Ensemble-based Algorithm Research Articles

Explaining predictors of discharge destination assessed along the patients’ acute stroke journey

Introduction: Accurate prediction of outcome destination at an early stage would help manage patients presenting with stroke. This study assessed the predictive ability of three machine learning (ML) algorithms to predict outcomes at four different stages as well as compared the predictive power of stroke scores.Methods: Patients presenting with acute stroke to the Canberra Hospital between 2015 and 2019 were selected retrospectively. 16 potential predictors and one target variable (discharge destination) were obtained from the notes. k-Nearest Neighbour (kNN) and two ensemble-based classification algorithms (Adaptive Boosting and Bootstrap Aggregation) were employed to predict outcomes. Predictive accuracy was assessed at each of the four stages using both overall and per-class accuracy. The contribution of each variable to the prediction outcome was evaluated by the ensemble-based algorithm and using the Relief feature selection algorithm. Various combinations of stroke scores were tested using the aforementioned models.Results: Of the three ML models, Adaptive Boosting demonstrated the highest accuracy (90%) at Stage 4 in predicting death while the highest overall accuracy (81.7%) was achieved by kNN (k=2/City-block distance). Feature importance analysis has shown that the most important features are the 24-hour Scandinavian Stroke Scale (SSS) and 24-hour National Institutes of Health Stroke Scale (NIHSS) scores, dyslipidaemia, hypertension and premorbid mRS score. For the initial and 24-hour scores, there was a higher correlation (0.93) between SSS scores than for NIHSS scores (0.81). Reducing the overall four scores to InitSSS/24hrNIHSS increased accuracy to 95% in predicting death (Adaptive Boosting) and overall accuracy to 85.4% (kNN). Accuracies at Stage 2 (pre-treatment, 11 predictors) were not far behind those at Stage 4.Conclusion: Our findings suggest that even in the early stages of management, a clinically useful prediction regarding discharge destination can be made. Adaptive Boosting might be the best ML model, especially when it comes to predicting death. The predictors’ importance analysis also showed that dyslipidemia and hypertension contributed to the discharge outcome even more than expected. Further, surprisingly using mixed score systems might also lead to higher prediction accuracies.

An AdaBoost-based algorithm to detect hospital-acquired pressure injury in the presence of conflicting annotations

Hospital-acquired pressure injury is one of the most harmful events in clinical settings. Patients who do not receive early prevention and treatment can experience a significant financial burden and physical trauma. Several hospital-acquired pressure injury prediction algorithms have been developed to tackle this problem, but these models assume a consensus, gold-standard label (i.e., presence of pressure injury or not) is present for all training data. Existing definitions for identifying hospital-acquired pressure injuries are inconsistent due to the lack of high-quality documentation surrounding pressure injuries. To address this issue, we propose in this paper an ensemble-based algorithm that leverages truth inference methods to resolve label inconsistencies between various case definitions and the level of disagreements in annotations. Application of our method to MIMIC-III, a publicly available intensive care unit dataset, gives empirical results that illustrate the promise of learning a prediction model using truth inference-based labels and observed conflict among annotators.

A Feature-Based Approach for Sentiment Quantification Using Machine Learning

Sentiment analysis has been one of the most active research areas in the past decade due to its vast applications. Sentiment quantification, a new research problem in this field, extends sentiment analysis from individual documents to an aggregated collection of documents. Sentiment analysis has been widely researched, but sentiment quantification has drawn less attention despite offering a greater potential to enhance current business intelligence systems. In this research, to perform sentiment quantification, a framework based on feature engineering is proposed to exploit diverse feature sets such as sentiment, content, and part of speech, as well as deep features including word2vec and GloVe. Different machine learning algorithms, including conventional, ensemble learners, and deep learning approaches, have been investigated on standard datasets of SemEval2016, SemEval2017, STS-Gold, and Sanders. The empirical-based results reveal the effectiveness of the proposed feature sets in the process of sentiment quantification when applied to machine learning algorithms. The results also reveal that the ensemble-based algorithm AdaBoost outperforms other conventional machine learning algorithms using a combination of proposed feature sets. The deep learning algorithm RNN, on the other hand, shows optimal results using word embedding-based features. This research has the potential to help diverse applications of sentiment quantification, including polling, trend analysis, automatic summarization, and rumor or fake news detection.

Evaluating the relevance of sequence conservation in the prediction of pathogenic missense variants.

Evolutionary information is the primary tool for detecting functional conservation in nucleic acid and protein. This information has been extensively used to predict structure, interactions and functions in macromolecules. Pathogenicity prediction models rely on multiple sequence alignment information at different levels. However, most accurate genome-wide variant deleteriousness ranking algorithms consider different features to assess the impact of variants. Here, we analyze three different ways of extracting evolutionary information from sequence alignments in the context of pathogenicity predictions at DNA and protein levels. We showed that protein sequence-based information is slightly more informative in the annotation of Clinvar missense variants than those obtained at the DNA level. Furthermore, to achieve the performance of state-of-the-art methods, such as CADD and REVEL, the conservation of reference and variant, encoded as frequencies of reference/alternate alleles or wild-type/mutant residues, should be included. Our results on a large set of missense variants show that a basic method based on three input features derived from the protein sequence profile performs similarly to the CADD algorithm which uses hundreds of genomic features. As expected, our method results in ~ 3% lower area under the receiver-operating characteristic curve (AUC). When compared with an ensemble-based algorithm (REVEL). Nevertheless, the combination of predictions of multiple methods can help to identify more reliable predictions. These observations indicate that for missense variants, evolutionary information, when properly encoded, plays the primary role in ranking pathogenicity.

Ensemble-based adaptive soft sensor for fault-tolerant biomass monitoring.

The accuracy and precision of soft sensors depend strongly on the reliability of underlying model inputs. These inputs (particularly readings of hardware sensors) are frequently subject to faults. This study aims to develop an adaptive soft sensor capable of reliable and robust biomass concentration predictions in the presence of faulty model inputs for a Pichia pastoris bioprocess. Hence, three soft sensor submodels were developed based on three independent model inputs (base addition, CO2 production, and mid‐infrared spectrum). An ensemble‐based algorithm combined the submodels to form an ensemble model, that is, an adaptive soft sensor, to achieve fault‐tolerant prediction. The algorithm's basic steps are as follows: the initial determination of submodel reliability is followed by selecting appropriate submodels to generate a reliable prediction via variance‐based weighting of the submodels. The adaptive soft sensor demonstrated high robustness and accuracy in biomass prediction in the presence of multiple simulated sensor faults (RMSE = 0.43 g L−1) and multiple real sensor faults (RMSE = 0.70 g L−1).

Ensemble-Based Electrical Resistivity Tomography with Data and Model Space Compression

Inversion of electrical resistivity tomography (ERT) data is an ill-posed problem that is usually solved through deterministic gradient-based methods. These methods guarantee a fast convergence but hinder accurate assessments of model uncertainties. On the contrary, Markov Chain Monte Carlo (MCMC) algorithms can be employed for accurate uncertainty appraisals, but they remain a formidable computational task due to the many forward model evaluations needed to converge. We present an alternative approach to ERT that not only provides a best-fitting resistivity model but also gives an estimate of the uncertainties affecting the inverse solution. More specifically, the implemented method aims to provide multiple realizations of the resistivity values in the subsurface by iteratively updating an initial ensemble of models based on the difference between the predicted and measured apparent resistivity pseudosections. The initial ensemble is generated using a geostatistical method under the assumption of log-Gaussian distributed resistivity values and a Gaussian variogram model. A finite-element code constitutes the forward operator that maps the resistivity values onto the associated apparent resistivity pseudosection. The optimization procedure is driven by the ensemble smoother with multiple data assimilation, an iterative ensemble-based algorithm that performs a Bayesian updating step at each iteration. The main advantages of the proposed approach are that it can be applied to nonlinear inverse problems, while also providing an ensemble of models from which the uncertainty on the recovered solution can be inferred. The ill-conditioning of the inversion procedure is decreased through a discrete cosine transform reparameterization of both data and model spaces. The implemented method is first validated on synthetic data and then applied to field data. We also compare the proposed method with a deterministic least-square inversion, and with an MCMC algorithm. We show that the ensemble-based inversion estimates resistivity models and associated uncertainties comparable to those yielded by a much more computationally intensive MCMC sampling.

Behavior of the iterative ensemble-based variational method in nonlinear problems

Abstract. The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

A novel stacked generalization ensemble-based hybrid LGBM-XGB-MLP model for Short-Term Load Forecasting

This paper proposes an effective computing framework for Short-Term Load Forecasting (STLF). The proposed technique copes with the stochastic variations of the load demand using a stacked generalization approach. This approach combines three models, namely, Light Gradient Boosting Machine (LGBM), eXtreme Gradient Boosting machine (XGB), and Multi-Layer Perceptron (MLP). The inner mechanism of Stacked XGB-LGBM-MLP model consists of generating a meta-data from XGB and LGBM models to compute the final predictions using MLP network. The performance of the proposed Stacked XGB-LGBM-MLP model is validated using two datasets from different locations: Malaysia and New England. The main contributions of this paper are: 1) A novel stacking ensemble-based algorithm is proposed; 2) An effective STLF technique is introduced; 3) A critical multi-study analysis for hyperparameter optimization with five techniques is comprehensively performed; 4) A performance comparative study using two datasets and reference models is conducted. Several case studies have been carried out to prove the performance superiority of the proposed model compared to both existing benchmark techniques and hybrid models.

Automated release rate inversion and plume bias correction for atmospheric radionuclide leaks: A robust and general remediation to imperfect radionuclide transport modeling

The release rate is vital in assessing the international environmental risk of atmospheric radionuclide leaks, and it usually can only be obtained through inversion. However, such inversion is vulnerable to the inevitable plume biases in radionuclide transport modeling, leading to inaccurate estimates and risk assessment. This paper describes an automated method that estimates the release rate while comprehensively correcting plume biases, including both the plume range and transport pattern. The spatial correlation of predictions is used to simplify the difficult task of direct plume adjustment to that of tuning the predictions inside a correlation-adjusted plume. An ensemble-based algorithm is proposed to automatically calculate the spatial correlation. The proposed method is validated using two radionuclide transport models with mild and severe plume biases and data from two wind tunnel experiments, and its performance is compared with that of the standard approach and a recent state-of-the-art method. The results demonstrate that our method corrects the plume biases with high accuracy (Pearson's Correlation Coefficient = 1.0000, Normalized Mean Square Error ≤ 1.03 × 10−3) and reduces the estimation error by nearly two orders of magnitude at best. The proposed approach achieves near-optimal performance with fully automated parameterization, keeping the lowest error levels in our validation cases for various measurement sets.

Ensemble-Based Algorithm for Synchrophasor Data Anomaly Detection

With the advent of phasor measurement units (PMUs), high resolution synchronized phasor measurements enables real time system monitoring and control. PMUs transmit data to local controllers in substations and phasor data concentrators for system wide monitoring and control application in the control center. They provide real-time phasor data for critical power system applications such as remedial action schemes, oscillation detection, and state estimation. The quality of phasor data from PMUs is critical for smart grid applications. Several methods are developed to detect anomalies in time series data, tailored for PMU data analysis. Nevertheless, applying stand alone methods (with fixed parameters) takes great tuning effort, and does not always achieve high accuracy. In this paper, we adopt an unsupervised ensemble learning approach to develop fast, scalable bad data/event detection for PMU data. The ensemble method invokes a set of base detectors to generate anomaly scores of the PMU data, and makes decisions by aggregating the scores from each detector. We develop two algorithms: 1) a learning algorithm that trains the ensemble model and 2) an online algorithm that infers the anomaly scores with the ensemble model over PMU data streams. The proposed method provides flag for data anomalies and triggers further analysis to differentiate between events and bad data. Using both simulated and real-world PMU data, we show that our ensemble model can be efficiently trained, can achieve high accuracy in detecting diversified errors/events, and outperforms its counterparts that use single standalone detection method.

Stochastic Simplex Approximate Gradient for Robust Life-Cycle Production Optimization: Applied to Brugge Field

In oil and gas industry, production optimization is a viable technique to maximize the recovery or the net present value (NPV). Robust optimization is one type of production optimization techniques where the geological uncertainty of reservoir is considered. When well operating conditions, e.g., well flow rates settings of inflow control valves and bottom-hole pressures, are the optimization variables, ensemble-based optimization (EnOpt) is the most popular ensemble-based algorithm for the robust life-cycle production optimization. Recently, a superior algorithm, stochastic simplex approximate gradient (StoSAG), was proposed. Fonseca and co-workers (2016, A Stochastic Simplex Approximate Gradient (StoSAG) for Optimization Under Uncertainty, Int. J. Numer. Methods Eng., 109(13), pp. 1756–1776) provided a theoretical argument on the superiority of StoSAG over EnOpt. However, it has not drawn significant attention in the reservoir optimization community. The purpose of this study is to provide a refined theoretical discussion on why StoSAG is generally superior to EnOpt and to provide a reasonable example (Brugge field) where StoSAG generates estimates of optimal well operating conditions that give a life-cycle NPV significantly higher than the NPV obtained from EnOpt.

Structured Clanning-Based Ensemble Optimization Algorithm: A Novel Approach for Solving Complex Numerical Problems

In this paper, a novel swarm intelligence-based ensemble metaheuristic optimization algorithm, called Structured Clanning-based Ensemble Optimization, is proposed for solving complex numerical optimization problems. The proposed algorithm is inspired by the complex and diversified behaviour present within the fission-fusion-based social structure of the elephant society. The population of elephants can consist of various groups with relationship between individuals ranging from mother-child bond, bond groups, independent males, and strangers. The algorithm tries to model this individualistic behaviour to formulate an ensemble-based optimization algorithm. To test the efficiency and utility of the proposed algorithm, various benchmark functions of different geometric properties are used. The algorithm performance on these test benchmarks is compared to various state-of-the-art optimization algorithms. Experiments clearly showcase the success of the proposed algorithm in optimizing the benchmark functions to better values.

Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.

An iterative boosting-based ensemble for streaming data classification

Among the many issues related to data stream applications, those involved in predictive tasks such as classification and regression, play a significant role in Machine Learning (ML). The so-called ensemble-based approaches have characteristics that can be appealing to data stream applications, such as easy updating and high flexibility. In spite of that, some of the current approaches consider unsuitable ways of updating the ensemble along with the continuous stream processing, such as growing it indefinitely or deleting all its base learners when trying to overcome a concept drift. Such inadequate actions interfere with two inherent characteristics of data streams namely, its possible infinite length and its need for prompt responses. In this paper, a new ensemble-based algorithm, suitable for classification tasks, is proposed. It relies on applying boosting to new batches of data aiming at maintaining the ensemble by adding a certain number of base learners, which is established as a function of the current ensemble accuracy rate. The updating mechanism enhances the model flexibility, allowing the ensemble to gather knowledge fast to quickly overcome high error rates, due to concept drift, while maintaining satisfactory results by slowing down the updating rate in stable concepts. Results comparing the proposed ensemble-based algorithm against eight other ensembles found in the literature show that the proposed algorithm is very competitive when dealing with data stream classification.

Scalable Robust Implementation of Reliable Streaming (SRIRS) with Tristate aware Quality of Service

In today's rapidly developing technological world, video streaming plays a vital role in mobile devices where the quality of streaming is significant. Quality of video streaming primarily depends on factors including: device's features, available bandwidth, and video codec. Existing video streaming techniques do not provide smooth streaming since the streaming quality depends only on estimating the available bandwidth ignoring the device's static and dynamic features. This research work concentrates on hybrid features of device, i.e. static and dynamic features and also the network features for enhancing video streaming quality. This is achieved by using the following three components (Tristate): Static grade point calculator, energy manager and hybrid bandwidth estimator for estimating quality states respectively. Using the statistical features extracted from the three components, the state machine decision maker with novel ensemble-based adaptive learning algorithm decides on the quality of the video to be streamed. Main objective of this work is to provide scalable, robust video streaming with the services of Tristate components and the development of a novel ensemble-based adaptive learning algorithm to achieve quality of service. This proposed technique is tested with cloud open stack platform under various network conditions like motion, driving and train. The experimental results are compared with those of the existing techniques and the results indicate that the proposed work outperforms other schemes in terms of metrics like PSNR, Bandwidth Estimation, and Smoothness in streaming, Power Consumption Rate, Freeze time and computational time.

A critical analysis of computational protein design with sparse residue interaction graphs.

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies.

Ensemble-based algorithm for error reduction in hydraulics in the context of flood forecasting

Over the last few years, a collaborative work between CERFACS, LNHE (EDF R&D), SCHAPI and CE-REMA resulted in the implementation of a Data Assimilation (DA) method on top of MASCARET in the framework of real-time forecasting. This prototype was based on a simplified Kalman filter where the description of the background error covariances is prescribed based on off-line climatology constant over time. This approach showed promising results on the Adour and Marne catchments as it improves the forecast skills of the hydraulic model using water level and discharge in-situ observations. An ensemble-based DA algorithm has recently been implemented to improve the modelling of the background error covariance matrix used to distribute the correction to the water level and discharge states when observations are assimilated from observation points to the entire state. It was demonstrated that the flow dependent description of the background error covariances with the EnKF algorithm leads to a more realistic correction of the hydraulic state with significant impact of the hydraulic network characteristics

Semi-Supervised Multi-View Learning for Gene Network Reconstruction.

The task of gene regulatory network reconstruction from high-throughput data is receiving increasing attention in recent years. As a consequence, many inference methods for solving this task have been proposed in the literature. It has been recently observed, however, that no single inference method performs optimally across all datasets. It has also been shown that the integration of predictions from multiple inference methods is more robust and shows high performance across diverse datasets. Inspired by this research, in this paper, we propose a machine learning solution which learns to combine predictions from multiple inference methods. While this approach adds additional complexity to the inference process, we expect it would also carry substantial benefits. These would come from the automatic adaptation to patterns on the outputs of individual inference methods, so that it is possible to identify regulatory interactions more reliably when these patterns occur. This article demonstrates the benefits (in terms of accuracy of the reconstructed networks) of the proposed method, which exploits an iterative, semi-supervised ensemble-based algorithm. The algorithm learns to combine the interactions predicted by many different inference methods in the multi-view learning setting. The empirical evaluation of the proposed algorithm on a prokaryotic model organism (E. coli) and on a eukaryotic model organism (S. cerevisiae) clearly shows improved performance over the state of the art methods. The results indicate that gene regulatory network reconstruction for the real datasets is more difficult for S. cerevisiae than for E. coli. The software, all the datasets used in the experiments and all the results are available for download at the following link: http://figshare.com/articles/Semi_supervised_Multi_View_Learning_for_Gene_Network_Reconstruction/1604827.

Improved Detection of Invasive Pulmonary Aspergillosis Arising during Leukemia Treatment Using a Panel of Host Response Proteins and Fungal Antigens.

Invasive pulmonary aspergillosis (IPA) is an opportunistic fungal infection in patients undergoing chemotherapy for hematological malignancy, hematopoietic stem cell transplant, or other forms of immunosuppression. In this group, Aspergillus infections account for the majority of deaths due to mold pathogens. Although early detection is associated with improved outcomes, current diagnostic regimens lack sensitivity and specificity. Patients undergoing chemotherapy, stem cell transplantation and lung transplantation were enrolled in a multi-site prospective observational trial. Proven and probable IPA cases and matched controls were subjected to discovery proteomics analyses using a biofluid analysis platform, fractionating plasma into reproducible protein and peptide pools. From 556 spots identified by 2D gel electrophoresis, 66 differentially expressed post-translationally modified plasma proteins were identified in the leukemic subgroup only. This protein group was rich in complement components, acute-phase reactants and coagulation factors. Low molecular weight peptides corresponding to abundant plasma proteins were identified. A candidate marker panel of host response (9 plasma proteins, 4 peptides), fungal polysaccharides (galactomannan), and cell wall components (β-D glucan) were selected by statistical filtering for patients with leukemia as a primary underlying diagnosis. Quantitative measurements were developed to qualify the differential expression of the candidate host response proteins using selective reaction monitoring mass spectrometry assays, and then applied to a separate cohort of 57 patients with leukemia. In this verification cohort, a machine learning ensemble-based algorithm, generalized pathseeker (GPS) produced a greater case classification accuracy than galactomannan (GM) or host proteins alone. In conclusion, Integration of host response proteins with GM improves the diagnostic detection of probable IPA in patients undergoing treatment for hematologic malignancy. Upon further validation, early detection of probable IPA in leukemia treatment will provide opportunities for earlier interventions and interventional clinical trials.

A SVD-based ensemble projection algorithm for calculating the conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation (CNOP) is an extension of the linear singular vector technique in the nonlinear regime. It represents the initial perturbation that is subjected to a given physical constraint, and results in the largest nonlinear evolution at the prediction time. CNOP-type errors play an important role in the predictability of weather and climate. Generally, when calculating CNOP in a complicated numerical model, we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space. The adjoint technique is widely used to calculate the gradient of the objective function. However, it is difficult and cumbersome to construct the adjoint model of a complicated numerical model, which imposes a limitation on the application of CNOP. Based on previous research, this study proposes a new ensemble projection algorithm based on singular vector decomposition (SVD). The new algorithm avoids the localization procedure of previous ensemble projection algorithms, and overcomes the uncertainty caused by choosing the localization radius empirically. The new algorithm is applied to calculate the CNOP in an intermediate forecasting model. The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm, and retains the general spatial characteristics of the latter. Hence, the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.