Logical analysis of numerical data

Boros, Endre; Hammer, Peter L.; Ibaraki, Toshihide; Kogan, Alexander

doi:10.1007/bf02614316

Cited by 164 publications

(126 citation statements)

References 7 publications

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“…Indeed, discretization is also useful when the method in question can only handle binary data, which is the case, among others, of the Logical Analysis of Data. In this context, in [29], the authors explore several combinatorial optimization approaches for discretizing the variables, as well as their computational complexity. In [202], the classification accuracy of SVM with original data and data discretized by state-of-the-art discretization algorithms are compared on both small and large scale data sets.…”

Section: Classification Treesmentioning

confidence: 99%

Supervised classification and mathematical optimization

Carrizosa

Morales

2013

Computers & Operations Research

124

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Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data.

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Section: Classification Treesmentioning

confidence: 99%

Supervised classification and mathematical optimization

Carrizosa

Morales

2013

Computers & Operations Research

124

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“…We configured our binarization procedure to obtain a larger number of variables (as indicated by n in the table) than is customary for most binary feature selection methods (e.g. [3]). …”

Section: Experimental Studymentioning

confidence: 99%

“…In this setting, we consider only binary datasets; however, for general datasets in R n , we note that there is a corresponding "binarization" with dimension that is at most polynomially larger than m, and in practice does not tend to be much larger than n [3,14]. A related (but not equivalent) problem for real-valued data is the maximum box problem [9].…”

Section: Problem Statement and Introductionmentioning

confidence: 99%

An Improved Branch-and-Bound Method for Maximum Monomial Agreement

Eckstein

Goldberg

2012

INFORMS Journal on Computing

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The N P-hard maximum monomial agreement (MMA) problem consists of finding a single logical conjunction that best fits a weighted dataset of "positive" and "negative" binary vectors. Computing classifiers using boosting methods involves a maximum agreement subproblem at each iteration, although such subproblems are typically solved by heuristic methods. Here, we describe an exact branch and bound method for maximum agreement over Boolean monomials, improving on the earlier work of Goldberg and Shan [14]. In particular, we develop a tighter upper bounding function and an improved branching procedure that exploits knowledge of the bound and the dataset, while having a lower branching factor. Experimental results show that the new method is able to solve larger problem instances and runs faster within a linear programming boosting procedure applied to medium-sized datasets from the UCI repository.

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“…There are a number of areas such as statistics, clustering, machine learning etc that are parallel to problems evaluated by LAD. However, it plays a significant role in the field of data classification through systematic identification of 'patterns' in the datasets [1] [2] [3]. There are a large number of real world data analysis applications such as economics, oil exploration, medical diagnosis etc.…”

Section: Introductionmentioning

confidence: 99%

Logical Analysis of Data-A Survey Paper

Chauhan¹,

Saxena²,

Tripathi³

2017

IJARCSSE

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Abstract-Logical analysis of data is a methodology used for analyzing observations and detecting structural information which provides a solution to problems such as classification, marketing, feature selection development of pattern-based decision support systems, detection of inconsistencies in databases etc. There are a number of areas such as statistics, clustering, machine learning etc that are parallel to problems evaluated by LAD. However, it plays a significant role in the field of data classification through systematic identification of 'patterns' in the datasets There are a large number of real world data analysis applications such as economics, oil exploration, medical diagnosis etc. that can be formulated using Logical analysis of data. Although, in the recent years medical and related disciplines have been the focus of LAD and there have been a considerable number of medical problems to which LAD is successfully applied. The goal of this paper is to provide an overview and a comparative study between different works related to Logical analysis of data (LAD) in the field of data classification. It gives an insight of how Logical analysis of data (LAD) has been successfully applied to various data analysis applications particularly medical science and related disciplines. It provides a brief description of some useful work done in the past in the field of data classification to provide an accurate data classification using a small training set. It particularly gives an overview about the work done by P.L Hammer and Renato Bruni and Gianpiero Bianchi in the field of data classification. It explores about the characteristics and challenges involved with the past research work and also contributes significant variations to them to provide a fast and accurate data classification.

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Logical analysis of numerical data

Cited by 164 publications

References 7 publications

Supervised classification and mathematical optimization

Supervised classification and mathematical optimization

An Improved Branch-and-Bound Method for Maximum Monomial Agreement

Logical Analysis of Data-A Survey Paper

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