A K-nearest neighbours method based on imprecise probabilities

Destercke, Sébastien

doi:10.1007/s00500-011-0773-5

Cited by 23 publications

(12 citation statements)

References 39 publications

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“…ϵ 0 settles the initial imprecision, while β determines how much imprecision increases with distance (details about the role of these parameters can be found in [14]). …”

Section: Resultsmentioning

confidence: 99%

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Multilabel predictions with sets of probabilities: The Hamming and ranking loss cases

Destercke¹

2015

Pattern Recognition

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a b s t r a c tIn this paper, we study how multilabel predictions can be obtained when our uncertainty is described by a convex set of probabilities. Such predictions, typically consisting of a set of potentially optimal decisions, are hard to make in large decision spaces such as the one considered in multilabel problems. However, we show that when considering the Hamming or the ranking loss, outer-approximating predictions can be efficiently computed from label-wise information, as in the precise case. We also perform some first experiments showing the behaviour of the partial predictions obtained through these approximations. Such experiments also confirm that predictions become partial on those labels where the precise prediction is likely to make an error.

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“…ϵ 0 settles the initial imprecision, while β determines how much imprecision increases with distance (details about the role of these parameters can be found in [14]). …”

Section: Resultsmentioning

confidence: 99%

“…The method we used was to apply, label-wise, the k-nn method using lower probabilities introduced in [14]. This means that from an initial training data set D, m data sets D j corresponding to binary classification problems are built, this decomposition being illustrated in Fig.…”

Section: Methodsmentioning

confidence: 99%

Multilabel predictions with sets of probabilities: The Hamming and ranking loss cases

Destercke¹

2015

Pattern Recognition

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“…In the experiments, the parameters of the k-nn algorithm were set to β = 0.75 and ε 0 = 0.99, so that results obtained when fixing the number k of neighbors to 1 display a sufficient completeness. ε 0 settles the initial imprecision, while β determines how much imprecision increases with distance (details about the role of these parameters can be found in [6]). We ran experiments on well-known multilabel data sets having real-valued features.…”

Section: Resultsmentioning

confidence: 99%

“…The method we used was to apply, label-wise, the k-nn method using lower probabilities introduced in [6] (in which details can be found). This means that from an initial training data set D, m data sets D j corresponding to binary classification problems are built, this decomposition being illustrated in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

Multilabel Prediction with Probability Sets: The Hamming Loss Case

Destercke

2014

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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In this paper, we study how multilabel predictions can be obtained when our uncertainty is described by a convex set of probabilities. Such predictions, typically consisting of a set of potentially optimal decisions, are hard to make in large decision spaces such as the one considered in multilabel problems. However, we show that when considering the Hamming loss, an approximate prediction can be efficiently computed from label-wise information, as in the precise case. We also perform some first experiments showing the interest of performing partial predictions in the multilabel case.

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“…In addition, the sliding model controller is removed, which can reduce the computational burden. The theory of imprecise probability provides a formal framework to determine an optimal decision under uncertainties of the state of system, which makes it suitable for a wide range of application areas [23,24]. In this paper, the theory of imprecise probability was used to design the stopping criteria.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability

Bai

Yang

et al. 2019

Symmetry

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A data-driven adaptive iterative learning (IL) method is proposed for the active control of structural vibration. Considering the repeatability of structural dynamic responses in the vibration process, the time-varying proportional-type iterative learning (P-type IL) method was applied for the design of feedback controllers. The model-free adaptive (MFA) control, a data-driven method, was used to self-tune the time-varying learning gains of the P-type IL method for improving the control precision of the system and the learning speed of the controllers. By using multi-source information, the state of the controlled system was detected and identified. The square root values of feedback gains can be considered as characteristic parameters and the theory of imprecise probability was investigated as a tool for designing the stopping criteria. The motion equation was driven from dynamic finite element (FE) formulation of piezoelectric material, and then was linearized and transformed properly to design the MFA controller. The proposed method was numerically and experimentally tested for a piezoelectric cantilever plate. The results demonstrate that the proposed method performs excellent in vibration suppression and the controllers had fast learning speeds.

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A K-nearest neighbours method based on imprecise probabilities

Cited by 23 publications

References 39 publications

Multilabel predictions with sets of probabilities: The Hamming and ranking loss cases

Multilabel predictions with sets of probabilities: The Hamming and ranking loss cases

Multilabel Prediction with Probability Sets: The Hamming Loss Case

Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability

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