in which several criteria simultaneously predicted higher risk level for specific PUs, was used as key-elements to provide guidance and assessment of the need for risk reduction and the method was, therefore, called Hotspot ruled ranking (HotsRank).

The Interplay between QSAR/QSPR Studiesand Partial Order Ranking and Formal Concept Analyses

The often observed scarcity of physical-chemical and well as toxicological data hampers the assessment of potentially hazardous chemicals released to the environment. In such cases Quantitative Structure-Activity Relationships/Quantitative Structure-Property Relationships (QSAR/QSPR) constitute an obvious alternative for rapidly, effectively and inexpensively generatng missing experimental values. However, typically further treatment of the data appears necessary, e.g., to elucidate the possible relations between the single compounds as well as implications and associations between the various parameters used for the combined characterization of the compounds under investigation. In the present paper the application of QSAR/QSPR in combination with Partial Order Ranking (POR) methodologies will be reviewed and new aspects using Formal Concept Analysis (FCA) will be introduced. Where POR constitutes an attractive method for, e.g., prioritizing a series of chemical substances based on a simultaneous inclusion of a range of parameters, FCA gives important information on the implications associations between the parameters. The combined approach thus constitutes an attractive method to a preliminary assessment of the impact on environmental and human health by primary pollutants or possibly by a primary pollutant well as a possible suite of transformation subsequent products that may be both persistent in and bioaccumulating and toxic. The present review focus on the environmental – and human health impact by residuals of the rocket fuel 1,1-dimethylhydrazine (heptyl) and its transformation products as an illustrative example.

A QSAR/QSTR study on the human health impact of the rocket fuel 1,1-dimethyl hydrazine and its transformation products: Multicriteria hazard ranking based on partial order methodologies

The possible impact of the rocket fuel 1,1-dimethyl hydrazine (heptyl) ( 1) and its transformation products on human health has been studied using (Quantitative) Structure Activity/Toxicity ((Q)SAR/(Q)STR) modelling, including both ADME models and models for acute toxicity, organ specific adverse haematological effects, the cardiovascular and gastrointestinal systems, the kidneys, the liver and the lungs, as well as a model predicting the biological activity of the compounds. It was predicted that all compounds studied are readily bioavailable through oral intake and that significant amounts of the compounds will be freely available in the systemic circulation. In general, the compounds are not predicted to be acutely toxic apart from hydrogen cyanide, whereas several compounds are predicted to cause adverse organ specific human health effects. Further, several compounds are predicted to exhibit high probabilities for potential carcinogenicity, mutagenicity, teratogenicity and/or embryotoxicity. The compounds were ranked based on their predicted human health impact using partial order ranking methodologies that highlight which compounds on a cumulative basis should receive the major attention, i.e., N-nitroso dimethyl amine, 1,1,4,4-tetramethyl tetrazene, trimethyl, trimethyl hydrazine, acetaldehyde dimethyl hydrazone, 1, 1-formyl 2,2-dimethyl hydrazine and formaldehyde dimethyl hydrazone, respectively.

Assessment of Chemicals Applying Partial Order Ranking Techniques

This review summarizes the use of partial order ranking (POR) techniques for the assessment of chemicals. Simple partial order ranking may advantageously be applied to give the single chemicals investigated an identity in relation to other substances. Thus, it constitutes an effective tool for the prioritization of chemicals, e.g., based on their PBT (Persistence, Bioaccumulating, Toxicity) characteristics. In more elaborate cases where a larger number of descriptors are taken into account, e.g., comprising physico-chemical characteristics, atmospheric parameters, geospecific factors, and possibly socio-economic factors, hierarchical partial order ranking (HPOR) may be applied. Thus, in a first ordering step, a series of meta-descriptors are generated that later subsequently may be used as descriptors in subsequent ordering. HPOR allows a sensible ranking model even if a relatively high number of descriptors are included. Finally, accumulation partial order ranking (APOR) is illustrated. Accumulating partial APOR is a technique where data from a series of individual tests of various characteristics are aggregated while maintaining the basics of the partial order ranking methodology. APOR offers prioritization based on mutual probabilities derived from the aggregated data. Alternatively, prioritization may be achieved based on averaged ranks derived from the APOR. The application APOR is demonstrated by an assessment of a series of potential PBT substances. In all cases, an absolute ranking can be achieved based on the average ranks of the single substances. Alternatively, ranking probabilities can be derived.

Partial Order Theory Applied to QSPR-QSAR Studies

There exists a great amount of information on ranking methods provided in the literature, a new appealing methodology that is generally dealt in a so mathematical fashion. Ranking strategies are applied in a wide range of scientific fields, such as Decision Support, Toxicology, Environmental Research, Analytical Chemistry, Food Chemistry, QSPR-QSAR, etc. When contrasted to other multi-criteria data analyzes, Partial Order Ranking results in a very transparent and suitable way to perform comparisons among a set of objects (such as molecules) according to their attributes (molecular descriptors) values. The scope of this review is to explore such sorting ideas and to provide the non-specialist reader with insights into this formalism applied to QSPR-QSAR studies. Several concepts are explained, revising some of the research developed by different experts on the topic.

Accumulating partial order ranking

Typically a prioritization between collections of objects involves several parameters and requires thus the application of multicriteria methodologies. Partial order ranking offers a non-parametric method that neither includes any assumptions about linearity nor any assumptions about distribution properties. Accumulating partial order ranking (APOR) is a novel technique where data from a series of individual tests of various characteristics are aggregated, however, maintaining the basics of the partial order ranking methodology. APOR offers prioritization based on mutual probabilities derived from the aggregated data. Alternatively prioritization may be achieved based on averaged ranks derived from the APOR. The present study illustrates the application APOR by an assessment of a series of chemical substances.

Hierarchical partial order ranking

Assessing the potential impact on environmental and human health from the production and use of chemicals or from polluted sites involves a multi-criteria evaluation scheme. A priori several parameters are to address, e.g., production tonnage, specific release scenarios, geographical and site-specific factors in addition to various substance dependent parameters. Further socio-economic factors may be taken into consideration. The number of parameters to be included may well appear to be prohibitive for developing a sensible model. The study introduces hierarchical partial order ranking (HPOR) that remedies this problem. By HPOR the original parameters are initially grouped based on their mutual connection and a set of meta-descriptors is derived representing the ranking corresponding to the single groups of descriptors, respectively. A second partial order ranking is carried out based on the meta-descriptors, the final ranking being disclosed though average ranks. An illustrative example on the prioritization of polluted sites is given.

Partial Order Ranking for the aqueous toxicity of aromatic mixtures

We apply a predictive method based on Partial Order Ranking that employs a single molecular descriptor in the model and that is simple enough to perform calculations by hand. A comparison of this procedure with results obtained from the least squares technique is carried out, using aqueous toxicity values elicited by 67 compounds and their aromatic mixtures, and the octanol/water partition coefficient as structural descriptor. Both techniques verify that, by means of a previous classification of the compounds in polar and non-polar groups, it is possible to predict the joint toxicological effect.

Application of a novel ranking approach in QSPR-QSAR

In this study we present a simple algorithm based on the Partial Order Ranking (POR) technique which allows to rank a series of compounds according to their molecular descriptor values. A training set composed of 82 normal boiling points for structurally diverse organic compounds is analyzed by considering a pool of 1202 molecular descriptors obtained from the Dragon 5 software and two “flexible” type of variables. The predictive performance of the proposed approach is assessed by means of a test set of 82 “unknown” structurally related molecules.

A combined QSAR and partial order ranking approach to risk assessment†

QSAR generated data appear as an attractive alternative to experimental data as foreseen in the proposed new chemicals legislation REACH. A preliminary risk assessment for the aquatic environment can be based on few factors, i.e. the octanol-water partition coefficient (Kow ), the vapour pressure (VP) and the potential biodegradability of the compound in combination with the predicted no-effect concentration (PNEC) and the actual tonnage in which the substance is produced. Application of partial order ranking, allowing simultaneous inclusion of several parameters leads to a mutual prioritisation of the investigated substances, the prioritisation possibly being further analysed through the concept of linear extensions and average ranks. The ranking uses endpoint values (log Kow and log VP) derived from strictly linear ‘noise-deficient’ QSAR models as input parameters. Biodegradation estimates were adopted from the BioWin module of the EPI Suite. The population growth impairment of Tetrahymena pyriformis was used as a surrogate for fish lethality. †Presented at CMTPI 2005: Computational Methods in Toxicology and Pharmacology Integrating Internet resources (Shanghai, China, October 29–November 1 2005).

QSPR modeling of the enthalpy of formation based on Partial Order Ranking

A new predictive method based on Partial Order Ranking is introduced in the realm of the QSPR–QSAR Theory using a single descriptor as variable and which is simple enough to perform calculations by hand. Comparisons are made with a model relying on the Least Squares Method subjected to the modeling of the Enthalpy of Formation from Elements exhibed by a set of 51 hydrocarbon molecules by means of a flexible type descriptor. The results achieved with the proposed method are quite satisfactory and its future aplicability seems to be very promising.

Giving Molecules an Identity. On the Interplay Between QSARs and Partial Order Ranking

The interplay between 'noise-deficient' QSAR and Partial Order Ranking, including analysis of average linear ranks, constitutes an effective tool in giving substances which have not been investigated experimentally an identity by comparison with experimentally well-characterized, structurally similar compounds. It is disclosed that experimentally well-characterized compounds may serve as substitutes for highly toxic compounds in experimental studies without exhibiting the same extreme toxicity, while from an overall viewpoint they exhibit analogous environmental characteristics.