Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Abstract This paper addresses decision problems with ordinal data (weights, criterion scores). A random sampling approach is proposed to generate quantitative values which are consistent with the underlying ordinal information. An attractive feature of the approach is that it is applicable with mixed (quantitative/ordinal) data. Another feature is that the approach can be extended to rankings with degrees of difference. The outcome of the approach is a distribution of performance scores. Stochastic dominance concepts are proposed to arrive at a final ranking of alternatives. An application of these procedures is given for a location study of nuclear power plants. <s> BIB001 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Abstract This paper presents a new fuzzy multicriteria classification method, called PROAFTN , for assigning alternatives to predefined categories. This method belongs to the class of supervised learning algorithms and enables to determine the fuzzy indifference relations by generalising the indices (concordance and discordance) used in the ELECTRE III method. Then, it assigns the fuzzy belonging degree of the alternatives to the categories. We also present a clinical application of the proposed method in the cytopathological diagnosis of acute leukaemia. <s> BIB002 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Abstract In this paper we describe a real-life application of an ordinal multicriteria method in the context of choosing a location for a waste treatment facility near Lappeenranta in South-Eastern Finland. The associated environmental impact assessment (EIA) procedure is briefly described. The application was characterized by two interesting properties: no preference information was available, and only ordinal measurements for the criteria were available. The large amount of data obtained was then analyzed using the SMAA-O method – Stochastic Multicriteria Acceptability Analysis with Ordinal criteria designed for this problem setting. SMAA-O converts ordinal information into cardinal data by simulating all possible mappings between ordinal and cardinal scales that preserve the given rankings. As with the basic SMAA-method, the decision makers' (DMs) unknown or partly known preferences are at the same time simulated by choosing weights randomly from appropriate distributions. The main results of the analysis are acceptability indices for alternatives describing the variety of preferences that could make each alternative the best choice. Based on these and additional considerations, the DMs made the final choice for the location of the plant. <s> BIB003 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Abstract Corporate credit risk assessment decisions involve two major issues: the determination of the probability of default and the estimation of potential future benefits and losses for credit granting. The former issue is addressed by classifying the firms seeking credit into homogeneous groups representing different levels of credit risk. Classification/discrimination procedures commonly employed for such purposes include statistical and econometric techniques. This paper explores the performance of the M.H.DIS method (Multi-group Hierarchical DIScrimination), an alternative approach that originates from multicriteria decision aid (MCDA). The method is used to develop a credit risk assessment model using a large sample of firms derived from the loan portfolio of a leading Greek commercial bank. A total of 1411 firms are considered in both training and holdout samples using financial information through the period 1994–1997. A comparison with discriminant analysis (DA), logit analysis (LA) and probit analysis (PA) is also conducted to investigate the relative performance of the M.H.DIS method as opposed to traditional tools used for credit risk assessment. <s> BIB004 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Credit ratings issued by international agencies are extensively used in practice to support investment and financing decisions. Furthermore, a considerable portion of the financial research has been devoted to the analysis of credit ratings, in terms of their effectiveness, and practical implications. This paper explores the development of appropriate models to replicate the credit ratings issued by a rating agency. The analysis is based on a multicriteria classification method used in the development of the model. Special focus is laid on testing the out-of-time and out-of-sample effectiveness of the models and a comparison is performed with other parametric and non-parametric classification methods. The results indicate that using publicly available financial data, it is possible to replicate the credit ratings of the firms with a satisfactory accuracy. <s> BIB005 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Collaborative filtering (CF) is a data analysis task appearing in many challenging applications, in particular data mining in Internet and e-commerce. CF can often be formulated as identifying patterns in a large and mostly empty rating matrix. In this paper, we focus on predicting unobserved ratings. This task is often a part of a recommendation procedure. We propose a new CF approach called interlaced generalized linear models (GLM); it is based on a factorization of the rating matrix and uses probabilistic modeling to represent uncertainty in the ratings. The advantage of this approach is that different configurations, encoding different intuitions about the rating process can easily be tested while keeping the same learning procedure. The GLM formulation is the keystone to derive an efficient learning procedure, applicable to large datasets. We illustrate the technique on three public domain datasets. <s> BIB006 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Objective: This work presents a novel approach for the automated prediction of the aesthetic result of breast cancer conservative treatment (BCCT). Cosmetic assessment plays a major role in the study of BCCT. Objective assessment methods are being preferred to overcome the drawbacks of subjective evaluation. Methodology: The problem is addressed as a pattern recognition task. A dataset of images of patients was classified in four classes (excellent, good, fair, poor) by a panel of international experts, providing a gold standard classification. As possible types of objective features we considered those already identified by domain experts as relevant to the aesthetic evaluation of the surgical procedure, namely those assessing breast asymmetry, skin colour difference and scar visibility. A classifier based on support vector machines was developed from objective features extracted from the reference dataset. Results: A correct classification rate of about 70% was obtained when categorizing a set of unseen images into the aforementioned four classes. This accuracy is comparable with the result of the best evaluator from the panel of experts. Conclusion: The results obtained are rather encouraging and the developed tool could be very helpful in assuring objective assessment of the aesthetic outcome of BCCT. <s> BIB007 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Although breast density is considered a strong predictor of breast cancer risk, its quantitative assessment is difficult. The aim of this study is to demonstrate that breast density assessment with a fully automated software is feasible and correlates with the semi-automated evaluation and the quantitative BI-RADS standards. A data set of 160 mammograms was evaluated by three blinded radiologists. Intra-observer (reader 1: k=0.71; reader 2: k=0.76; reader 3: k=0.62) and inter-observer (reader 1 vs reader 2: k=0.72; reader 2 vs reader 3: k=0.80; reader 3 vs reader 1: k=0.72) variability for the semi-automated software were good on a four-grade scale (D1/D2/D3/D4) and correlated with BI-RADS evaluation made by other two blinded radiologists (r=0.65, p<0.01). Inter-observer (reader 1 vs reader 2: k=0.85; reader 2 vs reader 3: k=0.91; reader 3 vs reader 1: k=0.85) variability for the semi-automated software was very good on a two-grade scale (D1-D2/D3-D4). The use of the fully automated software eliminated intra- and inter-observer differences, correlated with BI-RADS categories (r=0.62, p<0.01) and can replace the semi-automated one (Bland-Altman statistics). Our study demonstrates that automated estimation of breast density is feasible and eliminates subjectivity. Furthermore both the semi-automated and the fully automated density estimation are more accurate than BI-RADS quantitative evaluation and could also be used in the daily clinical practice. <s> BIB008 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Credit scoring is very important in business, especially in banks. We want to describe a person who is a good credit or a bad one by evaluating his/her credit. We systematically proposed three link analysis algorithms based on the preprocess of support vector machine, to estimate an applicant's credit so as to decide whether a bank should provide a loan to the applicant. The proposed algorithms have two major phases which are called input weighted adjustor and class by support vector machine-based models. In the first phase, we consider the link relation by link analysis and integrate the relation of applicants through their information into input vector of next phase. In the other phase, an algorithm is proposed based on general support vector machine model. A real world credit dataset is used to evaluate the performance of the proposed algorithms by 10-fold cross-validation method. It is shown that the genetic link analysis ranking methods have higher performance in terms of classification accuracy. <s> BIB009 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> A comprehensive understanding of cancer progression may shed light on genetic and molecular mechanisms of oncogenesis, and it may provide much needed information for effective diagnosis, prognosis, and optimal therapy. However, despite considerable effort in studying cancer progressions, their molecular and genetic basis remains largely unknown. Microarray experiments can systematically assay gene expressions across genome, therefore they have been widely used to gain insights on cancer progressions. In general, expression data may be obtained from different stages of the same samples. More often, data were obtained from individuals at different stages. Existing methods such as the Student’s t-test and clustering approaches focus on identification of differentially expressed genes in different stages, but they are not suitable for capturing real progression signatures across all progression stages. We propose an alternative approach, namely a multicategory logit model, to identify novel genes that show significant correlations across multiple stages. We have applied the approach on a real data set concerning prostate cancer progression and obtained a set of genes that show consistency trends across multiple stages. Further analysis based on Gene Ontology (GO) annotations, protein-protein interaction networks and KEGG pathways databases, as well as literature search demonstrates that our candidate list not only includes some well-known prostate cancer related genes such as MYC and AMACR, but also consists of novel genes (e.g. CKS2)that have been confirmed by very recent independent studies. Our results illustrate that ordinal analysis of cancer progression data has the potential to obtain a set of promising candidate genes. Such a list can be further prioritized by combining other existing biomedical knowledge to identify therapeutic targets and/or biomarkers of cancer progressions. <s> BIB010 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Within the multicriteria aggregation-disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM's preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM's preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach. In our methodology, besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives A'[subset, double equals]A, the DM is also requested to express the intensity of preference on pairs of alternatives from A', and to supply pairwise comparisons on the importance of criteria, and the sign and intensity of interaction among pairs of criteria. The output of our approach defines a set of fuzzy measures (capacities) such that the corresponding Choquet integral is compatible with the DM's preference information. Moreover, using linear programming, our decision model establishes two preference relations for any a,b[set membership, variant]A: the necessary weak preference relation, if for all compatible fuzzy measures the utility of a is not smaller than the utility of b, and the possible weak preference relation, if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b. <s> BIB011 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Introduction <s> Tissue microarray (TMA) data are commonly used to validate the prognostic accuracy of tumor markers. For example, breast cancer TMA data have led to the identification of several promising prognostic markers of survival time. Several studies have shown that TMA data can also be used to cluster patients into clinically distinct groups. Here we use breast cancer TMA data to cluster patients into distinct prognostic groups. <s> BIB012
Learning multicriteria (MC) models from data has recently gathered a substantial attention. Such trend has its reasons in the diverse set of applications which can be found in management BIB003 BIB001 , financial BIB004 BIB005 and medical BIB002 BIB008 fields, to name a few. Consequently, the very diversity of the multicriteria learning research topics led to a discussion and proposals in several different fields. Decision analysis, machine learning and statistics/econometrics are some of them. Hence, a rich terminology can be found due to this diverse fields of study. Sorting, ranking, dominance, among others, are some of the many names referring to multicriteria methods. Even though mostly all share the same fundamental principles, it is on the methods assumptions that most differences occur. Nevertheless, methods for learning ordinal data have been recently seen as a generalisation of some multicriteria techniques BIB011 . The importance of ordinal data is clear. Nowadays, industry tries to cope with current technological advancements and towards profit maximisation. Hence, more and more personalised products and services are being commercialised to a wider audience. Problems like credit scoring where the system evaluates the capability of one default his debts BIB004 BIB005 BIB009 by grading a customer credit profile in the scale Excelent Good Fair Poor, movies suggestion BIB006 , breast cancer diagnosis BIB007 , or gene analysis through the analysis of hyperactivity on certain proteins BIB012 BIB010 , are some examples of ordinal problems where data is structured by a "natural" order. As a result, new and robust computational methods capable to unravel reasoning's behind ones decisions also led to new theoretical developments. Regarding to these developments two major disciplines lead the research: Operations Research (OR) and Artificial Intelligence (AI). In this chapter it is presented a literature review over different areas that deal with ordinal data, in general, to the extent of what it is known nowadays. Section 2 starts by providing the terminology that will be used. Section 3 will focus on methods on the operations research side whereas techniques in the artificial intelligence field will be described in Section 4. Section 3 will be concerned mainly about aggregation models, fuzzy and rough set theory, and evolutionary algorithms approaches. Section 4 will be dedicated to inductive learning, a very large and important topic within AI. In this section different existing works in the literature will be identified as well as feature selection approaches (Section 4.1) and performance assessment metrics (Section 4.2). As remainder of this chapter, in Section 5, one will draw a summary of what has been achieved until now and what still poses as open problems.