Polyhedral Separability Through Successive LP

Astorino, Annabella; Gaudioso, Manlio

doi:10.1023/a:1013649822153

Cited by 65 publications

(61 citation statements)

References 23 publications

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“…The concept of h polyhedral separability was introduced in [40]. The sets A and B are ℎ polyhedrally separable if there is a set of ℎ hyperplanes { , }, with ∈ ,…”

Section: Text Classificationmentioning

confidence: 99%

“…In [40], also an algorithm for solving defined minimization problem is developed. The calculation of the descent direction at each iteration of this algorithm is reduced to a certain linear programming problem.…”

Section: Text Classificationmentioning

confidence: 99%

“…These inequality constraints ensure classifying the text into the right category (class) by allowing misclassifications ( , ) as in (19), (25), (26), (33), (39), and (40). In inequalities of (20) and (34) constraints, no misclassifications are allowed by determining the = =0.…”

Section: Pcf Algorithms For Text Categorizationmentioning

confidence: 99%

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Application of the Polyhedral Conic Functions Method in the Text Classification and Comparative Analysis

Sati

Ordin

2018

Scientific Programming

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In direct proportion to the heavy increase of online information data, the attention to text categorization (classification) has also increased. In text categorization problem, namely, text classification, the goal is to classify the documents into predefined classes (categories or labels). Recently various methods in data mining have been experienced for text classification in literature except polyhedral conic function (PCF) methods. In this paper, PCFs are used to classify the documents. The separation algorithms via PCFs which include linear programming subproblems with inequality constraints are presented. Numerical experiments are done on real-world text datasets. Comparisons are made between state-of-the-art methods by presenting obtained tenfold crossvalidation results, accuracy values, and running times in tables. The results verify that in text classification PCF methods are as effective in terms of accuracy values as state-of-the-art methods.

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“…The concept of h polyhedral separability was introduced in [40]. The sets A and B are ℎ polyhedrally separable if there is a set of ℎ hyperplanes { , }, with ∈ ,…”

Section: Text Classificationmentioning

confidence: 99%

Section: Text Classificationmentioning

confidence: 99%

See 1 more Smart Citation

Application of the Polyhedral Conic Functions Method in the Text Classification and Comparative Analysis

Sati

Ordin

2018

Scientific Programming

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“…(see [3,17,30,31,35,36,39,40] for examples). Despite its wide applications, the literature on implementable and convenient algorithms for solving it is little because the max-min functions f (x) and g(x) are nonconvex and nonsmooth even if f ij and g ij are all linear functions.…”

Section: Introductionmentioning

confidence: 99%

An aggregate deformation homotopy method for min-max-min problems with max-min constraints

Xiong

2008

Comput Optim Appl

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“…These methods therefore result in piecewise linear separating surfaces. A variant of this approach has been proposed in [2], where a predefined number of hyperplanes are simultaneously generated by minimizing a piecewise linear error function.…”

Section: Introductionmentioning

confidence: 99%

Accurately learning from few examples with a polyhedral classifier

Orsenigo

Vercellis

2007

Comput Optim Appl

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In the context of learning theory many efforts have been devoted to developing classification algorithms able to scale up with massive data problems. In this paper the complementary issue is addressed, aimed at deriving powerful classification rules by accurately learning from few data. This task is accomplished by solving a new mixed integer programming model that extends the notion of discrete support vector machines, in order to derive an optimal set of separating hyperplanes for binary classification problems. According to the cardinality of the set of hyperplanes, the classification region may take the form of a convex polyhedron or a polytope in the original space where the examples are defined. Computational tests on benchmark datasets highlight the effectiveness of the proposed model, that yields the greatest accuracy when compared to other classification approaches.

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Polyhedral Separability Through Successive LP

Cited by 65 publications

References 23 publications

Application of the Polyhedral Conic Functions Method in the Text Classification and Comparative Analysis

Application of the Polyhedral Conic Functions Method in the Text Classification and Comparative Analysis

An aggregate deformation homotopy method for min-max-min problems with max-min constraints

Accurately learning from few examples with a polyhedral classifier

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