Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature

Kucukoglu, Irem; Şimşek, Buket; Şimşek, Yılmaz

doi:10.1016/j.amc.2018.10.012

Cited by 17 publications

(30 citation statements)

References 14 publications

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“…Eventually, the following system containing (m + 1) × (n + 1) equations can be generated from Equations (37), (40), and (41):…”

Section: Methods Of the Solutionmentioning

confidence: 99%

“…These polynomials possess many beneficial properties, such as the continuity, the positivity, and the unity partition over the interval [0,1] 30 . It is also worth noting that different types of the BPs and their unifications have been widely investigated in recent years, for instance, see other studies 33‐37 . As we mentioned, the BPs have been utilized for solving many classes of problems during the past years.…”

Section: Introductionmentioning

confidence: 94%

“…30 It is also worth noting that different types of the BPs and their unifications have been widely investigated in recent years, for instance, see other studies. [33][34][35][36][37] As we mentioned, the BPs have been utilized for solving many classes of problems during the past years. The following examples include some but not all of the studies that have benefited from BPs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

Heydari

Avazzadeh

2020

Math Methods in App Sciences

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This article defines a novel version of nonlinear fourth‐order diffusion‐wave equation, which involves variable‐fractional differentiations with nonsingular kernel. This newly defined equation entails a highly accurate method for its numerical solution. The proposed scheme is based upon the orthonormal Bernstein polynomials and their operational matrices of variable‐order fractional differentiation together with the collocation method. In this paper, the formulation for obtaining these operational matrices are provided in details. The method converts the original problem to a system of algebraic equations that can be promptly solved using a software program. To clarify the validity and the high precision of the devised method, numerous illustrative examples with various boundary conditions are examined.

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“…Eventually, the following system containing (m + 1) × (n + 1) equations can be generated from Equations (37), (40), and (41):…”

Section: Methods Of the Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

Heydari

Avazzadeh

2020

Math Methods in App Sciences

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show abstract

“…The Bernstein polynomials are famous and an excellent tool used in approximation theory, numerical calculation, computer-aided geometric design (CAGD), etc. [27][28][29][30][31][32] Here, we try to rewrite the polynomials as an FNN in form (1.1) by constructing an activation function. For a positive integer n, we construct a function ∶ R → R as an activation function of FNN.…”

Section: Constructing An Fnn With (N + 2) Neurons To Represent the Bementioning

confidence: 99%

Construction of feedforward neural networks with simple architectures and approximation abilities

Chen

Cao

2020

Math Methods in App Sciences

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The universal approximation property of feedforward neural networks (FNNs) is the basis for all FNNs applications. In almost all existing FNN approximation studies, it is always assumed that the activation function of the network satisfies certain conditions, such as sigmoid or bounded continuity. This paper focuses on building simple architecture FNNs with approximation ability by constructing an activation function. First, for any continuous function defined on [0, 1] and an arbitrary accuracy > 0, an FNN is constructed, which has only one neuron and a fixed weight 1 and can approximate the function with an accuracy of. Thereafter, we study the representation of FNNs for polynomial functions by constructing a proper activation function. It is proved that any algebraic polynomial with the degree n can be represented by an FNN. Further, a piecewise function is constructed as an activation function of an FNN such that the FNN represents the famous Bernstein polynomials.

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“…These models did not consider the relationship between HFMD and potential impacting factors. With the development of artificial intelligence (AI), machine learning algorithms have shown their advantages in predictions and recognitions 21–23 . Gradient boosting tree (GBT) and random forest (RF) were found to be capable of identifying both mild and severe HFMD, which is helpful for early surveillance and control in HFMD 24,25 .…”

Section: Introductionmentioning

confidence: 99%

A method for hand-foot-mouth disease prediction using GeoDetector and LSTM model in Guangxi, China

Liang

Song

et al. 2019

Sci Rep

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Hand-foot-mouth disease (HFMD) is a common infectious disease in children and is particularly severe in Guangxi, China. Meteorological conditions are known to play a pivotal role in the HFMD. Previous studies have reported numerous models to predict the incidence of HFMD. In this study, we proposed a new method for the HFMD prediction using GeoDetector and a Long Short-Term Memory neural network (LSTM). The daily meteorological factors and HFMD records in Guangxi during 2014–2015 were adopted. First, potential risk factors for the occurrence of HFMD were identified based on the GeoDetector. Then, region-specific prediction models were developed in 14 administrative regions of Guangxi, China using an optimized three-layer LSTM model. Prediction results (the R-square ranges from 0.39 to 0.71) showed that the model proposed in this study had a good performance in HFMD predictions. This model could provide support for the prevention and control of HFMD. Moreover, this model could also be extended to the time series prediction of other infectious diseases.

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Multidimensional Bernstein polynomials and Bezier curves: Analysis of machine learning algorithm for facial expression recognition based on curvature

Cited by 17 publications

References 14 publications

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

Construction of feedforward neural networks with simple architectures and approximation abilities

A method for hand-foot-mouth disease prediction using GeoDetector and LSTM model in Guangxi, China

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