Fast Unsupervised Anomaly Detection in Traffic Videos

Anomaly detection in videos is the task of identifying frames from a video sequence that depict events that do not conform to expected behavior, which is an extremely challenging task due to the ambiguous and unbounded properties of anomalies. With the development of deep learning, video anomaly detection methods based on deep neural networks have made great progress. The existing methods mainly follow two routes, namely, frame reconstruction and frame prediction. Due to the powerful generalization ability of neural networks, the application of reconstruction-based methods is limited. Recently, anomaly detection methods based on prediction have achieved advanced performance. However, their performance suffers when they cannot guarantee lower prediction errors for normal events. In this paper, we propose a novel future frame prediction model based on a bidirectional retrospective generation adversarial network (BR-GAN) for anomaly detection. To predict a future frame with higher quality for normal events, first, we propose a bidirectional prediction combined with a retrospective prediction method to fully mine the bidirectional temporal information between the predicted frame and the input frame sequence. Then, the intensity and gradient loss between the predicted frame and the actual frame together with an adversarial loss are used for appearance (spatial) constraints. In addition, we propose a sequence discriminator composed of a 3-dimensional (3D) convolutional neural network to capture the long-term temporal relationships between frame sequences composed of predicted frames and input frames; this network plays a crucial role in maintaining the motion (temporal) consistency of the predicted frames for normal events. Such appearance and motion constraints further facilitate future frame prediction for normal events, and thus, the prediction network can be highly capable of distinguishing normal and abnormal patterns. Extensive experiments on benchmark datasets demonstrate that our method outperforms most existing state-of-the-art methods, validating the effectiveness of our method for anomaly detection.

Intelligent video surveillance systems with anomaly detection capabilities are indispensable for outdoor security. Video anomaly detection (VAD) is usually performed by learning patterns representing normal events and declaring an anomaly when an abnormal pattern is encountered. However, the features of normal patterns in a video often vary with time as real-world videos are non-stationary in nature, which makes its handling essential during VAD. To this end, we propose an approach for anomaly detection in videos, where a novel deep temporally recursive differencing network (DDN) diminishes the adverse effects of the non-stationary nature on VAD. The DDN consists of multiple layers of differencing operators of optimized orders, where every two consecutive layers are separated by a suitable nonlinearity. Spatial and temporal features are extracted from nonoverlapping blocks in video frames and fed to the DDN. While the spatial feature is obtained using a pretrained network, our temporal feature computation involves the use of FlowNetS with a new training strategy that does not require ground truth. The features at the output of DDN are used in a predictor based on autoregression and moving average of the regression errors. Then, the predictor's output estimates are compared to the corresponding actual values for anomaly detection, which also involves block-level selection and consistency check. Qualitative evaluation and quantitative comparison with several existing approaches on multiple standard datasets demonstrate the effectiveness of the proposed VAD approach. An ablation study highlighting the significance of the various components of our approach and a hyperparameter analysis are also provided.

Anomaly detection in crowd surveillance videos is a critical task for ensuring public safety and security. In this research paper, we propose a comprehensive framework for anomaly detection using deep learning techniques, specifically Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), and Generative Adversarial Networks (GANs). Our objective is to narrow the gap between computational complexity and detection effectiveness while satisfying the demand for explainability in anomaly detection systems. The proposed framework leverages the UCSD Ped2 dataset and focuses on incorporating spatial constraints to enhance anomaly detection performance. We introduce novel approaches for feature extraction and anomaly detection using GANs, aiming to capture essential spatial and temporal information while reducing computational complexity. Specifically, we develop encoders within the GAN framework to map input data to a lower-dimensional latent space and perform anomaly detection based on the similarity between latent codes. Through extensive experimentation and evaluation, we compare the performance of RNNs, CNNs, and GANs in detecting anomalies in crowd surveillance videos. Various evaluation metrics, including precision, recall, F1 score, ROC-AUC, and PR-AUC, is considered to assess the effectiveness of each approach. Additionally, they studied hyperparameters such as learning rate, batch size, network architecture, and GAN-specific parameters to optimize anomaly detection performance. Our results demonstrate the usefulness of the proposed framework in achieving robust and explainable anomaly detection in crowd surveillance videos. By combining advanced deep learning techniques with spatial constraints and explainability considerations, our research contributes to the development of more reliable and interpretable anomaly detection systems for real-world applications.

Anomaly detection in surveillance videos is a challenging task due to the diversity of anomalous video content and duration. In this paper, we consider video anomaly detection as a regression problem with respect to anomaly scores of video clips under weak supervision. Hence, we propose an anomaly detection framework, called Anomaly Regression Net (ARNet), which only requires video-level labels in training stage. Further, to learn discriminative features for anomaly detection, we design a dynamic multiple-instance learning loss and a center loss for the proposed AR-Net. The former is used to enlarge the inter-class distance between anomalous and normal instances, while the latter is proposed to reduce the intra-class distance of normal instances. Comprehensive experiments are performed on a challenging benchmark: ShanghaiTech. Our method yields a new state-of-the-art result for video anomaly detection on ShanghaiTech dataset.

The aim of the present research is to calculate the Relative Accuracy (R.A) and Root Mean Square Error (RMSE) for the location of Technical Institute, Mosul in Nineveh Governorate, Iraq. at the northern part of Mosul city by using surveying Instruments (GPS 1230 , Total Station 06 & Level NAK2), to calculate the coordinates and elevations of (16) Ground Control Points which covered the study area. The field data, remote sensing techniques and GIS software (Arc Map GIS10.3) are used to check the digital map of study area that helped the administrator to take the correct decision, determining positions of the future expansionist for buildings, roads, measuring lengths, areas and there coordinates, directions as well as the total costs estimation needed for any development from the final map. The gradient percentage between the highest and lowest points is calculated to be (9.954%). Relative accuracy for the based measured points (R.A) = 1:60000), and Root Mean Square error in Easting coordinates (RMSE) = ± 0.102m, in Northing coordinates (RMSN) = ± 0.096m, the Root Mean Square for the resultant (RMSR) = ± 0.099m, and Root Mean Square for Elevations ( RMSRL)= ± 0.005m. We Matched and correlated (10) measured points from study area with their graphic data positions on the aerial photo, determining the offsets for position and elevations as follows: (RMSE = ± 0.076m), (RMSN = ± 0.125m), (RMSR = ± 0.088m), and (Root Mean Square for Elevations = RMSRL= ± 0.045m). This research enable us after checking the results to produce new maps from Aerial photograph or Digital Image to use it for land uses and future extensions in whole study area.

BackgroundThe multileaf collimator (MLC) is a critical component to accurate intensity-modulated radiotherapy (IMRT) delivery. This study examined MLC positional accuracy via MLC logs from Varian machines from six institutions and three delivery techniques to evaluate typical positional accuracy and treatment and mechanical parameters that affect accuracy. Typical accuracy achieved was compared against TG-142 recommendations for MLC performance; more appropriate recommendations are suggested.MethodsOver 85,000 Varian MLC treatment logs were collected from six institutions and analyzed with FractionCHECK. Data were binned according to institution and treatment type to determine overall root mean square (RMS) and 95th percentile error values, and then to look for correlations between those errors and with mechanical and treatment parameters including mean and maximum leaf speed, gantry angle, beam-on time, mean leaf error, and number of segments.ResultsResults of treatment logs found that leaf RMS error and 95th percentile leaf error were consistent between institutions, but varied by treatment type. The step and shoot technique had very small errors: the mean RMS leaf error was 0.008 mm. For dynamic treatments the mean RMS leaf error was 0.32 mm, while volumetric-modulated arc treatment (VMAT) showed an RMS leaf error of 0.46 mm. Most MLC leaf errors were found to be well below TG-142 recommended tolerances. For the dynamic and VMAT techniques, the mean and maximum leaf speeds were significantly linked to the leaf RMS error. Additionally, for dynamic delivery, the mean leaf error was correlated with RMS error, whereas for VMAT the average gantry speed was correlated. For all treatments, the RMS error and the 95th percentile leaf error were correlated.ConclusionsRestricting the maximum leaf speed can help improve MLC performance for dynamic and VMAT deliveries. Furthermore, the tolerances of leaf RMS and error counts for all treatment types should be tightened from the TG-142 values to make them more appropriate for clinical performance. Values of 1 mm for the 95th percentile of leaf RMS error and 1.5 mm for the 95th percentile leaf error are suggested as action levels for all treatment types.

Anomaly detection plays a critical role in intelligent video surveillance. However, real-world video data obtained always contains large numbers of normal video data, along with large numbers of unlabeled data. A promising solution with one-class classification and semi-supervised learning may not be satisfactory as they fail to make good use of unlabeled data with only normal data available. In this paper, we introduced a new framework, called Positive Unlabeled learning-based Anomaly event Detection (PU-AD), to exploit the weakly-supervised information. To the best of our knowledge, this is the first work that introduces the PU idea and achieves detecting abnormal events with a limited number of partially labeled data. Experiments on real-world surveillance videos show that the proposed method outperforms the existing state-of-the-art methods.

We propose a novel unsupervised approach based on a two-stage object-centric adversarial framework that only needs object regions for detecting frame-level local anomalies in videos. The first stage consists in learning the correspondence between the current appearance and past gradient images of objects in scenes deemed normal, allowing us to either generate the past gradient from current appearance or the reverse. The second stage extracts the partial reconstruction errors between real and generated images (appearance and past gradient) with normal object behaviour, and trains a discriminator in an adversarial fashion. In inference mode, we employ the trained image generators with the adversarially learned binary classifier for outputting region-level anomaly detection scores. We tested our method on four public benchmarks, UMN, UCSD, Avenue and ShanghaiTech and our proposed object-centric adversarial approach yields competitive or even superior results compared to state-of-the-art methods.

For enhancing public safety, a surveillance system is essential. Specifically, video surveillance is the most popular way to maintain safety in public and private areas. The detection and recognition of abnormal activity is difficult due to a complex environment, video quality, and varying noise levels. Addressing the challenges of accuracy and video processing, the proposed study uses a cross-attention network with feature fusion to improve the recognition of abnormal activity in complex scenarios. Cross-attention helps to capture contextual information from different videos. The proposed model combines an innovative method of cross attention and feed-forward attention with latent space representation-based fusion, aiming to improve accuracy. The simulation of the study uses two benchmark datasets, UCF and UCSD and achieves remarkable performance with 97.1 % and 91.31 % accuracy. A simulation study has also demonstrated a comparative analysis with different convolution and attention networks for anomaly detection. This study proposes an effective video processing scheme with wide practical potential. The study also provides a new perspective and methodological basis for future research and applications in related fields.

OPINION article Front. Physiol., 22 January 2014Sec. Integrative Physiology Volume 4 - 2013 | https://doi.org/10.3389/fphys.2013.00403

Aiming at the key problems of traffic flow prediction and road condition recognition in Intelligent Transportation System (ITS), this paper puts forward an optimized framework of pattern recognition algorithm which integrates multi-source data and dynamic weight adjustment. Firstly, a spatio-temporal semantic model integrating sensor, traffic flow and event information is constructed, and graph neural network (GNN) is used to capture the link association. Then, an adaptive weighting mechanism based on attention and reinforcement learning (RL) is designed to improve the prediction robustness in complex scenes. Combined with Transformer-LSTM and Particle Swarm Optimization (PSO), the computational overhead is reduced and edge deployment is supported. Experiments are carried out based on PeMSD4 data and real-time data of an industrial park. The results show that the proposed method is superior to traditional and deep learning models in traffic flow forecasting performance. The root mean square error (RMSE) of 15-minute forecasting task is 23.4, the mean absolute percentage error (MAPE) is 8.7%, and the sudden congestion error is 28.9%. In the aspect of road condition recognition, the accuracy rate is 94.7% in normal weather, F1-score is 0.93, 88.4% in heavy rain, F1-score 0.85, 85.2% in sensor failure, and F1-score 0.82, which shows high robustness and reliability. At the same time, the parameters of the model are reduced from 43.2MB to 9.8MB, the reasoning delay is reduced from 121ms to 36ms, and the energy consumption is reduced from 293mJ to 87mJ, which has obvious lightweight characteristics and provides an efficient, accurate and adaptable solution for traffic flow prediction and road condition identification in ITS.

Many intelligent transportation systems (ITS) applications require accurate prediction of traffic parameters. Previous studies have shown that data driven machine learning methods like support vector regression (SVR) can effectively and accurately perform this task. However, these studies focus on highways, or a few road segments. We propose a robust and scalable method using n-SVR to tackle the problem of speed prediction of a large heterogenous road network. The traditional performance measures such as mean absolute percentage error (MAPE) and root mean square error (RMSE) provide little insight into spatial and temporal characteristics of prediction methods for a large network. This inadequacy can be a serious hurdle in effective implementation of prediction models for route guidance, congestion avoidance, dynamic traffic assignment and other ITS applications. We propose unsupervised learning techniques by employing k-means clustering, principal component analysis (PCA), and self organizing maps (SOM) to overcome this insufficiency. We establish the effectiveness of the developed methods by evaluation of spatial and temporal characteristics of prediction performance of the proposed variable window n-SVR method.

Electroencephalograph (EEG) is brain activity measurement technique that it is widely used by placing electrode on the scalp. The EEG recording signals are vulnerably contaminated by noise. Thus, it can lead to misperception in analyzing EEG signals. One of the noise that has major influence on the recorded EEG signals is ocular artifacts (OAs). In this paper, a new method to remove OAs automatically is proposed by combining between Complete Ensemble Empirical Mode Decomposition (CEEMD) and Independent Component Analysis (ICA). CEEMD-ICA-OD removes OAs based on the concentration of noise that is calculated by calculating entropy for every CEEMD decomposition. Every selected decomposition of CEEMD will be used as input to the ICA method. Then, ICA will decompose selected CEEMD decomposition into independent components (ICs). Then, Chauvenet Criterion (CC) as Outlier Detection (OD) method is used to detect OAs pattern. Every detected OAs pattern will be eliminated by zeroing process on OAs pattern so that the EEG signal information remains secure. The proposed method were compared with Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD) and Complete EEMD (CEEMD) with zeroing ICA combination for every comparison method. The performance measure of the proposed method and the benchmark method is calculated by using Root Mean Square Error (RMSE) and Signal to Noise Ratio (SNR) to show the performance quality in eliminating OAs. The experiment results show that the proposed method is successfully removing OAs better than the other methods with RMSE value and SNR value are 0.2491 and -0.3449, respectively.

Among the Earth Observation (EO) instruments used in environmental and agricultural applications, the SPOT4-VEGETATION (SPOT4-VGT) instrument allows daily monitoring of terrestrial vegetation cover through remote sensing, at regional and global levels. The characterization of the geometric and radiometric performances of remote sensing data and their temporal stability play an important role in the analysis of EO images and are essential in environmental and agricultural monitoring applications. The validation and characterization of the SPOT4-VGT image geometric performances and temporal stability are investigated in this letter. Three time series of data acquired during 1999, 2000 and 2001 were used for this purpose. These images were downlinked by several VGT L-band receiving stations and processed by the SPACE-VGT software. From analyses made, it can be concluded that the geometric characteristics of the VGT L-band images agree with the VGT International User Committee requirements: the multispectral registration has a root mean square (RMS) error in the range of 0.25±0.17 pixels for B2, B3 and MIR bands, and 0.48±0.21 pixels for B0 band; the multi-temporal registration has a RMS error in the range of 0.38±0.23 pixels; and the absolute geo-location has a RMS error in the range of ±660 m.

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Materials and methods Results Discussion Data availability References Decision letter Author response Article and author information Metrics Abstract Background: Oxygen uptake (VO2) is one of the most important measures of fitness and critical vital sign. Cardiopulmonary exercise testing (CPET) is a valuable method of assessing fitness in sport and clinical settings. There is a lack of large studies on athletic populations to predict VO2max using somatic or submaximal CPET variables. Thus, this study aimed to: (1) derive prediction models for maximal VO2 (VO2max) based on submaximal exercise variables at anaerobic threshold (AT) or respiratory compensation point (RCP) or only somatic and (2) internally validate provided equations. Methods: Four thousand four hundred twenty-four male endurance athletes (EA) underwent maximal symptom-limited CPET on a treadmill (n=3330) or cycle ergometer (n=1094). The cohort was randomly divided between: variables selection (nrunners = 1998; ncyclist = 656), model building (nrunners = 666; ncyclist = 219), and validation (nrunners = 666; ncyclist = 219). Random forest was used to select the most significant variables. Models were derived and internally validated with multiple linear regression. Results: Runners were 36.24±8.45 years; BMI = 23.94 ± 2.43 kg·m−2; VO2max=53.81±6.67 mL·min−1·kg−1. Cyclists were 37.33±9.13 years; BMI = 24.34 ± 2.63 kg·m−2; VO2max=51.74±7.99 mL·min−1·kg−1. VO2 at AT and RCP were the most contributing variables to exercise equations. Body mass and body fat had the highest impact on the somatic equation. Model performance for VO2max based on variables at AT was R2=0.81, at RCP was R2=0.91, at AT and RCP was R2=0.91 and for somatic-only was R2=0.43. Conclusions: Derived prediction models were highly accurate and fairly replicable. Formulae allow for precise estimation of VO2max based on submaximal exercise performance or somatic variables. Presented models are applicable for sport and clinical settling. They are a valuable supplementary method for fitness practitioners to adjust individualised training recommendations. Funding: No external funding was received for this work. Editor's evaluation The authors have established new formulas to predict maximum oxygen uptake for cyclists and runners based on submaximal exercise testing and anthropometric characteristics. This is an important study with a large and comprehensive dataset, which may be helpful for many exercise labs. The work is convincing, using appropriate and validated methodology in line with the current state-of-the-art, as shown by references to common exercise books. https://doi.org/10.7554/eLife.86291.sa0 Decision letter Reviews on Sciety eLife's review process Introduction The oxygen uptake (VO2) is considered an important metric in assessing cardiorespiratory fitness, health status, or endurance performance potential (Guazzi et al., 2012). With the application of standardised procedures and interpretation protocols, during graded exercise tests (GXT), the (maximal oxygen uptake) VO2max can be established (Bentley et al., 2007). GXT is the most widely used assessment to examine the dynamic relationship between exercise and integrated physiological systems (Albouaini et al., 2007; Bentley et al., 2007). The information from GXT during cardiopulmonary exercise testing (CPET) can be applied across the spectrum of sport performance, occupational safety screening, research, and clinical diagnostics (Guazzi et al., 2017). VO2 max is often used as a boundary between severe and extreme intensity domains and by definition requires maximal effort from the tested subject (Gaesser and Poole, 1996). However, it is not always recommended or possible to undertake a test to exhaustion (Guazzi et al., 2012). For the athletes, the proximity of competition or injury history can allow submaximal testing, but not testing to exhaustion (Sassi et al., 2006). Testing that requires maximal effort may be disruptive to the training process or interfere with race performance (Coutts et al., 2007; Lamberts et al., 2011). Due to practical constraints, tests to exhaustion or peak-power-output tests are often performed only two or three times a year (Coutts et al., 2007). However, VO2 values are widely used in sport science and the decision-making process (Mann et al., 2013). VO2 is widely considered one of the major endurance performance determinants (Joyner and Coyle, 2008). Using VO2max to guide the selection process, prescribing training intensity, assessing training adaptations, or predicting race times is a common practice in high-performance sports (Bassett and Howley, 2000; Bentley et al., 2007; Hawley and Noakes, 1992; Noakes et al., 1990). VO2max is also one of the critical vital signs coordinating the function of the cardiovascular, respiratory, and muscular systems, it is an indicator of overall body health status (Kaminsky et al., 2017). Quantifying VO2max provides additional input regarding clinical decision-making, risk stratification, evaluation of therapy, and physical activity guidelines (Guazzi et al., 2012). For patients undertaking a test to exhaustion is rarely needed or possible due to health restraints or cardiac risk (Guazzi et al., 2016). For many years researchers have studied indirect methods of estimating VO2max(Sartor et al., 2013). Protocols such as the Astrand-Ryhming Test, Six-Minute Walk Test, or YMCA Step Test have been established and validated (Astrand and Ryhming, 1954; Beutner et al., 2015; Carey, 2022; Jalili et al., 2018). Moreover, estimation of the VO2 and heart rate (HR) values below the ventilatory threshold can be based on cardiorespiratory kinetics assessment using randomised changes in the work rate known as a pseudo-random binary sequences testing (Hoffmann et al., 2022). However, with the development of technology, the accessibility of laboratory testing and mobile testing improved (Montoye et al., 2020; Pritchard et al., 2021). Therefore, new opportunities to develop more precise yet simple and accessible methods and models to assess VO2max occur (Jurov et al., 2023). This appears to be especially important considering the low prediction accuracy of most of the VO2max formulae that were validated in our previous study (Wiecha et al., 2023). Recently, we have been observing the development of prediction methods with the usage of machine learning (ML) and artificial intelligence (AI) (Ashfaq et al., 2022). Both ML and AI are used in sport science as forecasting and decision-making support tools (Abut and Akay, 2015; Bobowik and Wiszomirska, 2022; Chmait and Westerbeek, 2021; Hammes et al., 2022; Rossi et al., 2021). There is growing evidence that VO2max prediction based on ML models, especially support vector ML and artificial neural network models, exhibits more robust and accurate results compared to MLR only (Abut and Akay, 2015; Ashfaq et al., 2022). Therefore, in this research, with the support of ML, we look for algorithms and prediction patterns that allow us to use values obtained during submaximal CPET and somatic measurements to estimate maximal VO2max values in male runners and cyclists. We stipulate that prediction models allow for accurate calculation of VO2max based on somatic or submaximal CPET variables. Materials and methods We have applied the development and validation of the prediction TRIPOD guidelines to conduct the study (see Supplementary Material 1TRIPOD Checklist for Prediction Model Development and Validation) (Collins et al., 2015). The study is based on retrospective data analysis from the CPET registry collected from 2013 to 2021 at the medical clinic (Sportslab, Warsaw, Poland). All CPET have been performed at the individual request of participants, as a part of regular training monitoring or performance assessment. Ethical approval Request a detailed protocol The Institutional Review Board of the Bioethical Committee at the Medical University of Warsaw (AKBE/32/2021) has approved the study protocol. The regulations of the Declaration of Helsinki were met during all parts of the study. Each study participant delivered written consent to undergo CPET and participate in the study. Derivation cohort Request a detailed protocol We selected the cohort with the use of rigorous exclusion/inclusion criteria. Due to the insufficient number of women in our database and the number of potential variables in the regression models for adequate power, we had to limit ourselves to conduct analysis in the male population only (Martens and Logan, 2021). Out of 6439 healthy, adult male cyclists and long-distance runners that undergone CPET, 4423 met the criteria as further: (1) age ≥18 years, (2) declared regular cycling or running training for ≥3 months, (3) had no extreme outliers ≤ or ≥±3 standard deviations (SD) from mean for all of the testing variables (beyond ≥±3 SD in VO2max), (4) lack of any injury, medical condition, or addiction in medical history that may affect exercise capacity, (5) not taking any medications with a modifying effect on exercise capacity, (6) maximum exertion achieved during CPET. We defined the maximum exertion in CPET as the fulfilment of the minimum six of the following criteria: (1) respiratory exchange ratio (RER) ≥1.10, (2) present VO2 plateau (growth <100 mL·min–1 in VO2 despite increased running speed or cycling power), (3) respiratory frequency (fR) ≥45 breaths·min–1, (4) declared subjective exertion intensity during CPET ≥18 in the Borg scale (Borg, 1970), (5) blood lactate concentration [La-]b ≥8 mmol·L–1, (6) growth in speed/power ≥10% of respiratory compensation point (RCP) values after exceeding the RCP, (7) peak heart rate (HRpeak) ≥15 beats·min–1 below predicted maximal heart rate (HRmax) (Lach et al., 2021). Participants’ selection procedure has been shown in Figure 1. Figure 1 Download asset Open asset Flowchart of the preliminary inclusion and exclusion process. Abbreviations: EA, endurance athlete; CPET, cardiopulmonary exercise testing; SD, standard deviation; TE, treadmill; RER, respiratory exchange ratio; VO2, oxygen uptake (mL·min−1·kg−1); [La−]b, lactate concentration (mmol·L−1); fR, breathing frequency (breaths·min−1); RCP, respiratory compensation point; HRpeak, peak heart rate (beats·min−1); HRmax, maximal heart rate (bpm). At both stages of the selection, some participants met several (>1) exclusion criteria. Somatic measurements and CPET protocols Request a detailed protocol Body mass was measured with a body composition (BC) analyser (Tanita, MC 718, Japan) with the multifrequency of 5 kHz/50 kHz/250 kHz via the bioimpedance analysis and normal testing mode. The participants’ skin was cleaned with alcohol before placing the electrodes on the skin. Prior to the test, the participants received instructions to refrain from exercising for 2 hr, consume a light meal rich in carbohydrates 2–3 hr beforehand, and maintain hydration by drinking isotonic beverages. Additionally, they were advised to abstain from medications, caffeine, and cigarettes on the day of the test. Running CPET (TE) was performed on a mechanical treadmill (h/p/Cosmos Quasar, Germany). Cycling CPET (CE) was performed on Cyclus-2 (RBM elektronik-automation GmbH, Leipzig, Germany). Hans Rudolph V2 mask (Hans Rudolph, Inc, Shawnee, KS, USA), breath-by-breath method with Cosmed Quark CPET gas exchange analysing device (Cosmed Srl, Rome, Italy), and Quark PFT Suite to Omnia 1.6 software were utilised. The gas analyser device was regularly calibrated with the reference gas (16% O2; 5% CO2) in accordance with the manufacturer’s instructions (Airgas USA, LLC, Plumsteadville, PA, USA). From 2013 to 2021, three Cosmed Quark CPET units were used. HR was measured with the Cosmed torso belt (Cosmed srl, Rome, Italy). [La-]b was measured via enzymatic-amperometric electrochemical technique with Super GL2 analyser (Müller Gerätebau GmbH, Freital, Germany). The [La-]b analyser was regularly calibrated before each measurement series. The 40 m2 indoor, air-conditioned laboratory with 20–22°C temperature and 40–60% humidity, and 100 m ASL provided the same conditions for all BC and CPET. Each CPET began with a 5 min personalised warm-up (walk or easy jog with ‘conversational’ intensity for running, easy pedalling with ‘conversational’ intensity for cycling). Then after the preparation (about 5 min), the continuous progressive step test was conducted. Due to the population diversity (training status), the running test speed started from 7 to 12 km·hr–1 with a 1% treadmill incline. The choice of initial starting speed was determined by the interview and sports results achieved. For example, those running less than 60 min at a distance of 10 km started the test at 7 km/hr, while those running 10 km for less than 35 min started the test at an initial speed of 12 km/hr. The pace increased by 1 km·hr–1 every 2 min with no change in incline. The cycling test began at 60–150 W, depending on the athletes training status. The power increased by 20–30 W every 2 min. It was recommended to maintain a constant cadence of 80–90 (repetition·min–1) during the test. The tests were terminated due to exhaustion: volitional inability to continue the activity or/and VO2 and HR plateau with increasing load or/and observed disturbance of coordination in running or/and inability to maintain the set cadence. Due to the graded protocol used, the cycling power and running speed values have been calculated as a function of time to better reflect the actual level for the test moment being determined (Kuipers et al., 1985). Before the test, after every step, and 3 min after the termination of the effort technician took a 20 µL blood sample from a fingertip. Samples were collected during the test without interrupting the effort. The samples were taken from the initial puncture. The first blood drop was collected into the swab and the second blood drop was drawn for further analysis into the capillary. VO2max was recorded as the highest value (15 s intervals) before the termination of the test. HRmax was recorded as the highest value obtained at the end of the test, without averaging. The anaerobic threshold (AT) was established with the following criteria: (1) common start of VE/VO2 and VE/VCO2 curves, (2) end-tidal partial pressure of oxygen raised constantly with the end-tidal partial pressure of carbon dioxide (Beaver et al., 1986). The was established with the following criteria: (1) PetCO2 must decrease after reaching maximal amount, (2) the presence of fast nonlinear growth in VE (second deflection), (3) the VE/VCO2 ratio achieved minimum and started to rise, and (4) a nonlinear increase in VCO2 versus VO2 (lack of linearity) (Beaver et al., 1986). The [La-]b was estimated for AT and RCP in relation to power or speed (Wiecha et al., 2022). Data analysis Request a detailed protocol Our comprehensive ML approach enables the evaluation of each formula by preliminary variables precision (at the stage of selection), then accuracy (during the model’s building) and recall (in internal validation). Individual CPET results were saved into the Excel file (Microsoft Corporation, Redmond, WA, USA) and a custom-made script was used to generate the database in Excel (Python programming). Further, mean, SD, and 95% confidence intervals (CI) were calculated. The normality of the distribution of the data was examined using the Shapiro-Wilk test and intergroup differences were calculated using the Student’s t-test for independent variables. Three-step variable selection procedures based on random forests were applied using the R package VSURF in RStudio software (R Core Team, Vienna, Austria; version 3.6.4) (Genuer et al., 2016). For each level of measurement (AT, RCP) and their combination (AT+RCP), significant variables were identified separately. The first step was dedicated to eliminate irrelevant variables from the dataset. Second step aimed to select all variables related to the response for interpretation purposes. The third step refined the selection by eliminating redundancy in the set of variables selected by the second step, for prediction purposes (Genuer et al., 2017). Each time for variables selection, the anthropometric variables as in Tables 1–2 and the CPET parameters given in Tables 3–4 from a specific level of measurement (AT; RCP) and their combinations were visible. Table 1 Basic anthropometric characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDAge (years)36.235.6–36.98.4535.935.5–36.38.0535.534.9–36.28.14Height (cm)180.0179.6–180.56.04179.4179.1–179.76.13179.7179.2–180.26.61BM (kg)77.777.0–78.49.3577.777.3–78.19.2977.977.1–78.610.1BMI (kg·m–2)23.923.8–24.12.4324.124.0–24.22.4124.123.9–24.32.56BF (%)15.415.1–15.74.5515.515.3–15.74.5215.415.1–15.84.55FM (kg)12.211.9–12.64.6812.312.1–12.54.6512.311.9–12.74.92FFM (kg)65.565.0–66.06.4365.465.1–65.76.3165.665.1–66.16.86 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 2 Basic anthropometric characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDAge (years)37.336.6–38.09.1337.135.9–38.49.5037.636.5–38.88.46Height (cm)179.9179.4–180.46.27180.1179.2–181.06.96180.2179.4–181.06.13BM (kg)78.878.1–79.69.8079.177.7–80.510.479.878.4–81.310.9BMI (kg·m–2)24.324.1–24.62.6324.424.0–24.72.8024.624.2–25.02.96BF (%)16.415.7–17.14.9916.115.7–16.54.8116.215.5–16.84.87FM (kg)13.312.6–14.15.6613.012.6–13.45.2713.312.5–14.05.85FFM (kg)65.864.9–66.66.2565.865.4–66.36.0666.665.7–67.46.58 BM, body mass; BMI, body mass index; BF, body fat; FM, fat mass; FFM, fat-free mass; CI, 95% confidence interval; SD, standard deviation. Table 3 Cardiopulmonary exercise testing (CPET) characteristics for runners. Variable (unit)Derivation group n=1998Testing group n=666Validation group n=666MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)38.438.1–38.85.0138.538.3–38.74.8838.137.7–38.55.16RERAT0.870.86–0.870.040.870.86–0.870.040.870.86–0.870.04HRAT (beats·min–1)151.5150.8–152.310.3151.0150.6–151.510.8152.0151.2–152.810.8VEAT (L·min–1)79.178.1–80.012.278.377.8–78.912.077.276.3–78.212.0SPEEDAT (km·h–1)11.010.9–11.11.4511.011.0–11.11.3610.910.8–11.01.42LAAT (mmol·L–1)2.082.02–2.140.631.801.76–1.830.622.352.27–2.420.72rVO2RCP (mL·min–1·kg–1)47.547.0–48.05.8847.747.4–48.06.1547.346.8–47.86.16RERRCP1.001.00–1.000.041.001.00–1.000.041.001.00–1.000.03HRRCP (beats·min–1)173.4172.7–174.19.21173.2172.8–173.69.30174.3173.5–175.09.50VERCP (L·min–1)114.7113.5–116.015.9113.9113.1–114.616.7112.7111.4–114.016.2SPEEDRCP (km·h–1)14.013.9–14.11.7714.114.0–14.11.7013.913.8–14.11.75LARCP (mmol·L–1)4.724.63–4.821.044.404.34–4.451.044.814.69–4.931.14rVO2max (mL·min–1·kg–1)53.853.3–54.36.6754.354.0–54.66.9553.853.3–54.37.09 CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; SPEEDAT, velocity at anaerobic threshold; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; SPEEDRCP, velocity at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; rVO2max, maximal oxygen uptake relative to body mass. Table 4 Cardiopulmonary exercise testing (CPET) characteristics for cyclists. Variable (unit)Derivation group n=656Testing group n=219Validation group n=219MeanCISDMeanCISDMeanCISDrVO2AT (mL·min–1·kg–1)33.032.5–33.45.8433.232.4–33.95.6833.732.9–34.55.89RERAT0.870.87–0.870.040.870.87–0.880.040.870.87–0.880.04HRAT CI, 95% confidence interval; SD, standard deviation; rVO2AT, oxygen uptake at anaerobic threshold relative to body mass; RERAT, respiratory exchange ratio at anaerobic threshold; HRAT, heart rate at anaerobic threshold; VEAT, pulmonary ventilation at anaerobic threshold; power at anaerobic threshold relative to body mass; LAAT, blood lactate concentration at anaerobic threshold; rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass; RERRCP, respiratory exchange ratio at respiratory compensation point; HRRCP, heart rate at respiratory compensation point; VERCP, pulmonary ventilation at respiratory compensation point; LARCP, blood lactate concentration at respiratory compensation point; power at respiratory compensation point relative to body mass; rVO2max, maximal oxygen uptake relative to body mass. selection variables were in the further only selected parameters were into multiple linear regression The data for MLR model building were randomly into that is testing, validation and of the a only significant were in the Derived are by the of mean and mean analysis was used to the model’s precision and accuracy during validation and tests to the fulfilment of MLR test the of in MLR test assessment between and test of Each model was examined the and any have not been 2 package in RStudio (R Core Team, Vienna, Austria; version version for and software version were used in was considered as the Results Somatic measurements and CPET results data of the runners models for testing, and validation are in Table while cyclists are in Table The runners of and for testing, and validation the cyclists and differences between of runners and cyclists were in BMI and between testing in all between validation only in CPET results for runners models are in Table 3 and for cyclists in Table Runners in the cohort achieved relative to body mass VO2max of in testing group and in validation group cyclists mean was and for testing, and validation to body mass oxygen uptake at anaerobic threshold in runners for ± ± and ± of in testing, and validation it was ± ± and ± of rVO2max, relative to body mass oxygen uptake at respiratory compensation point in runners for ± ± and ± of for testing, and validation while in cyclists for ± ± and ± of rVO2max, There were no significant differences in values between testing, and validation the runners and cyclists between runners and cyclists results were all significant Prediction models based on AT and RCP Full of MLR prediction models for cyclists are in Table for runners in Table The models prediction performance is as with and for cyclists from for somatic parameters to for RCP equations. For runners from for to for AT and equations. for cyclists models was the for RCP and the highest for For from for AT and to for equation. observed for cyclists was the for RCP in the validation group and the highest for while in runners the for AT and and the highest for The performance of prediction is in Figure Figure 2 Download asset Open asset of prediction for Abbreviations: maximal oxygen anaerobic threshold; RCP, respiratory compensation point; All values are in performance for running while the performance for cycling equations. performance of the prediction model for for for AT and for somatic-only equation. Table 5 VO2max prediction for cyclists. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass power at anaerobic threshold relative to body mass rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass VERCP, pulmonary ventilation at respiratory compensation point BF, body fat BM, body mass Table VO2max prediction for runners. linear regression group group = = = = based on anaerobic threshold; RCP, based on respiratory compensation point; based on somatic variables mean mean maximal oxygen uptake relative to body mass rVO2AT, oxygen uptake at anaerobic threshold relative to body mass SPEEDAT, velocity at anaerobic threshold FFM, fat mass VEAT, pulmonary ventilation at anaerobic threshold HRAT, heart rate at anaerobic threshold BF, body fat rVO2RCP, oxygen uptake at respiratory compensation point relative to body mass SPEEDRCP, velocity at respiratory compensation point Models validation of each model for cyclists is in Table while for runners in Table the performance of our prediction was to that observed in the