Multicriteria classification and sorting methods: A literature review

The body of literature on classification methods which estimate boundaries between the groups (classes) by optimizing a function of the L
 p
 -norm distances of observations in each group from these boundaries, is maturing fast. The number of published research articles on this topic, especially on mathematical programming (MP) formulations and techniques for L
 p
 -norm classification, is now sizable. This paper highlights historical developments that have defined the field, and looks ahead at challenges that may shape new research directions in the next decade. In the first part, the paper summarizes basic concepts and ideas, and briefly reviews past research. Throughout, an attempt is made to integrate a number of the most important L
 p
 -norm methods proposed to date within a unified framework, emphasizing their conceptual differences and similarities, rather than focusing on mathematical detail. In the second part, the paper discusses several potential directions for future research in this area. The long-term prospects of L
 p
 -norm classification (and discriminant) research may well hinge upon whether or not the channels of communication between on the one hand researchers active in L
 p
 -norm classification, who tend to have their roots primarily in the decision sciences, the management sciences, computer science and engineering, and on the other hand practitioners and researchers in the statistical classification community, will be improved. This paper offers potential reasons for the lack of communication between these groups, and suggests ways in which L
 p
 -norm research may be strengthened from a statistical viewpoint. The results obtained in L
 p
 -norm classification studies are clearly relevant and of importance to all researchers and practitioners active in classification and discriminant analysis. The paper also briefly discusses artificial neural networks, a promising non-traditional method for classification which has recently emerged, and suggests that it may be useful to explore hybrid classification methods that take advantage of the complementary strengths of different methods, e.g., neural network and L
 p
 -norm methods.

Nontraditional approaches to statistical classification: Some perspectives on L_p-norm methods

Mathematical programming and multicriteria approaches to classification and discrimination are reviewed, with an emphasis on preference disaggregation. The latter include the UTADIS family and a new method, Multigroup Hierarchical DIScrimination (MHDIS). They are used to assess investing risk in 51 countries that have stock exchanges, according to 27 criteria. These criteria include quantitative and qualitative measures of market risk (volatility and currency fluctuations); range of investment opportunities; quantity and quality on market information; investor protection (security regulations treatment of minority shareholders); and administrative “headaches” (custody, settlement, and taxes). The model parameters are determined so that the results best match the risk level assigned to those countries by experienced international investment managers commissioned by The Wall Street Journal. Among the six evaluation models developed, one (MHDIS) classifies correctly all countries into the appropriate groups. Thus, this model is able to reproduce consistently the evaluation of the expert investment analysts. The most significant criteria and their weights for assessing global risk investing are also presented, along with their marginal utilities, leading to identifiers of risk groups and global utilities portraying the strength of each country's risk classification. The same method, MHDIS, outperformed the other five methods in a 10-fold validation experiment. These results are promising for the study of emerging new markets in fast-growing regions, which present fertile areas for investment growth but also

Multicriteria Preference Disaggregation for Classification Problems with an Application to Global Investing Risk

Combining discriminant methods in solving classification problems in two-group discriminant analysis

Minimizing deviations from the group mean: a new linear programming approach for the two-group classification problem

Several linear programming methods have been suggested as discrimination procedures. A least absolute deviations regression procedure is developed here which is simpler to use and does not suffer from any lack of invariance. A simulation study shows it to be at least as effective as any of the methods previously discussed for normal and heavy-tailed distributions.

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Chau-Kwor Lee

Papers

Discriminant Analysis Using Least Absolute Deviations