Box-Cox Transformation Research Articles

Data Distribution: Normal or Abnormal?

Determining if the frequency distribution of a given data set follows a normal distribution or not is among the first steps of data analysis. Visual examination of the data, commonly by Q-Q plot, although is acceptable by many scientists, is considered subjective and not acceptable by other researchers. One-sample Kolmogorov-Smirnov test with Lilliefors correction (for a sample size ≥ 50) and Shapiro-Wilk test (for a sample size < 50) are common statistical tests for checking the normality of a data set quantitatively. As parametric tests, which assume that the data distribution is normal (Gaussian, bell-shaped), are more robust compared to their non-parametric counterparts, we commonly use transformations (e.g., log-transformation, Box-Cox transformation, etc.) to make the frequency distribution of non-normally distributed data close to a normal distribution. Herein, I wish to reflect on presenting how to practically work with these statistical methods through examining of real data sets.

A Hybrid Data Preprocessing-Based Hierarchical Attention BiLSTM Network for Remaining Useful Life Prediction of Spacecraft Lithium-Ion Batteries.

As a crucial energy storage for the spacecraft power system, lithium-ion batteries degradation mechanisms are complex and involved with external environmental perturbations. Hence, effective remaining useful life (RUL) prediction and model reliability assessment confronts considerable obstacles. This article develops a new RUL prediction method for spacecraft lithium-ion batteries, where a hybrid data preprocessing-based deep learning model is proposed. First, to improve the correlation between battery capacity and features, the empirically selected high-dimensional features are linearized by using the Box-Cox transformation and then denoised via the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method. Second, the principal component analysis (PCA) algorithm is employed to perform feature dimensionality reduction, and the output of PCA is further processed by the sliding window technique. Third, a multiscale hierarchical attention bi-directional long short-term memory (MHA-BiLSTM) model is constructed to estimate the capacity in future cycles. Specifically, the MHA-BiLSTM model can predict the RUL of lithium-ion batteries by considering the correlation and significance of each cycle's information during the degradation process on different scales. Finally, the proposed method is validated based on multiple types of experiments under two lithium-ion battery datasets, demonstrating its superior performance in terms of feature extraction and multidimensional time series prediction.

Scientific Elegance in NIDS: Unveiling Cardinality Reduction, Box-Cox Transformation, and ADASYN for Enhanced Intrusion Detection

Scientific Elegance in NIDS: Unveiling Cardinality Reduction, Box-Cox Transformation, and ADASYN for Enhanced Intrusion Detection

Functional coefficient cointegration models with Box–Cox transformation

This paper considers a functional coefficient cointegration model where the dependent variable is subject to a Box–Cox transformation. A profile method is proposed to estimate the Box–Cox transformation parameter β0. We first approximate the functional coefficients by sieve method assuming that β0 is known. Then an extremum estimator of β0 is proposed based on a loss function which measures the relative variation of the regression residual compared to the variation in the transformed dependent variable. Finally, a plug-in estimator of the functional coefficients is obtained. Asymptotic properties of the proposed estimators are developed. Numerical results demonstrate the nice performance of the estimators and corroborate the theoretical development.

Time series analysis and forecasting of the number of canine rabies confirmed cases in Thailand based on national-level surveillance data

IntroductionRabies, a deadly zoonotic viral disease, accounts for over 50,000 fatalities globally each year. This disease predominantly plagues developing nations, with Thailand being no exception. In the current global landscape, concerted efforts are being mobilized to curb human mortalities attributed to animal-transmitted rabies. For strategic allocation and optimization of resources, sophisticated and accurate forecasting of rabies incidents is imperative. This research aims to determine temporal patterns, and seasonal fluctuations, and project the incidence of canine rabies throughout Thailand, using various time series techniques.MethodsMonthly total laboratory-confirmed rabies cases data from January 2013 to December 2022 (full dataset) were split into the training dataset (January 2013 to December 2021) and the test dataset (January to December 2022). Time series models including Seasonal Autoregressive Integrated Moving Average (SARIMA), Neural Network Autoregression (NNAR), Error Trend Seasonality (ETS), the Trigonometric Exponential Smoothing State-Space Model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (TBATS), and Seasonal and Trend Decomposition using Loess (STL) were used to analyze the training dataset and the full dataset. The forecast values obtained from the time series models applied to the training dataset were compared with the actual values from the test dataset to determine their predictive performance. Furthermore, the forecast projections from January 2023 to December 2025 were generated from models applied to the full dataset.ResultsThe findings revealed a total of 4,678 confirmed canine rabies cases during the study duration, with apparent seasonality in the data. Among the models tested with the test dataset, TBATS exhibited superior predictive accuracy, closely trailed by the SARIMA model. Based on the full dataset, TBATS projections suggest an annual average of approximately 285 canine rabies cases for the years 2023 to 2025, translating to a monthly average of 23 cases (range: 18–30). In contrast, SARIMA projections averaged 277 cases annually (range: 208–214).DiscussionThis research offers a new perspective on disease forecasting through advanced time series methodologies. The results should be taken into consideration when planning and conducting rabies surveillance, prevention, and control activities.

WERECE: An Unsupervised Method for Educational Concept Extraction Based on Word Embedding Refinement

The era of educational big data has sparked growing interest in extracting and organizing educational concepts from massive amounts of information. Outcomes are of the utmost importance for artificial intelligence–empowered teaching and learning. Unsupervised educational concept extraction methods based on pre-trained models continue to proliferate due to ongoing advances in semantic representation. However, it remains challenging to directly apply pre-trained large language models to extract educational concepts; pre-trained models are built on extensive corpora and do not necessarily cover all subject-specific concepts. To address this gap, we propose a novel unsupervised method for educational concept extraction based on word embedding refinement (i.e., word embedding refinement–based educational concept extraction (WERECE)). It integrates a manifold learning algorithm to adapt a pre-trained model for extracting educational concepts while accounting for the geometric information in semantic computation. We further devise a discriminant function based on semantic clustering and Box–Cox transformation to enhance WERECE’s accuracy and reliability. We evaluate its performance on two newly constructed datasets, EDU-DT and EDUTECH-DT. Experimental results show that WERECE achieves an average precision up to 85.9%, recall up to 87.0%, and F1 scores up to 86.4%, which significantly outperforms baselines (TextRank, term frequency–inverse document frequency, isolation forest, K-means, and one-class support vector machine) on educational concept extraction. Notably, when WERECE is implemented with different parameter settings, its precision and recall sensitivity remain robust. WERECE also holds broad application prospects as a foundational technology, such as for building discipline-oriented knowledge graphs, enhancing learning assessment and feedback, predicting learning interests, and recommending learning resources.

Comparing the Simple to Complex Automatic Methods with the Ensemble Approach in Forecasting Electrical Time Series Data

The importance of forecasting in the energy sector as part of electrical power equipment maintenance encourages researchers to obtain accurate electrical forecasting models. This study investigates simple to complex automatic methods and proposes two weighted ensemble approaches. The automated methods are the autoregressive integrated moving average; the exponential smoothing error–trend–seasonal method; the double seasonal Holt–Winter method; the trigonometric Box–Cox transformation, autoregressive, error, trend, and seasonal model; Prophet and neural networks. All accommodate trend and seasonal patterns commonly found in monthly, daily, hourly, or half-hourly electricity data. In comparison, the proposed ensemble approaches combine linearly (EnL) or nonlinearly (EnNL) the forecasting values obtained from all the single automatic methods by considering each model component’s weight. In this work, four electrical time series with different characteristics are examined, to demonstrate the effectiveness and applicability of the proposed ensemble approach—the model performances are compared based on root mean square error (RMSE) and absolute percentage errors (MAPEs). The experimental results show that compared to the existing average weighted ensemble approach, the proposed nonlinear weighted ensemble approach successfully reduces the RMSE and MAPE of the testing data by between 28% and 82%.

Application of Generative Autoencoders in the Detection of Anomalies in Hypercompressors

Hypercompressors are essential assets that compress high-flow-rates of ethylene to pressures between 100~350 MPa in the LDPE industry. They are sources of essential risks and costs. This work proposes an unsupervised and univariate monitoring method for detecting anomalies in hypercompressors through data collected from an online monitoring system in an actual installation. A variational autoencoder learns the process of generating shapelets associated with vibrational patterns. A combination of matrix profile algorithms automatically selects the training data set. A β-VAE composed of MLP layers is trained and applied on the input space so that a voting operation and a box-cox transformation on the absolute residual errors between the inputs and outputs lead to the upper outlier detection threshold, obtained by the Tukey fence method. The model detected suspicious vibration patterns classified a priori as potential anomalies.

Remaining useful life prediction for lithium-ion batteries based on sliding window technique and Box-Cox transformation

Accurate remaining useful life (RUL) prediction technique matters in lithium-ion battery use, optimization, and replacement. This article presents an RUL prediction method combining the sliding window (SW) technique and Box-Cox transformation (BCT). This method achieves online RUL prediction with acceptable accuracy, is independent of offline training data, and only brings a low computational burden. The SW technique is employed for gathering a certain amount of capacity data, which is subsequently transformed using BCT-related techniques to construct a capacity degradation model. The identified model is then extrapolated to predict battery RUL, and the prediction uncertainties are calculated through Monte Carlo (MC) simulation. A simple implementation shows that this hybrid method outperforms the history-based polynomial and BCT methods in battery RUL prediction. Given the segmented capacity degradation trend, a constraint can be imposed on the model parameter for optimization purposes. Experimental results demonstrate that the optimized method obtains lower root-mean-square errors (RMSEs) of RUL predictions during the last 20 % of the battery lifetime than the original one, and the precise RULs are predicted with standard deviations mainly within [1, 10] cycles.

Towards cleaner air in Siliguri: A comprehensive study of PM2.5 and PM10 through advance computational forecasting models for effective environmental interventions

This research addresses the escalating concern of air pollution, primarily due to fine particulate matter (PM2.5) and coarse particulate matter (PM10), in Siliguri city, West Bengal, India. Using a comprehensive dataset of daily 24-h average concentrations from February 2018 to February 2023, procured from the Central Pollution Control Board, six advanced computational models i.e., Artificial Neural Networks (ANN), Autoregressive Integrated Moving Averages (ARIMA), Extreme Learning Machine (ELM), Exponential Smoothing State Space Models (ETS), Naïve, and Trigonometric Seasonality, Box-Cox Transformation, ARMA Errors, Trend, and Seasonality (TBATS) were rigorously tested for predicting particulate matter concentrations. Daily data from 2018 to 2021 was used for training and the remaining for testing. The models in the testing phase were evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) along with R2. In the testing phase, the TBATS model emerged as the most accurate with the lowest RMSE values of 8.11 for PM2.5 and 12.33 for PM10, followed by the ARIMA model with an RMSE of 10.72 for PM2.5 and 18.10 for PM10. The ETS model also demonstrated reliable performance. In addition, by using the advantages of the most effective models, namely ARIMA and TBATS, the research makes forecasts for PM2.5 and PM10 levels from 2023 to 2025, on a monthly basis. These findings are helpful for air quality management in Siliguri and underscore the importance of using advanced computational models for pollution forecasting, encouraging further research on hybrid models with meteorological parameters.

The statistical challenge of analysing changes in dual energy computed tomography (DECT) urate volumes in people with gout

BackgroundDual energy computed tomography (DECT) allows direct visualization of monosodium urate crystal deposition in gout. However, DECT urate volume data are often highly skewed (mostly small volumes with the remainder considerably larger), making statistical analyses challenging in longitudinal research. The aim of this study was to explore the ability of various analysis methods to normalise DECT urate volume data and determine change in DECT urate volumes over time. MethodsSimulated datasets containing baseline and year 1 DECT urate volumes for 100 people with gout were created from two randomised controlled trials. Five methods were used to transform the DECT urate volume data prior to analysis: log-transformation, Box-Cox transformation, log(X-(min(X)-1)) transformation; inverse hyperbolic sine transformation, and rank order. Linear regression analyses were undertaken to determine the change in DECT urate volume between baseline and year 1. Cohen's d were calculated as a measure of effect size for each data treatment method. These analyses were then tested in a validation clinical trial dataset containing baseline and year 1 DECT urate volumes from 91 people with gout. ResultsNo data treatment method successfully normalised the distribution of DECT urate volumes. For both simulated and validation data sets, significant reductions in DECT urate volumes were observed between baseline and Year 1 across all data treatment methods and there were no significant differences in Cohen's d effect sizes. ConclusionsNormalising highly skewed DECT urate volume data is challenging. Adopting commonly used transformation techniques may not significantly improve the ability to determine differences in measures of central tendency when comparing the change in DECT urate volumes over time.

Evaluation of surface roughness of novel Al-based MMCs using Box-Cox transformation

Evaluation of surface roughness of novel Al-based MMCs using Box-Cox transformation

Deep learning-based cancer disease classification using Gene Expression Data

&lt;p&gt;Cancer disease caused a major death in worldwide. To prevent this, various cancer classification approaches are employed, which are mostly relied on clinical characteristics and histopathological characteristics. Deep learning-based classification models are very effective and accurate. As a result, this research established the Adam-based Deep Quantum Neural Network, which is the optimal deep learning-based cancer classification method. The information on gene expression is used to classify cancer. Using the Box-Cox transformation, which converts the data into a legible format, the data transformation procedure is carried out. Utilizing information gain, the features are chosen in order to choose the proper gene expression. Additionally, Deep QNN is used to classify cancer, and for better classification, which is trained via Adam optimization. The experimental result shows the developed model provide better classification result with respect to accuracy, true positive rate and true negative rate of 94.91%, 95.59% and 95.4%.&lt;/p&gt;

Universal recession constants and their potential to predict recession flow

Streamflow prediction during dry or recession periods is crucial for water resources management. The storage-discharge (S-Q) relationship is generally used to model recession flow in the basin. Since storage is practically unobservable, the S-Q relationship is often quantified by analyzing the relationship between -dQ/dt and Q, which Brutsaert and Nieber (1977) observed to be of a power-law type: -dQ/dt=kQα, for natural basins. Integration of the above equation yields an expression for the streamflow at any time, t, during the recession period. However, this approach relies on the availability of the streamflow data and, therefore, cannot be applied directly to ungauged or data-scarce basins. Thus, there exists a necessity for an alternative approach to predict streamflow in the ungauged basins during the recession period. In this study, we investigated recession curves from 413 basins in the United States and determined the existence of a universal relationship (k=kuQN-λu) between the storage coefficient (k) and the average past discharge (QN) that can serve as a proxy for basin storage. We tested the potential of universal recession constants (ku and λu) in predicting the recession flow in both gauged and ungauged basins. It is observed that the median NSEBC, i.e., NSE calculated using the Box-Cox transformation of discharge, was 0.78 for the gauged basins and 0.55 for the ungauged basins. Our findings provide a model-independent method for predicting the recession discharge, which can pave new avenues towards improving the predictions in ungauged basins.

Kernel estimator of extreme value index (EVI) and high quantiles for heavy-tailed distributions under dependence serials using the Box-Cox transformation

The Box-Cox transformation is used to render the data more conducive to statistical analysis. Its application to extreme values statistics improves the convergence rate of certain classical tail index estimators and reduces bias in the context of independent and identically distributed (i.i.d) random variables. In this paper, we explore a bias reduction estimator for the extreme value index under $\beta$-mixing serial dependence. Our approach is based on kernel estimation of the extreme value index and the Box-Cox transformation methodology. Under specific regular conditions, we establish the asymptotic normality of the proposed estimator and deduce an asymptotically unbiased estimator for high quantiles. Through a simulation study, we delineate the performance of our proposals, comparing them to alternative estimators recently introduced in the literature. We further illustrate these theoretical results by applying them to real wind speed data.

Leukocyte cytokine expression is associated with severity of autism in children

Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder with unknown etiology, high clinical heterogeneity and marked aberrations of the immune system. Evidence for an association between immune dysfunction and behavioral traits highlights the need for a study of the immune cell functional activity in order to search for pathogenesis mechanisms and potential targets for therapy at ASD. The purpose: to determine the expression levels of IL-1β, IL-2, IL-4, IL-6, IL-10, IL-18, IFNγ and TNFα in peripheral blood leukocytes of children with mild and severe ASD. The study included 81 children with ASD (77.8% boys) and 45 children with typical neurodevelopment (TDC, 71.1% boys). According to the Childhood Autism Rating Scale, 51 children (63.0%) had mild autistic symptoms (CARS score 32.0±1,5) and 30 children had severe ASD symptoms (CARS score 39.0±3,4). Cytokines expression in leukocytes was determined by quantitative PCR with SYBRGreen. The data were transformed using Box–Cox transformation. The differences between groups were assessed by one-way ANOVA and Dunn’s test for multiple comparisons. In leukocytes of children with ASD, regardless of the severity, the expression of IL-1β, IL-18 and IL-2, was significantly reduced compared to TDC. Moreover, in children with mild ASD, low expression of TNFα, compared with TDC was found. In children with severe ASD, the expression of the main cytokine of Th1 – IFNγ, was significantly increased, without an increased expression of an important cytokine of Treg – IL-10. Activation of the Th1 adaptive immune response without compensation by cytokines of Treg, the number of which is reduced in ASD, can lead to increased inflammation, even in the central nervous system, and correlates with the severity of ASD clinical symptoms. Despite extensive immunological evidence suggesting immune system dysregulation, further research is required to clarify the relationship between immune system cell function and ASD pathology.

Forecasting husbandry development using time series

Building time series models based on historical data is a pressing challenge in the agricultural sector. This is essential, as analysing and predicting processes related to the food security of the state, region, and business entities are of paramount importance in management. With the help of forecasts, enterprises can adjust their production activities in such a way as to satisfy demand and deliver products to consumers on time. The research aims to predict the trends in the growth of cattle and cow populations and identify the most suitable forecasting timeframe. Statistical methods related to autoregression are used for this type of analysis: autoregressive models, moving average models or a combination of both, integrated variable structure models, and models that include seasonal effects and exogenous factors with an autoregressive and moving average component in the model. Monthly statistical data on the number of cattle and cows are used, among them mean, standard deviation, minimum and maximum values, asymmetry, and kurtosis. The dynamics of the decrease in the number of cattle and cows are shown. The studied series were checked for stationarity. The time series data for the cattle population underwent a Box-Cox transformation. The optimal parameters of the models used are given. Predictive values for periods (months) were obtained and the change in the number of cattle over the last 15 years was analysed. Constructed time series are compared with the actual values, which are illustrated in the graphs. Estimates of rootmean-square deviation, and mean absolute percentage error for different forecasting terms are given. By comparing these estimates for different time intervals, the optimal period for the forecast (24 months) was determined. This study allows farms and enterprises in the industry to predict a possible number of products (milk, meat) that could be collected or obtained in the future. It helps to take the necessary management steps: plan resource needs, improve efficiency, increase profits, reduce costs, and adapt to changes in the market

Likelihood-type confidence regions for optimal sensitivity and specificity of a diagnostic test

New methods are proposed that provide approximate joint confidence regions for the optimal sensitivity and specificity of a diagnostic test, i.e., sensitivity and specificity corresponding to the optimal cutpoint as defined by the Youden index criterion. Such methods are semi-parametric or non-parametric and attempt to overcome the limitations of alternative approaches. The proposed methods are based on empirical likelihood pivots, giving rise to likelihood-type regions with no predetermined constraints on the shape and automatically range-respecting. The proposal covers three situations: the binormal model, the binormal model after the use of Box-Cox transformations and the fully non-parametric model. In the second case, it is also shown how to use two different transformations, for the healthy and the diseased subjects. The finite sample behaviour of our methods is investigated using simulation experiments. The simulation results also show the advantages offered by our methods when compared with existing competitors. Illustrative examples, involving three real datasets, are also provided.

Predicting punching shear in RC interior flat slabs with steel and FRP reinforcements using Box-Cox and Yeo-Johnson transformations

This study presents a new approach for predicting the punching shear strength of reinforced concrete flat plates reinforced with steel and fiber-reinforced polymer (FRP) bars, using four machine learning regression models. A dataset of 505 interior flat plates from previous literature was used to develop the models. Input variables were transformed using Box-Cox and Yeo-Johnson transformations to improve predictive power by reducing white noise. The SHapley Additive exPlanations (SHAP) framework was utilized as the Explainable Artificial Intelligence (XAI) method to decipher model execution and feature the main info factors for anticipating the punching shear capacity. Additionally, design codes and equations from the literature are compared to the efficiency and accuracy of the power transformation featured XGBoost model. The findings demonstrate that the suggested prediction model performed very well and is appropriate for estimating the punching shear capacity of slab-column connections reinforced with steel and FRP bars. Moreover, the power transferred XGBoost model performed better than other numerical equations because it had the highest mean R2 (0.93) and lowest MAPE (0.20) for testing, which suggests that machine learning models may be able to offer an elective strategy to currently used mechanics-based models for configuration practice.

Associations of fine particulate matter exposure with sleep disorder indices in adults and mediating effect of body fat

Exposure to particulate matter (PM) may be a risk factor for obstructive sleep apnea (OSA) and obesity. However, whether body fat accumulation exerts mediating effects on the association between air pollutant exposure and OSA aggravation remains unclear.This study retroactively acquired the polysomnographic data (sleep variables) and body composition information from 2893 patients in a northern Taiwan sleep center. The levels of exposure to various air pollutants were estimated using an adjusted method based on data from governmental air quality monitoring stations near registered residential addresses instead of only referencing the nearest station. The sleep disorder indices and body fat metrics, which served as the outcomes of interest, were transformed using the Box-Cox transformation. Multiple linear regression models and causal mediation analysis were employed to investigate the associations between the analyzed parameters and the estimated air pollutant exposure at various time scales (1-, 6-, and 12-month).Significant associations were observed between the increased interquartile range (IQR) of short-term (1-month) exposure to PM ≤ 10 μm (PM10), PM ≤ 2.5 μm (PM2.5), and the apnea–hypopnea index (AHI), oxygen desaturation index (ODI), and arousal index (ArI). Short-term (1-month) exposure to PM10 and PM2.5 was significantly associated with increased trunk fat percentage. Causal mediation analysis revealed that short-term (1-month) exposure to PM10 and PM2.5 affected trunk fat percentage, thereby partially meditating the elevations in AHI, ODI, and ArI.PM exposure may directly increase sleep disorder indices and alter body fat, thereby mediating the worsening of OSA manifestations (i.e., increased AHI, ODI, and ArI).