Proposed Normalization Method Research Articles

Criteria for choosing the type of model and method of data normalization in the index approach of social process analysis

Subject. We analyze the method of calculating the global knowledge index, results of ranking countries according to one of the components of the resulting index, calculated using additive and multiplicative models for data on a natural scale and normalized under various methods. Objectives. The aim is to identify alternative normalization methods to eliminate distortions in the ranking of countries to improve the accuracy of the results, as part of the analysis of the data normalization method used in the global knowledge index, to substantiate the expediency of replacing the currently used additive model with a multiplicative one. Methods. The study employs quantitative methods of statistical analysis. The information base of the study consists of official data from the World Bank and the UNESCO Institute of Statistics. Results. We compared three methods of normalization: the "minimum-maximum" method, which is proposed by the compilers of the index, the "distance to a reference" method, and the standardization method. The study proved that using the "distance to a reference" method, the ratios for data on a natural scale and normalized, as well as their distribution laws, are preserved. The preservation of the order of countries when calculating the resulting indicator on a natural scale and after normalization is observed when combining the proposed normalization method with a multiplicative model. Conclusions. When calculating the components of the global knowledge index, it is recommended to use a weighted geometric average, as well as to switch to the normalization method through "distance to a reference" to exclude violations of relationships between the initial and normalized data.

Is normalization in Life Cycle Assessment sustainable? Alternative approach based on natural constraints

Life cycle assessment, a widely used methodology of environmental impact assessment, employs the step called normalization to allow comparison and contextualization of the multiple environmental impacts driven by human activities. However, the currently used normalization references based on total human impacts do not reflect any sustainability limits. This leads to a paradox where the more humanity causes an impact, the less important it appears in the results. We propose that normalization references be based on natural constraints, values that delimit the level of impact which can be expected to cause no significant harm. Such approach can be applied to most characterization methodologies, as we demonstrate on the case of Environmental Footprint methodology with 16 impact categories. In this work we quantify such normalization references, we compare them to the currently used values and we statistically test the difference on the case of 60 processes from common LCA databases. The results show that the proposed normalization method significantly changes the relative ranking of most of the impact categories. According to our findings, the proposed method may alter the ranking of assessed scenarios and change the conclusions and recommendations of LCA studies. This shift in the rationale for normalization can provide a different perspective on results interpretation and thus offer more robust policy guidance.

A database of the healthy human spinal cord morphometry in the PAM50 template space

Abstract Measures of spinal cord morphometry computed from magnetic resonance images serve as relevant prognostic biomarkers for a range of spinal cord pathologies, including traumatic and non-traumatic spinal cord injury and neurodegenerative diseases. However, interpreting these imaging biomarkers is difficult due to considerable intra- and inter-subject variability. Yet, there is no clear consensus on a normalization method that would help reduce this variability and more insights into the distribution of these morphometrics are needed. In this study, we computed a database of normative values for six commonly used measures of spinal cord morphometry: cross-sectional area, anteroposterior diameter, transverse diameter, compression ratio, eccentricity, and solidity. Normative values were computed from a large open-access dataset of healthy adult volunteers (N = 203) and were brought to the common space of the PAM50 spinal cord template using a newly proposed normalization method based on linear interpolation. Compared to traditional image-based registration, the proposed normalization approach does not involve image transformations and, therefore, does not introduce distortions of spinal cord anatomy. This is a crucial consideration in preserving the integrity of the spinal cord anatomy in conditions such as spinal cord injury. This new morphometric database allows researchers to normalize based on sex and age, thereby minimizing inter-subject variability associated with demographic and biological factors. The proposed methodology is open-source and accessible through the Spinal Cord Toolbox (SCT) v6.0 and higher.

A road adhesion coefficient-tire cornering stiffness normalization method combining a fractional-order multi-variable gray model with a LSTM network and vehicle direct yaw-moment robust control.

A normalization method of road adhesion coefficient and tire cornering stiffness is proposed to provide the significant information for vehicle direct yaw-moment control (DYC) system design. This method is carried out based on a fractional-order multi-variable gray model (FOMVGM) and a long short-term memory (LSTM) network. A FOMVGM is used to generate training data and testing data for LSTM network, and LSTM network is employed to predict tire cornering stiffness with road adhesion coefficient. In addition to that, tire cornering stiffness represented by road adhesion coefficient can be used to built vehicle lateral dynamic model and participate in DYC robust controller design. Simulations under different driving cycles are carried out to demonstrate the feasibility and effectiveness of the proposed normalization method of road adhesion coefficient and tire cornering stiffness and vehicle DYC robust control system, respectively.

A novel method for efficient estimation of brain effective connectivity in EEG

Background and Objective: Brain connectivity plays a pivotal role in understanding the brain’s information processing functions by providing various details including magnitude, direction, and temporal dynamics of inter-neuron connections. While the connectivity may be classified as structural, functional and causal, a complete in-vivo directional analysis is guaranteed by the latter and is referred to as Effective Connectivity (EC). Two most widely used EC techniques are Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) which are based on multivariate autoregressive models. The drawbacks of these techniques include poor frequency resolution and the requirement for experimental approach to determine signal normalization and thresholding techniques in identifying significant connectivities between multivariate sources.Methods: In this study, the drawbacks of DTF and PDC are addressed by proposing a novel technique, termed as Efficient Effective Connectivity (EEC), for the estimation of EC between multivariate sources using AR spectral estimation and Granger causality principle. In EEC, a linear predictive filter with AR coefficients obtained via multivariate EEG is used for signal prediction. This leads to the estimation of full-length signals which are then transformed into frequency domain by using Burg spectral estimation method. Furthermore, the newly proposed normalization method addressed the effect on each source in EEC using the sum of maximum connectivity values over the entire frequency range. Lastly, the proposed dynamic thresholding works by subtracting the first moment of causal effects of all the sources on one source from individual connections present for that source.Results: The proposed method is evaluated using synthetic and real resting-state EEG of 46 healthy controls. A 3D-Convolutional Neural Network is trained and tested using the PDC and EEC samples. The result indicates that compared to PDC, EEC improves the EEG eye-state classification accuracy, sensitivity and specificity by 5.57%, 3.15% and 8.74%, respectively.Conclusion: Correct identification of all connections in synthetic data and improved resting-state classification performance using EEC proved that EEC gives better estimation of directed causality and indicates that it can be used for reliable understanding of brain mechanisms. Conclusively, the proposed technique may open up new research dimensions for clinical diagnosis of mental disorders.

Integral bremsstrahlung energy as an inbuilt standard in energy‐dispersive electron probe microanalysis

AbstractTo improve the accuracy of the energy‐dispersive electron probe microanalysis (EPMA EDS) without measuring the probe current, it is proposed to normalize the measured analyte net X‐ray intensity to the bremsstrahlung integral energy of the analyzed sample. The integral energy is calculated using a modified Kramers formula, the parameters of which have been refined based on processing the spectra of single‐element samples (4 ≤ Z ≤ 83), acquired in the incident electrons energy range from 10 to 25 keV. The dependence of the bremsstrahlung integral energy on the atomic number of the sample and the incident electrons energy is obtained, and recommendations are given for calculating the mean atomic number of multicomponent samples. It is shown that even with a significant variation (within a factor of 2 or more) of the probe current or the X‐ray gathering solid angle, the use of the proposed normalization method improves the reproducibility of analysis to a value characteristic of measurements at a stable probe current and a standing solid angle. The method is recommended for the development of standardless EPMA EDS.

Normalization of gearbox vibration signal for tooth crack diagnosis under variable speed conditions

AbstractVariable speed conditions introduce Amplitude Modulation (AM) and Frequency Modulation (FM) effects into gearbox vibration signals, which makes it difficult to distinguish between changes of tooth crack severity and speed changes. To overcome this problem, the AM and FM effects caused by speed variation need to be removed. Order tracking techniques are used to remove the FM effect. Some methods have been reported to reduce the AM effect. However, they attenuated crack information since they focused on the entire vibration signal. Besides, the performance of the reported methods on removing the AM effect was not quantitatively evaluated. In this study, a novel normalization method focusing on the Crack Induced Impulses (CII) is proposed to remove the AM effect without attenuating the tooth crack information. A modified Adaptive Chirp Mode Decomposition method is developed to obtain the CII under variable speed conditions. The peak envelope of the CII is determined using spline interpolation of its envelope peaks and is employed to remove the AM effect of the CII by normalization. Two metrics are introduced to quantitatively evaluate the performance of the proposed normalization method on removing the AM effect and preserving the tooth crack information. The effectiveness of the proposed normalization method is demonstrated using simulated gearbox signals and experimental gearbox datasets. The proposed method benefits tracking tooth crack severity progression under variable speed conditions.

Verification of Normalization Method to Improve Usability and Versatility among Users of Applications that Predict Continuous Motion Using Electromyography.

In applications using electromyography (EMG), it is important to ensure high performance for all users (versatility among users) and to enable use without prior preparation (usability). Some of the current applications that use EMG normalize the signal through methods based on the measured maximum absolute value of EMG (maEMG), such as dynamic contraction (DC). However, usability is low when using DC because the reference value must be measured first every time the application is used. Further, the versatility among users is low because of the nonlinearity of EMG and the fact that maEMG varies among users. This study aimed to improve usability and versatility among users for continuous classification tasks using EMG. To this end, we developed a normalization method using sliding-window and z-score normalization techniques. The results reveal that the proposed method exhibits higher usability and versatility among users than DC. The proposed method does not require any calibration time, suggesting improved usability, while yielding the same classification accuracy as DC (57% for three target tasks) for a model trained using a subject's own data. Further, for a model trained with other users' data, the proposed method yields a classification accuracy of 53%, which is 18% higher than that of DC (35%), suggesting versatility among users. These results demonstrate that the proposed normalization method improves usability and versatility for users of practical applications that use EMG and perform continuous classification, such as prosthetic hands.

Non-linear Normalization for Non-UMI Single Cell RNA-Seq.

Single cell RNA-seq data, like data from other sequencing technology, contain systematic technical noise. Such noise results from a combined effect of unequal efficiencies in the capturing and counting of mRNA molecules, such as extraction/amplification efficiency and sequencing depth. We show that such technical effects are not only cell-specific, but also affect genes differently, thus a simple cell-wise size factor adjustment may not be sufficient. We present a non-linear normalization approach that provides a cell- and gene-specific normalization factor for each gene in each cell. We show that the proposed normalization method (implemented in “SC2P" package) reduces more technical variation than competing methods, without reducing biological variation. When technical effects such as sequencing depths are not balanced between cell populations, SC2P normalization also removes the bias due to uneven technical noise. This method is applicable to scRNA-seq experiments that do not use unique molecular identifier (UMI) thus retain amplification biases.

Consistency and consensus improvement models driven by a personalized normalization method with probabilistic linguistic preference relations

Probabilistic linguistic preference relation (PLPR) provides an effective and flexible tool with which preference degrees of decision-makers can be captured when they vacillatingly express linguistic preference values among several linguistic terms. Individual consistency and group consensus are two important research topics of PLPRs in group decision making (GDM). Considering the problems associated with these two topics, this study proposes a novel GDM framework with consistency-driven and consensus-driven optimization models based on a personalized normalization method for managing complete and incomplete PLPRs. First, existing limitations of the traditional normalization method for probabilistic linguistic term sets (PLTSs) managing ignorance information are specifically discussed. Given the potential valuable information hidden in PLTSs, a personalized normalization method is newly proposed through a two-stage decision-making process with a comprehensive fusion mechanism. Then, based on the proposed normalization method for PLTSs, consistency-driven optimization models that aim to minimize the overall adjustment amount of a PLPR are constructed to improve consistency. Moreover, the developed models are extended to improve consistency and estimate the missing values of an incomplete PLPR. Subsequently, a consensus-driven optimization model that aims to maximize group consensus by adjusting experts’ weights is constructed to support the consensus-reaching process. Finally, an illustrative example, followed by some comparative analyses is presented to demonstrate the application and advantages of the proposed approach.

Analysis of demand–supply gaps in public transit systems based on census and GTFS data: a case study of Calgary, Canada

Bridging the gap between demand and supply in transit service is crucial for public transportation management, as planning actions can be implemented to generate supply in high demand areas or to improve upon inefficient deployment of transit service in low transit demand areas. This study aims to introduce feasible approaches for measuring gap types 1 and 2. Gap type 1 measures the gap between public transit capacity and the number of public transit riders per area, while gap type 2 measures the gap between demand and supply as a normalized index. Gap type 1 provides a value that is more realistic than gap type 2, but it requires detailed passenger data that is not always readily available. Gap type 2 is a practical alternative when the detailed passenger data is unavailable because it uses a weighting scheme to estimate demand values. It also uses a newly proposed normalization method called M-score, which allows for a longitudinal gap analysis where yearly gap patterns and trends can be observed and compared. A 5-year gap analysis of Calgary transit is used as a case study. This work presents a new perspective of hourly gaps and proposes a gap measurement approach that contributes to public transit system planning and service improvement.

Noise-robust line detection using normalized and adaptive second-order anisotropic Gaussian kernels

Abstract Line detection is an essential procedure for many tasks in computer vision. Although literature is rich in proposals for this topic, most of existing methods are vulnerable to noise, especially when lines are fairly narrow. In order to design a line detector that minimizes the impact of noise, regardless of the scale or direction of the lines, in this paper, we present a framework for multiscale line detection based on second-order anisotropic Gaussian kernels. Firstly, we model a line segment using a directional Gaussian function. Secondly, with the help of a newly proposed normalization method, we enable the second-order anisotropic Gaussian kernels to quantitatively measure the line prominence as well as the line scale. Subsequently, based on a noise-robustness analysis in terms of the signal-to-noise ratio, an adaptive anisotropy factor is proposed. By incorporating postprocessing techniques, an automated line detector using the normalized and adaptive second-order anisotropic Gaussian kernels is developed. The performance of the proposed method is quantitatively evaluated by comparing it with five competing methods on a publicly available dataset.

Self-compacting concrete strength prediction using surrogate models

Despite the extensive use of self-compacting concrete in constructions over the last decades, there is not yet a robust quantitative method, available in the literature, which can reliably predict its strength based on its mix components. Τhis limitation is due to the highly nonlinear relation between the self-compacting concrete’s compressive strength and the mixed components. In this paper, the application of artificial neural networks for predicting the mechanical characteristics of self-compacting concrete has been investigated. Specifically, surrogate models (such as artificial neural network models and a new proposed normalization method) have been used for predicting the 28-day compressive strength of admixture-based self-compacting concrete (based on experimental data available in the literature). The comparison of the derived results with the experimental findings demonstrates the ability of artificial neural networks to approximate the compressive strength of self-compacting concrete in a reliable and robust manner. Furthermore, the proposed formula for the normalization of data has been proven effective and robust compared to available ones.

Rhythm-based heartbeat duration normalization for atrial fibrillation detection

BackgroundScreening of atrial fibrillation (AF) for high-risk patients including all patients aged 65 years and older is important for prevention of risk of stroke. Different technologies such as modified blood pressure monitor, single lead ECG-based finger-probe, and smart phone using plethysmogram signal have been emerging for this purpose. All these technologies use irregularity of heartbeat duration as a feature for AF detection. We have investigated a normalization method of heartbeat duration for improved AF detection. MethodAF is an arrhythmia in which heartbeat duration generally becomes irregularly irregular. From a window of heartbeat duration, we estimate the possible rhythm of the majority of heartbeats and normalize duration of all heartbeats in the window based on the rhythm so that we can measure the irregularity of heartbeats for both AF and non-AF rhythms in the same scale. Irregularity is measured by the entropy of distribution of the normalized duration. Then we classify a window of heartbeats as AF or non-AF by thresholding the measured irregularity. The effect of this normalization is evaluated by comparing AF detection performances using duration with the normalization, without normalization, and with other existing normalizations. ResultsSensitivity and specificity of AF detection using normalized heartbeat duration were tested on two landmark databases available online and compared with results of other methods (with/without normalization) by receiver operating characteristic (ROC) curves. ROC analysis showed that the normalization was able to improve the performance of AF detection and it was consistent for a wide range of sensitivity and specificity for use of different thresholds. Detection accuracy was also computed for equal rates of sensitivity and specificity for different methods. Using normalized heartbeat duration, we obtained 96.38% accuracy which is more than 4% improvement compared to AF detection without normalization. ConclusionsThe proposed normalization method was found useful for improving performance and robustness of AF detection. Incorporation of this method in a screening device could be crucial to reduce the risk of AF-related stroke. In general, the incorporation of the rhythm-based normalization in an AF detection method seems important for developing a robust AF screening device.

Normalization of metabolomics data with applications to correlation maps

In metabolomics, the goal is to identify and measure the concentrations of different metabolites (small molecules) in a cell or a biological system. The metabolites form an important layer in the complex metabolic network, and the interactions between different metabolites are often of interest. It is crucial to perform proper normalization of metabolomics data, but current methods may not be applicable when estimating interactions in the form of correlations between metabolites. We propose a normalization approach based on a mixed model, with simultaneous estimation of a correlation matrix. We also investigate how the common use of a calibration standard in nuclear magnetic resonance (NMR) experiments affects the estimation of correlations. We show with both real and simulated data that our proposed normalization method is robust and has good performance when discovering true correlations between metabolites. The standardization of NMR data is shown in simulation studies to affect our ability to discover true correlations to a small extent. However, comparing standardized and non-standardized real data does not result in any large differences in correlation estimates. Source code is freely available at https://sourceforge.net/projects/metabnorm/ alexandra.jauhiainen@ki.se Supplementary data are available at Bioinformatics online.

A normalization method for solving the combined economic and emission dispatch problem with meta-heuristic algorithms

Solving the economic and emission dispatch (ED/MED) problems separately becomes more complex when the combined version (CEED) of the two aforementioned cases is considered. The basic idea is to achieve the lowest possible cost with the smallest amount of pollutant and this problem is known as the combined economic–emission dispatch (CEED). A new approach for solving the CEED is presented in this paper. The idea consists of normalizing the two conflicting objective functions, ED and MED, using the mean and standard deviation of the members contained in the population-based meta-heuristic algorithms implemented in this study thus preventing units and scale differences when optimizing the CEED problem. The mathematical model for each problem (ED, MED, and CEED) presented in this study is optimized implementing a nonlinear optimization package named TOMLAB available for MATLAB, which helps us to determine the best possible solution for the tested instances. A novel meta-heuristic named Virus Optimization Algorithm (VOA) is implemented along with seven well-known algorithmic tools, which are the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Harmony Search (HS), Differential Evolution (DE), FireFly algorithm (FF), Gravitational Search Algorithm (GSA), and Seeker Optimization Algorithm (SOA). A comprehensive statistical study is performed to determine the quality of the solutions delivered by the algorithmic tools when compared with TOMLAB. From the test instances, it was observed that the proposed normalization method does not only show to be feasible, but also helps the algorithms to achieve similar results from that coming when solving the ED and MED separately. Furthermore, among the eight meta-heuristic tools (VOA, GA, PSO, HS, DE, FF, GSA, and SOA), VOA showed outstanding performance in both solution quality and computational efficiency.

Visual word density-based nonlinear shape normalization method for handwritten Chinese character recognition

In handwritten Chinese character recognition, the performance of a system is largely dependent on the character normalization method. In this paper, a visual word density-based nonlinear normalization method is proposed for handwritten Chinese character recognition. The underlying rationality is that the density for each image pixel should be determined by the visual word around this pixel. Visual vocabulary is used for mapping from a visual word to a density value. The mapping vocabulary is learned to maximize the ratio of the between-class variation and the within-class variation. Feature extraction is involved in the optimization stage, hence the proposed normalization method is beneficial for the following feature extraction. Furthermore, the proposed method can be applied to some other image classification problems in which scene character recognition is tried in this paper. Experimental results on one constrained handwriting database (CASIA) and one unconstrained handwriting database (CASIA-HWDB1.1) demonstrate that the proposed method outperforms the start-of-the-art methods. Experiments on scene character databases chars74k and ICDAR03-CH show that the proposed method is promising for some image classification problems.

Similarities Between Proton and Neutron Induced Dark Current Distribution in CMOS Image Sensors

Several CMOS image sensors were exposed to neutron or proton beams (displacement damage dose range from 4 TeV/g to 1825 TeV/g) and their radiation-induced dark current distributions are compared. It appears that for a given displacement damage dose, the hot pixel tail distributions are very similar, if normalized properly. This behavior is observed on all the tested CIS designs (4 designs, 2 technologies) and all the tested particles (protons from 50 MeV to 500 MeV and neutrons from 14 MeV to 22 MeV). Thanks to this result, all the dark current distribution presented in this paper can be fitted by a simple model with a unique set of two factors (not varying from one experimental condition to another). The proposed normalization method of the dark current histogram can be used to compare any dark current distribution to the distributions observed in this work. This paper suggests that this model could be applied to other devices and/or irradiation conditions.

실시간 객체 검출을 위한 개선된 Haar-like Feature 정규화 방법

본 논문에서는 객체 검출에 사용되는 Haar-like feature의 정규화 방법에 대해 다룬다. 기존의 Haar-like feature의 분산 정규화는 후보 윈도우 픽셀들에 대한 표준편차 계산에 사용되는 별도의 적분 영상 생성을 위해 많은 연산을 필요로 했으며 밝기 변화가 작은 영역에서 오검출이 증가하는 문제를 가지고 있으나, 제안하는 정규화 방법은 별도의 적분 영상을 사용하지 않아 처리 속도가 빠르며 제안하는 방법을 사용하여 학습시킨 분류기는 밝기 변화에 대해 강건한 성능을 보인다. 실험 결과 제안한 방법을 사용했을 때 객체 검출기의 처리 속도는 26% 향상 되었으며, 제안한 방법을 사용하여 학습시킨 분류기들은 5% 이상 향상된 검출률을 보였으며, 밝기 변화가 심한 경우는 45% 향상된 검출률을 보였다. This paper describes a normalization method of Haar-like features used for object detection. Previous method which performs variance normalization on Haar-like features requires a lot of calculations, since it uses an additional integral image for calculating the standard deviation of intensities of pixels in a candidate window and increases possibility of false detection in the area where variance of brightness is small. The proposed normalization method can be performed much faster than the previous method by not using additional integral image and classifiers which are trained with the proposed normalization method show robust performance in various lighting conditions. Experimental result shows that the object detector which uses the proposed method is 26% faster than the one which uses the previous method. Detection rate is also improved by 5% without increasing false alarm rate and 45% for the samples whose brightness varies significantly.

Radiometric Correction of Multitemporal Satellite Imagery

Problem statement: Repeated observation of a given area over time yiel ds potential for many forms of change detection analysis. These repe ated observations are confounded in terms of radiometric consistency due to changes in sensor ca libration over time, differences in illumination, observation angles and variation in atmospheric eff ects. Also major problem with satellite images is that regions below clouds are not covered by sensor . Cloud detection, removal and data prediction in cloudy region is essential for image interpretation . Approach: This study demonstrated applicability of empirical relative radiometric normalization met hods to a set of multitemporal cloudy images acquired by Resourcesat-1 LISS III sensor. Objectiv e of this study was to detect and remove cloud cover and normalize an image radiometrically. Cloud detection was achieved by using Average Brightness Threshold (ABT) algorithm. The detected cloud removed and replaced with data from another images of the same area. We proposed a new method in which cloudy pixels are replaced with predicted pixel values obtained by regression. Afte r cloud removal, the proposed normalization method was applied to reduce the radiometric influe nce caused by non surface factors. This process identified landscape elements whose reflectance val ues are nearly constant over time, i.e., the subset of non-changing pixels are identified using frequency based correlation technique. Further, we proposed another method of radiometric correction in frequen cy domain, Pseudo-Invariant Feature regression and this process removed landscape elements such as vegetation whose reflectance values are not constant over time. It takes advantage of vegetatio n being typically high frequency area, can be removed by low pass filter. Results: The quality of radiometric normalization is statis tically assessed by R 2 value and Root Mean Square Error (RMSE) between each pair of analogous band. Further we verified that difference in mean and sta ndard deviation is reduced after normalization of subject image with respect to reference image. Resu lts are compared with commonly used No Change regression method in spatial domain. Conclusion: Cloud removal depends on spatial registration between the two images (reference imag e and cloudy subject image). Visual inspection shows proposed cloudy pixel prediction method performs better than replacing cloudy pixels with another image of the same area. Statistical analysi s also shows that average RMSE of all bands is more in No Change method. Correlation in Fourier domain does not require water body in the scene, while No Change method does require.