scholarly journals On the Optimization of Regression-Based Spectral Reconstruction

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5586
Author(s):  
Yi-Tun Lin ◽  
Graham D. Finlayson
Keyword(s):  
Relative Error ◽  
Absolute Error ◽  
Percentage Error ◽  
Worst Case ◽  
Regression Methods ◽  
Spectral Reconstruction ◽  
Ill Posed ◽  
The Mean ◽  
Error Metric ◽  
Regularization Strategy

Spectral reconstruction (SR) algorithms attempt to recover hyperspectral information from RGB camera responses. Recently, the most common metric for evaluating the performance of SR algorithms is the Mean Relative Absolute Error (MRAE)—an ℓ1 relative error (also known as percentage error). Unsurprisingly, the leading algorithms based on Deep Neural Networks (DNN) are trained and tested using the MRAE metric. In contrast, the much simpler regression-based methods (which actually can work tolerably well) are trained to optimize a generic Root Mean Square Error (RMSE) and then tested in MRAE. Another issue with the regression methods is—because in SR the linear systems are large and ill-posed—that they are necessarily solved using regularization. However, hitherto the regularization has been applied at a spectrum level, whereas in MRAE the errors are measured per wavelength (i.e., per spectral channel) and then averaged. The two aims of this paper are, first, to reformulate the simple regressions so that they minimize a relative error metric in training—we formulate both ℓ2 and ℓ1 relative error variants where the latter is MRAE—and, second, we adopt a per-channel regularization strategy. Together, our modifications to how the regressions are formulated and solved leads to up to a 14% increment in mean performance and up to 17% in worst-case performance (measured with MRAE). Importantly, our best result narrows the gap between the regression approaches and the leading DNN model to around 8% in mean accuracy.

scholarly journals Reconstructing Spectra from RGB Images by Relative Error Least-Squares Regression

2020 ◽  
Vol 2020 (28) ◽  
pp. 264-269
Author(s):  
Yi-Tun Lin ◽  
Graham D. Finlayson
Keyword(s):  
Least Squares ◽  
Relative Error ◽  
Mean Squared Error ◽  
Evaluation Criteria ◽  
Absolute Error ◽  
Percentage Error ◽  
Least Squares Regression ◽  
Worst Case ◽  
Regression Methods ◽  
Spectral Reconstruction

Spectral reconstruction (SR) algorithms attempt to map RGB- to hyperspectral-images. Classically, simple pixel-based regression is used to solve for this SR mapping and more recently patch-based Deep Neural Networks (DNN) are considered (with a modest performance increment). For either method, the 'training' process typically minimizes a Mean-Squared-Error (MSE) loss. Curiously, in recent research, SR algorithms are evaluated and ranked based on a relative percentage error, so-called MeanRelative-Absolute Error (MRAE), which behaves very differently from the MSE loss function. The most recent DNN approaches - perhaps unsurprisingly - directly optimize for this new MRAE error in training so as to match this new evaluation criteria.<br/> In this paper, we show how we can also reformulate pixelbased regression methods so that they too optimize a relative spectral error. Our Relative Error Least-Squares (RELS) approach minimizes an error that is similar to MRAE. Experiments demonstrate that regression models based on RELS deliver better spectral recovery, with up to a 10% increment in mean performance and a 20% improvement in worst-case performance depending on the method.

scholarly journals Novel Spatiotemporal Feature Extraction Parallel Deep Neural Network for Forecasting Confirmed Cases of Coronavirus Disease 2019

2020 ◽  
Author(s):  
Chiou-Jye Huang ◽  
Yamin Shen ◽  
Ping-Huan Kuo ◽  
Yung-Hsiang Chen
Keyword(s):  
Neural Network ◽  
Deep Neural Network ◽  
Absolute Error ◽  
Mean Absolute Percentage Error ◽  
The Other ◽  
Percentage Error ◽  
Model Assessment ◽  
Absolute Percentage Error ◽  
Spatiotemporal Feature ◽  
The Mean

AbstractThe coronavirus disease 2019 pandemic continues as of March 26 and spread to Europe on approximately February 24. A report from April 29 revealed 1.26 million confirmed cases and 125 928 deaths in Europe. This study proposed a novel deep neural network framework, COVID-19Net, which parallelly combines a convolutional neural network (CNN) and bidirectional gated recurrent units (GRUs). Three European countries with severe outbreaks were studied—Germany, Italy, and Spain—to extract spatiotemporal feature and predict the number of confirmed cases. The prediction results acquired from COVID-19Net were compared to those obtained using a CNN, GRU, and CNN-GRU. The mean absolute error, mean absolute percentage error, and root mean square error, which are commonly used model assessment indices, were used to compare the accuracy of the models. The results verified that COVID-19Net was notably more accurate than the other models. The mean absolute percentage error generated by COVID-19Net was 1.447 for Germany, 1.801 for Italy, and 2.828 for Spain, which were considerably lower than those of the other models. This indicated that the proposed framework can accurately predict the accumulated number of confirmed cases in the three countries and serve as a crucial reference for devising public health strategies.

scholarly journals Prediction by using Artificial Neural Networks and Box-Jenkins methodologies: Comparison Study

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Mohammed Habib Al- Sharoot ◽  
Emaan Yousif Abdoon
Keyword(s):  
Neural Networks ◽  
Exchange Rate ◽  
Absolute Error ◽  
Percentage Error ◽  
Neural Network Approach ◽  
Decision Making Processes ◽  
The Mean ◽  
Us Dollar ◽  
Stable Economy ◽  
Better Than

The variations in exchange rate, especially the sudden unexpected increases and decreases, have significant impact on the national economy of any country. Iraq is no exception; therefore, the accurate forecasting of exchange rate of Iraqi dinar to US dollar plays an important role in the planning and decision-making processes as well as the maintenance of a stable economy in Iraq. This research aims to compare Box-Jenkins methodology to neural networks in terms of forecasting the exchange rate of Iraqi dinar to US dollar based on data provided by the Iraqi Central Bank for the period  30/01/2004 and 30/12/2014. Based on the Mean Square Error (MSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE) as criteria to compare the two methodologies, it was concluded that Box-Jenkins is better than neural network approach in forecasting.

Modeling of Fixed Joints Stiffness Based on Modified Least-Square

2014 ◽  
Vol 536-537 ◽  
pp. 1365-1368
Author(s):  
Ming De Duan ◽  
Hao Liang Feng ◽  
Kang Hua Liu ◽  
Jun Yong Lu
Keyword(s):  
Experimental Data ◽  
Regression Analysis ◽  
Relative Error ◽  
Machine Tools ◽  
Mean Absolute Percentage Error ◽  
Least Square ◽  
Percentage Error ◽  
Regression Equations ◽  
Absolute Percentage Error ◽  
The Mean

According to experimental data, the model of fixed Joints stiffness in machine tools was built by least square of relative error. The new regression equations were obtained by regression analysis. Compared to the original equations with Gaussian least-square, the relative error of new regression equations is within 3.5%, which reduces by 12.5% and the mean absolute percentage error (MAPE) decreases by 18.0%, 12.4%and 19.0% respectively.

scholarly journals Short-Term Load Forecasting Using Convolutional Neural Networks in COVID-19 Context: The Romanian Case Study

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4046
Author(s):  
Andrei M. Tudose ◽  
Irina I. Picioroaga ◽  
Dorian O. Sidea ◽  
Constantin Bulac ◽  
Valentin A. Boicea
Keyword(s):  
Power Systems ◽  
Mean Squared Error ◽  
Load Forecasting ◽  
Absolute Error ◽  
Percentage Error ◽  
Linear Regression Method ◽  
Short Term ◽  
Short Term Load Forecasting ◽  
The Mean ◽  
The Impact

Short-term load forecasting (STLF) is fundamental for the proper operation of power systems, as it finds its use in various basic processes. Therefore, advanced calculation techniques are needed to obtain accurate results of the consumption prediction, taking into account the numerous exogenous factors that influence the results’ precision. The purpose of this study is to integrate, additionally to the conventional factors (weather, holidays, etc.), the current aspects regarding the global COVID-19 pandemic in solving the STLF problem, using a convolutional neural network (CNN)-based model. To evaluate and validate the impact of the new variables considered in the model, the simulations are conducted using publicly available data from the Romanian power system. A comparison study is further carried out to assess the performance of the proposed model, using the multiple linear regression method and load forecasting results provided by the Romanian Transmission System Operator (TSO). In this regard, the Mean Squared Error (MSE), the Mean Absolute Error (MAE), the Mean Absolute Percentage Error (MAPE), and the Root Mean Square Error (RMSE) are used as evaluation indexes. The proposed methodology shows great potential, as the results reveal better error values compared to the TSO results, despite the limited historical data.

scholarly journals A new hybrid of Fuzzy C-Means Method and Fuzzy Linear Regression Model in Predicting Manufacturing Income

2018 ◽  
Vol 7 (4.30) ◽  
pp. 473
Author(s):  
Nurfarawahida Ramly ◽  
Mohd Saifullah Rusiman ◽  
Norziha Che Him ◽  
Maria Elena Nor ◽  
Supar Man ◽  
...  
Keyword(s):  
Linear Regression ◽  
Mean Absolute Error ◽  
Human Perception ◽  
Absolute Error ◽  
Percentage Error ◽  
Fuzzy Linear Regression ◽  
Fuzzy C Means ◽  
Fuzzy Linear Regression Model ◽  
The Mean ◽  
Ambiguous Data

Analysis by human perception could not be solved using traditional method since uncertainty within the data have to be dealt with first. Thus, fuzzy structure system is considered. The objectives of this study are to determine suitable cluster by using fuzzy c-means (FCM) method, to apply existing methods such as multiple linear regression (MLR) and fuzzy linear regression (FLR) as proposed by Tanaka and Ni and to improve the FCM method and FLR model proposed by Zolfaghari to predict manufacturing income. This study focused on FLR which is suitable for ambiguous data in modelling. Clustering is used to cluster or group the data according to its similarity where FCM is the best method. The performance of models will measure by using the mean square error (MSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE). Results shows that the improvisation of FCM method and FLR model obtained the lowest value of error measurement with MSE=1.825 , MAE=115932.702 and MAPE=95.0366. Therefore, as the conclusion, a new hybrid of FCM method and FLR model are the best model for predicting manufacturing income compared to the other models.

scholarly journals The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation

2021 ◽  
Vol 7 ◽  
pp. e623
Author(s):  
Davide Chicco ◽  
Matthijs J. Warrens ◽  
Giuseppe Jurman
Keyword(s):  
Machine Learning ◽  
Regression Analysis ◽  
Binary Classification ◽  
Ground Truth ◽  
Absolute Error ◽  
Supervised Machine Learning ◽  
Coefficient Of Determination ◽  
Target Range ◽  
Percentage Error ◽  
The Mean

Regression analysis makes up a large part of supervised machine learning, and consists of the prediction of a continuous independent target from a set of other predictor variables. The difference between binary classification and regression is in the target range: in binary classification, the target can have only two values (usually encoded as 0 and 1), while in regression the target can have multiple values. Even if regression analysis has been employed in a huge number of machine learning studies, no consensus has been reached on a single, unified, standard metric to assess the results of the regression itself. Many studies employ the mean square error (MSE) and its rooted variant (RMSE), or the mean absolute error (MAE) and its percentage variant (MAPE). Although useful, these rates share a common drawback: since their values can range between zero and +infinity, a single value of them does not say much about the performance of the regression with respect to the distribution of the ground truth elements. In this study, we focus on two rates that actually generate a high score only if the majority of the elements of a ground truth group has been correctly predicted: the coefficient of determination (also known as R-squared or R2) and the symmetric mean absolute percentage error (SMAPE). After showing their mathematical properties, we report a comparison between R2 and SMAPE in several use cases and in two real medical scenarios. Our results demonstrate that the coefficient of determination (R-squared) is more informative and truthful than SMAPE, and does not have the interpretability limitations of MSE, RMSE, MAE and MAPE. We therefore suggest the usage of R-squared as standard metric to evaluate regression analyses in any scientific domain.

Modeling and Predicting Tensile Strength of Tungsten Alloy by Using PSO-SVR

2012 ◽  
Vol 455-456 ◽  
pp. 1497-1503
Author(s):  
J.L. Tang ◽  
C.Z. Cai ◽  
X.J. Zhu ◽  
G.L. Wang ◽  
D.F. Cao
Keyword(s):  
Tensile Strength ◽  
Mean Absolute Error ◽  
Back Propagation ◽  
Absolute Error ◽  
Back Propagation Neural Network ◽  
Influential Factors ◽  
Tungsten Alloy ◽  
Percentage Error ◽  
The Mean ◽  
Bpnn Model

In this paper, the support vecstor regression (SVR) approach combined with particle swarm optimization (PSO) is proposed to establish a model for predicting tungsten tensile strength base on the tension experimental data of tungsten alloy under two influential factors, including tungsten content and deformation magnitude. Comparing the prediction result of PSO-SVR model with that of back propagation neural network (BPNN) model, it is shown that the prediction precision of SVR model is higher evaluated by identical training and test samples. The mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE) of SVR model, all are smaller than those of BPNN. This study suggests that SVR is an effective and powerful tool for predicting the tensile strength of tungsten alloy.

scholarly journals An Intelligent Prediction Method of the Karst Curtain Grouting Volume Based on Support Vector Machine

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jiandong Niu ◽  
Bin Wang ◽  
Haifa Wang ◽  
Zhiwei Deng ◽  
Jianxin Liu ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Prediction Method ◽  
Absolute Error ◽  
Small Samples ◽  
Percentage Error ◽  
Support Vector ◽  
High Dimensions ◽  
Curtain Grouting ◽  
Practical Engineering ◽  
The Mean

The prediction of the grouting volume is a very important task in the grouting quality control. Because of the concealment and complexity of the karst curtain grouting engineering, there is little research on the prediction of the karst curtain grouting volume (KCGV), and the prediction is hindered by the practical problems of small samples, high dimensions, and nonlinearity. In the study, based on the basic idea of support vector machine (SVM), a multiparameter comprehensive intelligent prediction method of the KCGV is proposed, which overcomes the limitation of few sample data in practical engineering. This method takes the grouting construction conditions and the slurry conditions which control the slurry diffusion as the input parameters, which are the basic data which can be easily obtained in the field grouting process. This feature greatly improves the prediction accuracy and generalization performance of the method. The intelligent prediction method of the KCGV based on SVM is applied to a typical karst curtain grouting project. The mean absolute error of the prediction results is 3.47 L/m, and the mean absolute percentage error of the prediction results is 5.97%. The results show that the proposed prediction method has an excellent prediction effect on the KCGV and can provide practical and beneficial help for the field karst curtain grouting project.

scholarly journals Adaptive Grouping Distributed Compressive Sensing Reconstruction of Plant Hyperspectral Data

2017 ◽  
Author(s):  
Ping Xu ◽  
Junfeng Liu ◽  
Lingyun Xue ◽  
Jingcheng Zhang ◽  
Bo Qiu
Keyword(s):  
Compressive Sensing ◽  
Data Storage ◽  
Sampling Rate ◽  
Absolute Error ◽  
Hyperspectral Data ◽  
Percentage Error ◽  
Reconstruction Method ◽  
Quantitative Remote Sensing ◽  
Distributed Compressive Sensing ◽  
The Mean

With the development of hyperspectral technology, to establish an effective spectral data compressive reconstruction method that can improving data storage, transmission and maintaining spectral information is critical for quantitative remote sensing research and application in vegetation. By introducing the idea of compressive sensing in compressed reconstruction, the spectral adaptive grouping distributed compressive sensing algorithm is proposed, which enables a distributed compressed sensing reconstruction of plant hyperspectral data. The experimental results showed that comparing with orthogonal matching pursuit(OMP) and gradient projection reconstruction(GPSR), the proposed algorithm can significantly improve the visual effect of image reconstruction in the spatial domain. The PSNR in low sampling rate(sampling rate is lower than 0.2) increases by 13.72dB than OMP and 1.66dB than GPSR. In the spectral domain, the average normalized root mean square error、the mean absolute percentage error and the mean absolute error of the proposed algorithm is35.38%，31.83% and 33.33% lower than GPSR respectively.. Therefore, the proposed algorithm can achieve relatively high reconstructed efficiency.

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