Separation via polyhedral conic functions

Gasimov, Rafail N.; Öztürk, Gürkan

doi:10.1080/10556780600723252

Cited by 53 publications

(55 citation statements)

References 9 publications

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“…Accuracy value, %100, is obtained on both of the algorithms since PCF algorithm (Algorithm 3) ends after a finite number of iterations and the function : → R defined in the linear programming subproblem strictly separates the sets A and B. This theorem is proved in [8]. But it is clear that, according to the used dataset, obtained accuracy value in Algorithm 4 can be lower than Algorithm 3 because of using misclassifications for both of the classes.…”

Section: Methodsmentioning

confidence: 91%

“…Polyhedral conic functions (PCFs) have been introduced in 2006 by Gasimov andÖztürk to separate two different labeled point sets, in other words, to split two discrete datasets [8].…”

Section: Classification Via Polyhedral Conic Functions (Pcfs)mentioning

confidence: 99%

“…For text classification, besides the commonly used supervised classification techniques, we wish to experience polyhedral conic functions as supervised classification functions : → that map documents to labels (classes) [8]. In the following state-of-the-art review, we sketch out some of learning techniques used for text categorization in literature.…”

Section: Introductionmentioning

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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Section: Methodsmentioning

confidence: 91%

“…Polyhedral conic functions (PCFs) have been introduced in 2006 by Gasimov andÖztürk to separate two different labeled point sets, in other words, to split two discrete datasets [8].…”

Section: Classification Via Polyhedral Conic Functions (Pcfs)mentioning

confidence: 99%

Section: Introductionmentioning

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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“…One of the main application areas is the nonconvex vector optimization, where these functions were used to characterize efficient solutions (see e.g., [7,14,17,22,30,33]). Another application area of these functions is the single objective mathematical programming (see e.g., [11][12][13][25][26][27]) where the conical supporting surfaces were used to develop optimality conditions and algorithms for calculating optimal solutions. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Existence and characterization theorems in nonconvex vector optimization

Kasimbeyli

2014

J Glob Optim

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This paper presents existence conditions and characterization theorems for minimal points of nonconvex vector optimization problems in reflexive Banach spaces. Characterization theorems use special class of monotonically increasing sublinear scalarizing functions which are defined by means of elements of augmented dual cones. It is shown that the Hartley cone-compactness is necessary and sufficient to guarantee the existence of a properly minimal point of the problem. The necessity is proven in the case of finite dimensional space.

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“…Polyhedral conic function was first introduced to literature by Gasimov and Öztürk [10] and extended and used for object localization and classification by Cevikalp and Triggs [4]. Extended polyhedral classifier uses the following function.…”

Section: A Extended Polyhedral Conic Classifiermentioning

confidence: 99%

Car Localization in Aerial Images Taken from Quadcopter

2018

RTET-2018,AAEBM-18,BEHSS-18,BLEIS-18,CEECE-2018 April 24-26, 2018 Pattaya (Thailand)

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Abstract-Unmanned aerial vehicles (UAV) are popular research platforms that find increasing amount of applications in many areas, such as military, civil, commercial, and entertainment due to their high maneuverability, vertical take-off and landing abilities, and suitability for use in indoor and outdoor spaces. Today, small, and single board computers with very high CPU/processor capacities are developed, and by means of these processors, which will be inserted into unmanned aerial vehicle platforms, many realtime machine vision applications became possible. This study discusses the problem of car localization in aerial images taken from unmanned aerial vehicles. Within this context, a new dataset was created by using quadcopter-type unmanned aerial vehicles and various cameras. Both Polyhedral Conic Classifier and You Only Look Once (YOLO) algorithm, which is currently one of the fastest methods in literature, and uses deep learning architecture, were used to locate the cars in collected images, and the results were compared.

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Separation via polyhedral conic functions

Cited by 53 publications

References 9 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

Existence and characterization theorems in nonconvex vector optimization

Car Localization in Aerial Images Taken from Quadcopter

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