Manifold Learning: Generalization Ability and Tangent Proximity

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional Data Manifold (DM) embedded in a high-dimensional observation space from a given set of data points sampled from the manifold. We derive asymptotic expansion and local lower and upper bounds for the maximum reconstruction error in a small neighborhood of an arbitrary point. The expansion and bounds are defined in terms of the distance between tangent spaces to the original DM and the Reconstructed Manifold (RM) at the selected point and its reconstructed value, respectively. We propose an amplification of the ML, called Tangent Bundle ML, in which proximity is required not only between the DM and RM but also between their tangent spaces. We present a new geometrically motivated Grassman & Stiefel Eigenmaps algorithm that solves this problem and gives a new solution for the ML also.     

Multiple criteria classification with an application in water resources planning

A new kind of multiple criteria decision aid (MCDA) problem, multiple criteria classification (MCC), is studied in this paper. Traditional classification methods in MCDA focus on sorting alternatives into groups ordered by preference. MCC is the classification of alternatives into nominal groups, structured by the decision maker (DM), who specifies multiple characteristics for each group. Starting with illustrative examples, the features, definition and structures of MCC are presented, emphasizing criterion and alternative flexibility. Then an analysis procedure is proposed to solve MCC problems systematically. Assuming additive value functions, an optimization model with constraints that incorporate various classification strategies is constructed to solve MCC problems. An application of MCC in water resources planning is carried out and some future extensions are suggested.     

Extremist vs. centrist decision behavior: quasi-convex utility functions for interactive multi-objective linear programming problems

This paper presents the fundamental theory and algorithms for identifying the most preferred alternative for a decision maker (DM) having a non-centrist (or extremist) preferential behavior. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives. The approach is different than other methods that consider the centrist preferential behavior.In this paper, an interactive approach is presented to solve the multiple objective linear programming (MOLP) problem. The DM's underlying preferential function is represented by a quasi-convex value (utility) function, which is to be maximized. The method presented in this paper solves MOLP problems with quasi-convex value (utility) functions by using paired comparison of alternatives in the objective space. From the mathematical point of view, maximizing a quasi-convex (or a convex) function over a convex set is considered a difficult problem to solve, while solutions for quasi-concave (or concave) functions are currently available. We prove that our proposed approach converges to the most preferred alternative.We demonstrate that the most preferred alternative is an extreme point of the MOLP problem, and we develop an interactive method that guarantees obtaining the global most preferred alternative for the MOLP problem. This method requires only a finite number of pivoting operations using a simplex-based method, and it asks only a limited number of paired comparison questions of alternatives in the objective space. We develop a branch and bound algorithm that extends a tree of solutions at each iteration until the MOLP problem is solved. At each iteration, the decision maker has to identify the most preferred alternatives from a given subset of efficient alternatives that are adjacent extreme points to the current basis. Through the branch and bound algorithm, without asking many questions from the decision maker, all branches of the tree are implicitly enumerated until the most preferred alternative is obtained. An example is provided to show the details of the algorithm. Some computational experiments are also presented.Scope and purposeThis paper presents the fundamental theory, algorithm, and examples for identifying the most preferred alternative (solution) for a decision maker (DM) having a non-centrist (or extremist) preferential behavior for Multiple Objective Linear Programming (MOLP) problems. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives.Although widely applied, Linear Programming is limited to a single objective function. In many real world situations, DMs are faced with multiple objective problems in that several competing and conflicting objectives have to be considered. For these problems, there exist many alternatives that are feasible and acceptable. However, the DM is interested in finding “the most preferred alternative”. In the past three decades, many methods have been developed for solving MOLP problems.One class of these methods is called “interactive”, in which the DM responds to a set of questions interactively so that his/her most preferred alternative can be obtained. In most of these methods, the value (utility) function (that presents the DM's preference) is assumed to be linear or additive, concave, pseudo-concave, or quasi-concave. However, for MOLP problems, there has not been any effort to recognize and solve the quasi-convex utility functions, which are among the most difficult class of problems to solve. The quasi-convex class of utility functions represents an extremist preferential behavior, while the other aforementioned methods (such as quasi-concave) represent a conservative behavioral preference. It is shown that the method converges to the optimal (the most preferred) alternative. The approach is computationally feasible for moderately sized problems.     

Expressiveness and robustness measures for the evaluation of an additive value function in multiple criteria preference disaggregation methods: An experimental analysis

An additive value function is one of the prevailing preference models in Multiple Criteria Decision Aiding (MCDA). Its indirect elicitation through pairwise questions is often applied due to lowering the cognitive effort on the part of a Decision Maker (DM). A practical usefulness of this approach is influenced by both expressiveness of the assumed model and robustness of the recommendation computed with its use. We experimentally evaluate the above characteristics in view of using an additive value function in the preference disaggregation context. The simulation results are quantified with the following four measures: (1) the share of decision scenarios for which a set of compatible value functions is non-empty, (2) the minimal difference between comprehensive values of reference alternatives compared pairwise by the DM, (3) the number of pairs of alternatives for which the necessary preference relation confirmed by all compatible functions holds, and (4) the number of non-trivial certain inferences which cannot be derived directly from the preference information. We discuss how these measures are influenced by the settings with different numbers of alternatives, criteria, pairwise comparisons, and performance distributions. We also study how the results change when applying various procedures for selection of the characteristic points which define the shape of per-criterion marginal value functions. In this regard, we compare four existing discretization algorithms with a new supervised technique proposed in this paper. Overall, we indicate that expressiveness and robustness are contradictory objectives, and a compromise between them needs to be reached to increase the usefulness of an additive value model in the preference disaggregation methods.     

A method for multiple attribute decision-making with the fuzzy preference relation on alternatives

This paper investigates the multiple attribute decision-making (MADM) problem with preference information on alternatives. A new method is proposed to solve the MADM problem, where the decision maker (DM) gives his/her preference on alternatives in a fuzzy relation. To reflect the DM's subjective preference information, a linear goal programming model is constructed to determine the weight vector of attributes and then to rank the alternatives. Finally, a numerical example is used to illustrate the use of the proposed method.     

MULTICRITERIA SORTING METHODOLOGY: APPLICATION TO FINANCIAL DECISION PROBLEMS

Abstract

The primary objective in the sorting approach is to assign a set of alternatives into predefined classes. This type of problem is often encountered in many real world decision problems. During the last two decades several new approaches have been proposed to overcome the shortcomings of traditional statistical and econometric techniques. This paper focuses on the multicriteria decision aid (MCDA) approach; it briefly reviews the main MCDA sorting techniques, and presents the multigroup hierarchical discrimination method. This new MCDA sorting technique is applied to the portfolio selection problem. A comparison with discriminant analysis is also performed. Furthermore, the efficiency of the proposal approach can be easily improved for solving large-scale problems in a multiprocessing environment.     

Group decision making in manufacturing systems: An approach using spatial preference information and indifference zone

Decision making is an essential activity in manufacturing systems when designing production lines, scheduling, etc. Many decision making problems are characterized by multiple conflicting criteria and a large number of alternatives. For these complex decision making problems, it is rational to involve a group of decision makers (DM) for considering different aspects of the problem. This paper proposes an approach for supporting the decision making group to reduce disagreement in the group and obtain a common solution. The proposed approach allows the DMs to specify a region of acceptance, known as indifference zone, in the objective space as preference inputs. This makes the proposed approach applicable to problems with a large number of alternatives. The use of indifference zone concept captures the uncertain nature of preference articulation. Moreover, the indifference zone is shown beneficial in reducing the difficulty of reaching a group common solution. The properties of the proposed method are investigated analytically and with numerical experiments. Finally, the usefulness of the proposed method is shown by tackling a real-world packaging line configuration problem with a large alternative set.     

Learning criteria weights of an optimistic Electre Tri sorting rule

Multiple criteria sorting methods assign alternatives to predefined ordered categories taking multiple criteria into consideration. The Electre Tri method compares alternatives to several profiles separating the categories. Based on such comparisons, each alternative is assigned to the lowest (resp. highest) category for which it is at least as good as the lower profile (resp. is strictly preferred by the higher profile) of the category, and the corresponding assignment rule is called pessimistic (resp. optimistic). We propose algorithms for eliciting the criteria weights and majority threshold in a version of the optimistic Electre Tri rule, which raises additional difficulties w.r.t. the pessimistic rule. We also describe an algorithm that computes robust alternatives׳ assignments from assignment examples. These algorithms proceed by solving mixed integer programs. Several numerical experiments are conducted to test the proposed algorithms on the following issues: learning ability of the algorithm to reproduce the DM׳s preference, robustness analysis and ability to identify conflicting preference information in case of inconsistencies in the learning set. Experiments show that eliciting the criteria weights in an accurate way requires quite a number of assignment examples. Furthermore, considering more criteria increases the information requirement. The present empirical study allows us to draw some lessons in view of practical applications of Electre Tri using the optimistic rule.     

Interactive approaches for biobjective problems with progressively changing solution sets

In this study, we develop interactive approaches to find a satisfactory alternative of a decision maker (DM) having a quasiconvex preference function where the alternative set changes progressively. In this environment, we keep searching the available set of alternatives and estimating the preference function of the DM. As new alternatives emerge, we make better use of the available preference information and eventually converge to a preferred alternative of the DM. We test our approaches on biobjective, multi‐item, multi‐round auction problems. The results show that our approaches work well in terms of both the preference function value of the obtained solution and the amount of preference information required.     

Interactive and nonparametric modeling of preferences on an ordinal scale using small data

In this study, we consider learning preference structure of a Decision Maker (DM). Many preference modeling problems in a variety of fields such as marketing, quality control and economics involve possibly interacting criteria, and an ordinal scale is used to express preference of objects. In these cases, typically underlying preference structure of the DM and distribution of criteria values are not known, and only a few data can be collected about the preferences of the DM.For developing a preference model under such circumstances, we propose using nonparametric Statistical Learning approaches interactively. In particular, we employ Active Learning by asking a preference question to the DM at each step and try to reach a close approximation to the correct model in a small number of steps. Our experimental analysis proves that the proposed approach outperforms a “naive” approach where subsequent questions are asked randomly. In the study, we also provide algorithmic recommendations for modeling different underlying value functions, if information is available about the form of the preference structure and/or distribution of criteria values.This study can be regarded as a pioneering approach considering that Statistical Learning based approaches in the literature have been developed and tested based on a relatively large preference information and they do not interact with the DM in model developing process while Multi Criteria Decision Aid based approaches typically ignore interactions among the criteria, suffer from generalization ability, and have no concern about predicting equally good everywhere in the criteria domain.     

Extending Malakooti's model for ranking multicriteria alternatives with preference strength and partial information

The paper deals with a multiple attribute decision making methodology when a decision maker (DM) specifies his/her preferences in imprecise ways, which is basically an extended version of Malakooti's prior work. Usually, it is said that the DM is willing, or able, to provide partial information, because of time pressure, lack of domain knowledge, or data and the like. In this paper, we consider two categories of partial preference information. First, partial information is related to holistic preference judgments about some pair of alternatives. Second, in a situation where the characteristics of some attributes considered are abstract, or noncommensurate, it is sometimes difficult to make an exact performance evaluation of alternatives with respect to those attributes. To circumvent this difficulty, we allow the DM to specify partial information on performance evaluations, which is similar to the types of preference judgments on some pairs of alternatives. Prioritizing multiple attribute alternatives under two categories of partial information causes an intractable nonlinear program, which is the first issue we try to resolve in the paper. We further propose a measure of preference strength as a decision rule. With partial information, often the use of strict dominance rule yields a larger number of nondominated candidates than the DM wants. The paper assumes a situation where the DM is not willing to provide additional information to reduce the number of nondominated candidates, but he/she wants to have a single optimal candidate or rank ordering of alternatives. It is then necessary to develop a method like one we propose as a preference strength measure.     

Neclle: Network-based communicative language-learning environment focusing on communicative gaps

This paper focuses on the problem of language transfer in foreign language learning. The transfer often leads to a communicative gap, which is caused by the difference between a learner's mother language (ML) and the target language (TL). This paper first analyzes the semantic relations between the ML and the TL. Then it proposes a CGM (Communicative Gap Model) because of the meaning difference between both languages. We have developed a computer assisted language-learning system called Neclle (Network-based Communicative Language-Learning Environment) in order to support foreign language learning through communication using a text based chat tool. Neclle has a software agent called Ankle (Agent for Kanji Learning), which observes the conversation between a learner and a native speaker, looks up a communicative gap in the learner's utterance automatically according to CGM, the student model and the word dictionary of both languages, intervenes into the conversation, and gives an instruction for bridging the gap. Then, the learner can not only be aware of the gap but also acquire its cultural background from the native speaker. In our case study, Chinese students used Neclle for Japanese language learning. Japanese language had incorporated with Chinese kanji but the meaning of a kanji sometimes differed between two languages. Therefore, the Chinese learners who want to study Japanese language have to pay much attention to the meaning gap between Chinese and Japanese language. In the evaluation of Neclle, nine Chinese students talked with Japanese students about three topics with Neclle for 1 h 30 min. The results of the experiment showed that it was very useful for Japanese language learning.     

Applications of Machine Learning: Towards knowledge synthesis

This paper shows, by discussing a number of Machine Learning (ML) applications, that the existing ML techniques can be effectively applied in knowledge acquisition for expert systems, thereby alleviating the known knowledge acquisition bottleneck. Analysis in domains of practical interest indicates that the performance accuracy of knowledge induced through learning from examples compares very favourably with the accuracy of best human experts. Also, in addition to accuracy, there are encouraging examples regarding the clarity and meaningfulness of induced knowledge. This points towards automated knowledge synthesis, although much further research is needed in this direction. The state of the art of some approaches to Machine Learning is assessed relative to their practical applicability and the characteristics of a problem domain.     

Machine Learning and Artificial Neural Network for Predicting Heart Failure Risk

Heart failure is now widely spread throughout the world. Heart disease affects approximately 48% of the population. It is too expensive and also difficult to cure the disease. This research paper represents machine learning models to predict heart failure. The fundamental concept is to compare the correctness of various Machine Learning (ML) algorithms and boost algorithms to improve models’ accuracy for prediction. Some supervised algorithms like K-Nearest Neighbor (KNN), Support Vector Machine (SVM), Decision Trees (DT), Random Forest (RF), Logistic Regression (LR) are considered to achieve the best results. Some boosting algorithms like Extreme Gradient Boosting (XGBoost) and CatBoost are also used to improve the prediction using Artificial Neural Networks (ANN). This research also focuses on data visualization to identify patterns, trends, and outliers in a massive data set. Python and Scikit-learns are used for ML. Tensor Flow and Keras, along with Python, are used for ANN model training. The DT and RF algorithms achieved the highest accuracy of 95% among the classifiers. Meanwhile, KNN obtained a second height accuracy of 93.33%. XGBoost had a gratified accuracy of 91.67%, SVM, CATBoost, and ANN had an accuracy of 90%, and LR had 88.33% accuracy.     

An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management

This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socio-economic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, co-operative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.     

Preference Learning for Cognitive Modeling: A Case Study on Entertainment Preferences

Learning from preferences, which provide means for expressing a subject's desires, constitutes an important topic in machine learning research. This paper presents a comparative study of four alternative instance preference learning algorithms (both linear and nonlinear). The case study investigated is to learn to predict the expressed entertainment preferences of children when playing physical games built on their personalized playing features ( entertainment modeling). Two of the approaches are derived from the literature-the large-margin algorithm (LMA) and preference learning with Gaussian processes-while the remaining two are custom-designed approaches for the problem under investigation: meta-LMA and neuroevolution. Preference learning techniques are combined with feature set selection methods permitting the construction of effective preference models, given suitable individual playing features. The underlying preference model that best reflects children preferences is obtained through neuroevolution: 82.22% of cross-validation accuracy in predicting reported entertainment in the main set of game survey experimentation. The model is able to correctly match expressed preferences in 66.66% of cases on previously unseen data (p -value = 0.0136) of a second physical activity control experiment. Results indicate the benefit of the use of neuroevolution and sequential forward selection for the investigated complex case study of cognitive modeling in physical games.     

部分权重信息下对方案有偏好的多属性决策法

研究只有部分权重信息且对方案有偏好的多属性决策问题．首先对方案的偏好信息以互反判断矩阵和互补判断矩阵这两种形式给出的情形，分别建立一个目标规划模型，通过求解这两个模型可确定属性的权重；然后提出一种基于目标规划模型的多属性决策方法；最后通过实例说明了该方法的可行性和有效性。     

基于覆盖的多标记学习方法研究

多标记学习是实际应用中的一类常见问题,覆盖算法在单标记学习中表现出了优秀的性能,但无法处理多标记情况。将覆盖算法推广到多标记学习中,针对多标记学习的特点和评价指标,对算法的学习和构造过程进行了改造,给出待分类样本对各类别的隶属度。将算法应用于基因数据集和自然场景数据集的学习中,实验结果表明算法能够取得较好的分类效果,且相比于大多数同类算法有更高的性能。     

An interactive sorting method for additive utility functions

In this paper, we consider the problem of placing alternatives that are defined by multiple criteria into preference-ordered categories. We consider a method that estimates an additive utility function and demonstrate that it may misclassify many alternatives even when substantial preference information is obtained from the decision maker (DM) to estimate the function. To resolve this difficulty, we develop an interactive approach. Our approach occasionally requires the DM to place some reference alternatives into categories during the solution process and uses this information to categorize other alternatives. The approach guarantees to place all alternatives correctly for a DM whose preferences are consistent with any additive utility function. We demonstrate that the approach works well using data derived from ranking global MBA programs as well as on several randomly generated problems.