Intervals' Numbers (INs) interpolation/extrapolation

Kaburlasos, Vassilis G.; Papakostas, George A.; Pachidis, Theodore; Athinellis, Alex

doi:10.1109/fuzz-ieee.2013.6622318

Cited by 15 publications

(5 citation statements)

References 31 publications

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“…h of INs is feasible based on the fact that the algebraic operations of ELMs [2], [10] can be carried out in cones of T1/T2 INs [17]. Therefore, potential future work includes an extension of ELMs to a cone of INs with substantial expected benefits regarding the data processing speed.…”

Section: Discussionmentioning

confidence: 99%

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Kaburlasos

Papakostas

2015

IEEE Comput. Intell. Mag.

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This paper describes the recognition of image patterns based on novel representation learning techniques by considering higher-level (meta-)representations of numerical data in a mathematical lattice. In particular, the interest here focuses on lattices of (Type-1) Inter vals' Numbers (INs), where an IN represents a distribution of image features including orthogonal moments. A neural classif ier, namely fuzzy lattice reasoning (f lr) fuzzy-ART-MAP (FAM), or f lrFAM for short, is described for learning distributions of INs; hence, Type-2 INs emerge. Four benchmark image pattern recognition applications are demonstrated. The results obtained by the proposed techniques compare well with the results obtained by alternative methods from the literature. Furthermore, due to the isomorphism between the lattice of INs and the lattice of fuzzy numbers, the proposed techniques are straightforward applicable to Type-1 and/or Type-2 fuzzy systems. The far-reaching potential for deep learning in big data applications is also discussed.

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Section: Discussionmentioning

confidence: 99%

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Kaburlasos

Papakostas

2015

IEEE Comput. Intell. Mag.

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“…INs have been employed in logic and reasoning applications [14,15]. Furthermore, they have been employed in interpolation/extrapolation applications [16].…”

Section: Introductionmentioning

confidence: 99%

Time-Series of Distributions Forecasting in Agricultural Applications: An Intervals’ Numbers Approach

Bazinas

Vrochidou

Lytridis

et al. 2021

The 7th International Conference on Time Series and Forecasting

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This work represents any distribution of data by an Intervals’ Number (IN), hence it represents all-order data statistics, using a “small” number of L intervals. The INs considered are induced from images of grapes that ripen. The objective is the accurate prediction of grape maturity. Based on an established algebra of INs, an optimizable IN-regressor is proposed, implementable on a neural architecture, toward predicting future INs from past INs. A recursive scheme tests the capacity of the IN-regressor to learn the physical “law” that generates the non-stationary time-series of INs. Computational experiments demonstrate comparatively the effectiveness of the proposed techniques.

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“…An IN is a mathematical object that can represent either a fuzzy interval or a distribution of samples [2,[28][29][30]. Applications of INs have been reported to neural networks (NNs) as well as to fuzzy inference systems (FIS) [23,[31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

WINkNN: Windowed Intervals’ Number kNN Classifier for Efficient Time-Series Applications

et al. 2020

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Our interest is in time series classification regarding cyber–physical systems (CPSs) with emphasis in human-robot interaction. We propose an extension of the k nearest neighbor (kNN) classifier to time-series classification using intervals’ numbers (INs). More specifically, we partition a time-series into windows of equal length and from each window data we induce a distribution which is represented by an IN. This preserves the time dimension in the representation. All-order data statistics, represented by an IN, are employed implicitly as features; moreover, parametric non-linearities are introduced in order to tune the geometrical relationship (i.e., the distance) between signals and consequently tune classification performance. In conclusion, we introduce the windowed IN kNN (WINkNN) classifier whose application is demonstrated comparatively in two benchmark datasets regarding, first, electroencephalography (EEG) signals and, second, audio signals. The results by WINkNN are superior in both problems; in addition, no ad-hoc data preprocessing is required. Potential future work is discussed.

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Intervals' Numbers (INs) interpolation/extrapolation

Cited by 15 publications

References 31 publications

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications

Time-Series of Distributions Forecasting in Agricultural Applications: An Intervals’ Numbers Approach

WINkNN: Windowed Intervals’ Number kNN Classifier for Efficient Time-Series Applications

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