Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Discretization can turn numeric attributes into discrete ones. Feature selection can eliminate some irrelevant and/or redundant attributes. Chi2 is a simple and general algorithm that uses the /spl chi//sup 2/ statistic to discretize numeric attributes repeatedly until some inconsistencies are found in the data. It achieves feature selection via discretization. It can handle mixed attributes, work with multiclass data, and remove irrelevant and redundant attributes. <s> BIB001 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <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> Feature Selection Algorithms on Ordinal Data <s> Abstract Feature selection is used to improve the efficiency of learning algorithms by finding an optimal subset of features. However, most feature selection techniques can handle only certain types of data. Additional limitations of existing methods include intensive computational requirements and inability to identify redundant variables. In this paper, we present a novel, information-theoretic algorithm for feature selection, which finds an optimal set of attributes by removing both irrelevant and redundant features. The algorithm has a polynomial computational complexity and is applicable to datasets of a mixed nature. The method performance is evaluated on several benchmark datasets by using a standard classifier (C4.5). <s> BIB003 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Feature selection (FS) is a major issue in developing efficient pattern recognition systems. FS refers to the selection of the most appropriate subset of features that describes (adequately) a given classification task. The objective of this paper is to perform a thorough analysis of the performance and efficiency of feature selection algorithms (FSAs). The analysis covers a variety of important issues with respect to the functionality of FSAs, such as: (a) their ability to identify relevant features, (b) the performance of the classification models developed on a reduced set of features, (c) the reduction in the number of features, and (d) the interactions between different FSAs with the techniques used to develop a classification model. The analysis considers a variety of FSAs and classification methods. <s> BIB004 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <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> BIB005 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Most existing algorithms for ordinal regression usually seek an orientation for which the projected samples are well separated, and seriate intervals on that orientation to represent the ranks. However, these algorithms only make use of one dimension in the sample space, which would definitely lose some useful information in its complementary subspace. As a remedy, we propose an algorithm framework for ordinal regression which consists of two phases: recursively extracting features from the decreasing subspace and learning a ranking rule from the examples represented by the new features. In this framework, every algorithm that projects samples onto a line can be used as a feature extractor and features with decreasing ranking ability are extracted one by one to make best use of the information contained in the training samples. Experiments on synthetic and benchmark datasets verify the usefulness of our framework. <s> BIB006 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Identifying a subset of features that preserves classification accuracy is a problem of growing importance, because of the increasing size and dimensionality of real-world data sets. We propose a new feature selection method, named Quadratic Programming Feature Selection (QPFS), that reduces the task to a quadratic optimization problem. In order to limit the computational complexity of solving the optimization problem, QPFS uses the Nystrom method for approximate matrix diagonalization. QPFS is thus capable of dealing with very large data sets, for which the use of other methods is computationally expensive. In experiments with small and medium data sets, the QPFS method leads to classification accuracy similar to that of other successful techniques. For large data sets, QPFS is superior in terms of computational efficiency. <s> BIB007 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Measures of statistical dependence such as the correlation coefficient and mutual information have been widely used in variable selection. The use of correlation has been inspired by the concept of regression whereas the use of mutual information has been largely motivated by information theory. In a statistical sense, however, the concept of dependence is much broader, and extends beyond correlation and mutual information. In this paper, we explore the fundamental notion of statistical dependence in the context of variable selection. In particular, we discuss the properties of dependence as proposed by Renyi, and evaluate their significance in the variable selection context. We, also, explore a measure of dependence that satisfies most of these desired properties, and discuss its applicability as a substitute for correlation coefficient and mutual information. Finally, we compare these measures of dependence to select important variables for regression with real world data. <s> BIB008 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Ordinal regression (also known as ordinal classification) is a supervised learning task that consists of automatically determining the implied rating of a data item on a fixed, discrete rating scale. This problem is receiving increasing attention from the sentiment analysis and opinion mining community, due to the importance of automatically rating increasing amounts of product review data in digital form. As in other supervised learning tasks such as (binary or multiclass) classification, feature selection is needed in order to improve efficiency and to avoid overfitting. However, while feature selection has been extensively studied for other classification tasks, is has not for ordinal regression. In this paper we present four novel feature selection metrics that we have specifically devised for ordinal regression, and test them on two datasets of product review data. <s> BIB009 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> We present four new feature selection methods for ordinal regression and test them against four dierent baselines on two large datasets of product reviews. <s> BIB010 </s> Multicriteria Models for Learning Ordinal Data: A Literature Review <s> Feature Selection Algorithms on Ordinal Data <s> Feature selection is a topic of growing interest mainly due to the increasing amount of information, being an essential task in many machine learning problems with high dimensional data. The selection of a subset of relevant features help to reduce the complexity of the problem and the building of robust learning models. This work presents an adaptation of a recent quadratic programming feature selection technique that identifies in one-fold the redundancy and relevance on data. Our approach introduces a non-probabilistic measure to capture the relevance based on Minimum Spanning Trees. Three different real datasets were used to assess the performance of the adaptation. The results are encouraging and reflect the utility of feature selection algorithms. <s> BIB011
Nowadays, it is relatively easy to solve problems with millions of instances, each of them with a reasonable number of features. However, it is common to have access to datasets with significantly higher number of features than instances leading to the well known problem of the curse of dimensionality. Feature selection (FS) techniques provide the means to overcome this issue by identifying the most valuable features so that good and simple class discrimination models can be obtained. Furthermore, a noise reduced dataset can be achieved since these methods can "clean" data from features with noise BIB004 . There are three types of feature selection algorithms: Filter, wrapper and embedded. The former is independent of the classifier being usually done before the learning phase. Wrapper algorithms iteratively select subset of features and assess the learning models performance to determine how useful that set of features are whereas embedded algorithms select automatically features during the model construction BIB004 BIB007 . Fig. 9 succinctly depicts the three approaches. Feature selection on ordinal data is a relatively young topic. In BIB001 a χ 2 statistic method is used to discretize numeric features as a way to select features. Even though the method proposed by Liu BIB001 was identified as being limited to a firstorder feature-class correlation (i.e., are linearly correlated), such should not be seen as a drawback. Once highly complex learning machines could easily cope with the data complexity and infer a linear relation with the features and classes, or more precisely, perform overfitting on data BIB008 BIB011 . Nevertheless, Last et al in BIB003 proposed an information-theoretic method for feature selection by performing a discretization over the features in order to minimise classes entropy. Even though ordinal data can contain only discrete features fitting well to this technique, there are datasets with continuous features (see for instance BIB005 ). In such scenarios, applying a discretization technique can lead to loss of accuracy in the model design. Despite being mentioned the capability to handle ordinal data, no experiment has been conducted, neither their methods were designed for this type of problems. Through a completely different approach, Xia et al. BIB006 presents a recursive approach to extract features where it learns consecutively new rules from instances represented by the new features. Other techniques in the ordinal context have been referred to Baccianella et al in BIB009 BIB010 . Using only the filter approach for feature selection, authors used several measures to identify feature relevance through the minimisation of the instances variance over all classes, similarity, information gain and negative correlation according to the class label, specifically developed for ordinal problems. Finally, Sousa et al. BIB011 explored a concept introduced by Rodriguez et al. BIB007 where they tackle the FS problem in one-step process through quadratic programming as represented in Equation BIB002 . The quadratic term (Q in Equation (6)) would capture the redundancy whereas the linear term (F in Equation (6)) would capture the relevance. Here α is the trade-off between relevance and redundancy which can be empirically defined. In order to capture the ordinal relation on data in this setting, authors chosen the Minimum Spanning Trees (MST) as the linear term (F) to assess the increase of complexity when a subset of features is removed. However, one of the issues identified in this approach concerns to the fact that authors did not take advantage of the ordinal information that could be explicitly included on data (quadratic term).