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In this paper, the graphic representation method is used to study the multiple characteristics of heart sounds from a resting state to a state of motion based on single- and four-channel heart-sound signals. Based on the concept of integration, we explore the representation method of heart sound and blood pressure during motion. To develop a single- and four-channel heart-sound collector, we propose new concepts such as a sound-direction vector of heart sound, a motion–response curve of heart sound, the difference value, and a state-change-trend diagram. Based on the acoustic principle, the reasons for the differences between multiple-channel heart-sound signals are analyzed. Through a comparative analysis of four-channel motion and resting-heart sounds, from a resting state to a state of motion, the maximum and minimum similarity distances in the corresponding state-change-trend graphs were found to be 0.0038 and 0.0006, respectively. In addition, we provide several characteristic parameters that are both sensitive (such as heart sound amplitude, blood pressure, systolic duration, and diastolic duration) and insensitive (such as sound-direction vector, state-change-trend diagram, and difference value) to motion, thus providing a new technique for the diverse analysis of heart sounds in motion.

Vibrational spectroscopy techniques, such as Fourier-transform infrared (FTIR) and Raman spectroscopy, have been successful methods for studying the interaction of light with biological materials and facilitating novel cell biology analysis. Spectrochemical analysis is very attractive in disease screening and diagnosis, microbiological studies and forensic and environmental investigations because of its low cost, minimal sample preparation, non-destructive nature and substantially accurate results. However, there is now an urgent need for multivariate classification protocols allowing one to analyze biologically derived spectrochemical data to obtain accurate and reliable results. Multivariate classification comprises discriminant analysis and class-modeling techniques where multiple spectral variables are analyzed in conjunction to distinguish and assign unknown samples to pre-defined groups. The requirement for such protocols is demonstrated by the fact that applications of deep-learning algorithms of complex datasets are being increasingly recognized as critical for extracting important information and visualizing it in a readily interpretable form. Hereby, we have provided a tutorial for multivariate classification analysis of vibrational spectroscopy data (FTIR, Raman and near-IR) highlighting a series of critical steps, such as preprocessing, data selection, feature extraction, classification and model validation. This is an essential aspect toward the construction of a practical spectrochemical analysis model for biological analysis in real-world applications, where fast, accurate and reliable classification models are fundamental. A tutorial for multivariate classification analysis of vibrational spectroscopy data (Fourier-transform infrared, Raman and near-IR) is presented. Guidelines are provided for data preprocessing, data selection, feature extraction, classification and model validation.

Bias correcting and downscaling climate model simulations requires reconstructing spatial and intervariable dependences of the observations. However, the existing univariate bias correction methods often fail to account for such dependences. While the multivariate bias correction methods have been developed to address this issue, they do not consistently outperform the univariate methods due to various assumptions. In this study, using 20 state-of-the-art coupled general circulation models (GCMs) daily mean, maximum and minimum temperature (T mean , T max and T min ) from the Coupled Model Intercomparison Project phase 6 (CMIP6), we comprehensively evaluated the Super Resolution Deep Residual Network (SRDRN) deep learning model for climate downscaling and bias correction. The SRDRN model sequentially stacked 20 GCMs with single or multiple input-output channels, so that the biases can be efficiently removed based on the relative relations among different GCMs against observations, and the intervariable dependences can be retained for multivariate bias correction. It corrected biases in spatial dependences by deeply extracting spatial features and making adjustments for daily simulations according to observations. For univariate SRDRN, it considerably reduced larger biases of T mean in space, time, as well as extremes compared to the quantile delta mapping (QDM) approach. For multivariate SRDRN, it performed better than the dynamic Optimal Transport Correction (dOTC) method and reduced greater biases of T max and T min but also reproduced intervariable dependences of the observations, where QDM and dOTC showed unrealistic artifacts (T max < T min ). Additional studies on the deep learning-based approach may bring climate model bias correction and downscaling to the next level.

•A principal component analysis (PCA)-based supervised machine learning (SML) method is developed.•PCA-based SML is proposed to enhance fault detection and diagnosis (FDD) of photovoltaic (PV) systems.•The developed FDD approach uses feature extraction and selection, and fault classification tools.•The detection performance is studied using several PV system faults.•The results show good diagnosis efficiency and higher classification accuracy in PV systems. Fault detection and diagnosis (FDD) in the photovoltaic (PV) array has become a challenge due to the magnitudes of the faults, the presence of maximum power point trackers, non-linear PV characteristics, and the dependence on isolation efficiency. Thus, the aim of this paper is to develop an improved FDD technique of PV systems faults. The common FDD technique generally has two main steps: feature extraction and selection, and fault classification. Multivariate feature extraction and selection is very important for multivariate statistical systems monitoring. It can reduce the dimension of modeling data and improve the monitoring accuracy. Therefore, in the proposed FDD approach, the principal component analysis (PCA) technique is used for extracting and selecting the most relevant multivariate features and the supervised machine learning (SML) classifiers are applied for faults diagnosis. The FDD performance is established via different metrics using data extracted from different operating conditions of the grid-connected photovoltaic (GCPV) system. The obtained results confirm the feasibility and effectiveness of the proposed approaches for fault detection and diagnosis.

Objectives To develop radiomics-based nomograms for preoperative microvascular invasion (MVI) and recurrence-free survival (RFS) prediction in patients with solitary hepatocellular carcinoma (HCC) ≤ 5 cm. Methods Between March 2012 and September 2019, 356 patients with pathologically confirmed solitary HCC ≤ 5 cm who underwent preoperative gadoxetate disodium–enhanced MRI were retrospectively enrolled. MVI was graded as M0, M1, or M2 according to the number and distribution of invaded vessels. Radiomics features were extracted from DWI, arterial, portal venous, and hepatobiliary phase images in regions of the entire tumor, peritumoral area ≤ 10 mm, and randomly selected liver tissue. Multivariate analysis identified the independent predictors for MVI and RFS, with nomogram visualized the ultimately predictive models. Results Elevated alpha-fetoprotein, total bilirubin and radiomics values, peritumoral enhancement, and incomplete or absent capsule enhancement were independent risk factors for MVI. The AUCs of MVI nomogram reached 0.920 (95% CI: 0.861–0.979) using random forest and 0.879 (95% CI: 0.820–0.938) using logistic regression analysis in validation cohort ( n = 106). With the 5-year RFS rate of 68.4%, the median RFS of MVI-positive (M2 and M1) and MVI-negative (M0) patients were 30.5 (11.9 and 40.9) and > 96.9 months ( p < 0.001), respectively. Age, histologic MVI, alkaline phosphatase, and alanine aminotransferase independently predicted recurrence, yielding AUC of 0.654 (95% CI: 0.538–0.769, n = 99) in RFS validation cohort. Instead of histologic MVI, the preoperatively predicted MVI by MVI nomogram using random forest achieved comparable accuracy in MVI stratification and RFS prediction. Conclusions Preoperative radiomics-based nomogram using random forest is a potential biomarker of MVI and RFS prediction for solitary HCC ≤ 5 cm. Key Points • The radiomics score was the predominant independent predictor of MVI which was the primary independent risk factor for postoperative recurrence. • The radiomics-based nomogram using either random forest or logistic regression analysis has obtained the best preoperative prediction of MVI in HCC patients so far. • As an excellent substitute for the invasive histologic MVI, the preoperatively predicted MVI by MVI nomogram using random forest (MVI-RF) achieved comparable accuracy in MVI stratification and outcome, reinforcing the radiologic understanding of HCC angioinvasion and progression.

Handling missing values is a crucial step in preprocessing data in Machine Learning. Most available algorithms for analyzing datasets in the feature selection process and classification or estimation process analyze complete datasets. Consequently, in many cases, the strategy for dealing with missing values is to use only instances with full data or to replace missing values with a mean, mode, median, or a constant value. Usually, discarding missing samples or replacing missing values by means of fundamental techniques causes bias in subsequent analyzes on datasets. Aim : Demonstrate the positive impact of multivariate imputation in the feature selection process on datasets with missing values. Results : We compared the effects of the feature selection process using complete datasets, incomplete datasets with missingness rates between 5 and 50%, and imputed datasets by basic techniques and multivariate imputation. The feature selection algorithms used are well-known methods. The results showed that the datasets imputed by multivariate imputation obtained the best results in feature selection compared to datasets imputed by basic techniques or non-imputed incomplete datasets. Conclusions : Considering the results obtained in the evaluation, applying multivariate imputation by MICE reduces bias in the feature selection process.

Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often adapt univariate approaches or rely on assumptions specific to certain domains or problems, presenting limitations. A recent promising alternative is to map multivariate time series into high-level network structures such as multiplex networks, with past work relying on connecting successive time series components with interconnections between contemporary timestamps. In this work, we first define a novel cross-horizontal visibility mapping between lagged timestamps of different time series and then introduce the concept of multilayer horizontal visibility graphs. This allows describing cross-dimension dependencies via inter-layer edges, leveraging the entire structure of multilayer networks. To this end, a novel parameter-free topological measure is proposed and common measures are extended for the multilayer setting. Our approach is general and applicable to any kind of multivariate time series data. We provide an extensive experimental evaluation with both synthetic and real-world datasets. We first explore the proposed methodology and the data properties highlighted by each measure, showing that inter-layer edges based on cross-horizontal visibility preserve more information than previous mappings, while also complementing the information captured by commonly used intra-layer edges. We then illustrate the applicability and validity of our approach in multivariate time series mining tasks, showcasing its potential for enhanced data analysis and insights.

Animal models of nerve injury are important for studying nerve injury and repair, particularly for interventions that cannot be studied in humans. However, the vast majority of gait analysis in animals has been limited to univariate analysis even though gait data is highly multi-dimensional. As a result, little is known about how various spatiotemporal components of the gait relate to each other in the context of peripheral nerve injury and trauma. We hypothesize that a multivariate characterization of gait will reveal relationships among spatiotemporal components of gait with biological relevance to peripheral nerve injury and trauma. We further hypothesize that legitimate relationships among said components will allow for more accurate classification among distinct gait phenotypes than if attempted with univariate analysis alone. DigiGait data was collected of mice across groups representing increasing degrees of damage to the neuromusculoskeletal sequence of gait; that is (a) healthy controls, (b) nerve damage only via total nerve transection + reconnection of the femoral and sciatic nerves, and (c) nerve, muscle, and bone damage via total hind-limb transplantation. Multivariate relationships among the 30+ spatiotemporal measures were evaluated using exploratory factor analysis and forward feature selection to identify the features and latent factors that best described gait phenotypes. The identified features were then used to train classifier models and compared to a model trained with features identified using only univariate analysis. 10-15 features relevant to describing gait in the context of increasing degrees of traumatic peripheral nerve injury were identified. Factor analysis uncovered relationships among the identified features and enabled the extrapolation of a set of latent factors that further described the distinct gait phenotypes. The latent factors tied to biological differences among the groups (e.g. alterations to the anatomical configuration of the limb due to transplantation or aberrant fine motor function due to peripheral nerve injury). Models trained using the identified features generated values that could be used to distinguish among pathophysiological states with high statistical significance (p < .001) and accuracy (>80%) as compared to univariate analysis alone. This is the first performance evaluation of a multivariate approach to gait analysis and the first demonstration of superior performance as compared to univariate gait analysis in animals. It is also the first study to use multivariate statistics to characterize and distinguish among different gradations of gait deficit in animals. This study contributes a comprehensive, multivariate characterization pipeline for application in the study of any pathologies in which gait is a quantitative translational outcome metric.

Naive Bayesian classification algorithm is widely used in big data analysis and other fields because of its simple and fast algorithm structure. Aiming at the shortcomings of the naive Bayes classification algorithm, this paper uses feature weighting and Laplace calibration to improve it, and obtains the improved naive Bayes classification algorithm. Through numerical simulation, it is found that when the sample size is large, the accuracy of the improved naive Bayes classification algorithm is more than 99%, and it is very stable; when the sample attribute is less than 400 and the number of categories is less than 24, the accuracy of the improved naive Bayes classification algorithm is more than 95%. Through empirical research, it is found that the improved naive Bayes classification algorithm can greatly improve the correct rate of discrimination analysis from 49.5 to 92%. Through robustness analysis, the improved naive Bayes classification algorithm has higher accuracy.

The contribution of chemometrics to important stages throughout the entire analytical process such as experimental design, sampling, and explorative data analysis, including data pretreatment and fusion, was described in the first part of the tutorial “Chemometrics in analytical chemistry.” This is the second part of a tutorial article on chemometrics which is devoted to the supervised modeling of multivariate chemical data, i.e., to the building of calibration and discrimination models, their quantitative validation, and their successful applications in different scientific fields. This tutorial provides an overview of the popularity of chemometrics in analytical chemistry.