A simple algorithm for convex hull determination in high dimensions

Khosravani, H.; Ruano, A. E.; Ferreira, Pedro

doi:10.1109/wisp.2013.6657492

Cited by 10 publications

(7 citation statements)

References 2 publications

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“…These approaches include interesting analyses of CHs exploited for the online classifier training (Khosravani et al 2013;Wang et al 2013a). In these techniques, SVMs are updated dynamically when new vectors arrive to the system (based on the skeleton samples-being the vertices of convex hulls-extracted either offline or online, when new vectors appear).…”

Section: Clustering-based Methodsmentioning

confidence: 99%

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Selecting training sets for support vector machines: a review

2018

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Support vector machines (SVMs) are a supervised classifier successfully applied in a plethora of real-life applications. However, they suffer from the important shortcomings of their high time and memory training complexities, which depend on the training set size. This issue is especially challenging nowadays, since the amount of data generated every second becomes tremendously large in many domains. This review provides an extensive survey on existing methods for selecting SVM training data from large datasets. We divide the state-of-the-art techniques into several categories. They help understand the underlying ideas behind these algorithms, which may be useful in designing new methods to deal with this important problem. The review is complemented with the discussion on the future research pathways which can make SVMs easier to exploit in practice.

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Section: Clustering-based Methodsmentioning

confidence: 99%

“…Other common measures include precision, recall and the F-measure (Khosravani et al 2013). -Size of the refined training set (↓) The main objective of training set selection algorithms is to minimize the cardinality of the training set (ideally without decaying the SVM classification performance).…”

Section: Quantitative Measuresmentioning

confidence: 99%

Selecting training sets for support vector machines: a review

2018

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“…We now introduce the new PDDM for computing fast, precise, and sound over-approximations of the convex hull of two polyhedra. This is in contrast to existing approximation methods, which either optimize for closer approximations [Bentley et al 1982;Khosravani et al 2013;Sartipizadeh and Vincent 2016;Zhong et al 2014] but sacrifice the soundness required for verification, or have exponential complexity [Xu et al 1998], making them too expensive for our application. Double description method.…”

Section: Partial Double Description Methods (Pddm)mentioning

confidence: 98%

PRIMA: general and precise neural network certification via scalable convex hull approximations

Niklas

Makarchuk

Singh

et al. 2022

Proc. ACM Program. Lang.

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Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge. In this paper, we take a major step forward in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex abstractions involving multiple neurons via novel convex hull approximation algorithms that leverage concepts from computational geometry. The algorithms have polynomial complexity, yield fewer constraints, and minimize precision loss. We evaluate the effectiveness of PRIMA on a variety of challenging tasks from prior work. Our results show that PRIMA is significantly more precise than the state-of-the-art, verifying robustness to input perturbations for up to 20%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively. Further, PRIMA enables, for the first time, the precise verification of a realistic neural network for autonomous driving within a few minutes.

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“…Hence, _ is an imbalanced dataset whose size is , , × (i.e., 51 features and 1 target column). To enable MOGA to generate models applicable to the whole range of data where the classifier is going to be used, we included all convex points [36] of _ into the training set. To obtain the convex points, the Approxhull algorithm [37,38] is used, resulting in 13023 samples, among which 11732 were normal and 1291 abnormal.…”

Section: Constructing the Input Dataset For Mogamentioning

confidence: 99%

An intelligent support system for automatic detection of cerebral vascular accidents from brain CT images

Hajimani

Ruano

2017

Computer Methods and Programs in Biomedicine

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Values of specificity of 98% and sensitivity of 98% were obtained, at pixel level, by an ensemble of non-dominated models generated by MOGA, in a set of 150 CT slices (1,867,602pixels), marked by a NeuroRadiologist. This approach also compares favorably at a lesion level with three other published solutions, in terms of specificity (86% compared with 84%), degree of coincidence of marked lesions (89% compared with 77%) and classification accuracy rate (96% compared with 88%).

show abstract

A simple algorithm for convex hull determination in high dimensions

Cited by 10 publications

References 2 publications

Selecting training sets for support vector machines: a review

Selecting training sets for support vector machines: a review

PRIMA: general and precise neural network certification via scalable convex hull approximations

An intelligent support system for automatic detection of cerebral vascular accidents from brain CT images

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