Rand Index Research Articles

MCluster-VAEs: An end-to-end variational deep learning-based clustering method for subtype discovery using multi-omics data

The discovery of cancer subtypes based on unsupervised clustering helps in providing a precise diagnosis, guide treatment, and improve patients’ prognoses. Instead of single-omics data, multi-omics data can improve the clustering performance because it obtains a comprehensive landscape for understanding biological systems and mechanisms. However, heterogeneous data from multiple sources raises high complexity and different kinds of noise, which are detrimental to the extraction of clustering information. We propose an end-to-end deep learning based method, called Multi-omics Clustering Variational Autoencoders (MCluster-VAEs), that can extract cluster-friendly representations on multi-omics data. First, a unified network architecture with an attention mechanism was developed for accurately modeling multi-omics data. Then, using a novel objective function built from the Variational Bayes technique, the model was trained to effectively obtain the posterior estimation of the clustering assignments. Compared with 12 other state-of-the-art multi-omics clustering methods, MCluster-VAEs achieved an outstanding performance on benchmark datasets from the TCGA database. On the Pan Cancer dataset, MCluster-VAEs achieved an adjusted Rand index of approximately 0.78 for cancer category recognition, an increase of more than 18% compared with other methods. Furthermore, a survival analysis and clinical parameter enrichment tests conducted on 10 cancer datasets demonstrated that MCluster-VAEs provides comparable and even better results than many common integrative approaches. These results demonstrate that MCluster-VAEs are a powerful new tool for dissecting complex multi-omics relationships and providing new insights for cancer subtype discovery.

Mining regular behaviors based on spatiotemporal trajectory multi‐dimensional features

In the military and civilian surveillance domain, it is of great significance to mine regular behaviours of targets for situation awareness and command decision support. Most of the existing trajectory clustering algorithms only consider the similarity of spatial position of the trajectory, without sufficient multi-dimensional information such as time, course and velocity. Some approaches based on information fusion take these multi-dimensional information into account, but the features with different dimensions fused by weight coefficients are not robust and universal for different scenarios. In this paper, a regular behaviour mining method based on spatiotemporal trajectory multi-dimensional features and density clustering is proposed. Firstly, multi-dimensional Hausdorff similarity is defined to measure spatiotemporal trajectory from different feature dimensionalities. Different from methods based on information fusion, the proposed method defines trajectory density in feature similarity of different dimensions and adaptively determines parameters according to feature distribution in different dimensions. Experimental results in simulated and radar measured trajectory data show that the proposed method can be accurate and robust in clustering evaluation indexes such as Purity, Precision, Recall and Rand Index from different scenarios, which has a good application prospect in intelligent surveillance tasks.

Distributed denial of service attack detection in E-government cloud via data clustering

One of the main essential security issues of cloud computing is the detection and prevention of network intrusions. The gaps in the network directly affect the security of the cloud as it is the foundation of it. Attacks in the cloud are launched either by compromised nodes of the network outside of the cloud or by virtual machines (VMs) within the cloud network. So, monitoring both external and internal traffic of the cloud network is of great importance. In this paper, a machine learning method performing accurate clustering of network data to detect DDoS attacks has been proposed. The method uses a feature selection technique to increase the efficiency of data clustering. To provide the feature selection the PCA algorithm has been used. For the dataset formed on selected features, the DBSCAN (density-based spatial clustering of applications with noise), Agglomerative Clustering, and k-means algorithms are applied. In the experiment, the clustering results of the methods using fewer features were higher on all metrics than the clustering results of the methods using all the features. Сompared to the standard algorithms, the PCA + DBSCAN, PCA + Agglomerative, and PCA + k-means algorithms obtained higher values on the Adjusted Rand Index metric and reached 0.8989, 0.9130, 0.9094 values, respectively. The effectiveness of the approach also was evaluated on the other clustering metrics and obtained high results. The proposed system can be installed in both internal and external cloud infrastructure. This allows, to detect attacks on the external cloud network, as well as on the internal physical network or in the virtual network between hypervisors. DDoS attacks detection system.

Visualization of emergency department clinical data for interpretable patient phenotyping

Visual summarization of clinical data collected on patients contained within the electronic health record (EHR) may enable precise and rapid triage at the time of patient presentation to an emergency department (ED). The triage process is critical in the appropriate allocation of resources and in anticipating eventual patient disposition, typically admission to the hospital or discharge home. EHR data are high-dimensional and complex, but offer the opportunity to discover and characterize underlying data-driven patient phenotypes. Data-driven phenotypes are intended to relieve reliance on weak labels like diagnosis codes and to aid in identifying populations of existing patients that are most similar to a specific patient. These phenotypes will enable improved, personalized therapeutic decision making and prognostication. In this work, we focus on the challenge of two-dimensional patient projections. A low dimensional embedding offers visual interpretability lost in higher dimensions. While linear dimensionality reduction techniques such as principal component analysis are often used towards this aim, they are insufficient to describe the variance of patient data. This linear reduction does not account for higher order, non-linear interactions of variables. In this work, we employ the newly-described non-linear embedding technique called uniform manifold approximation and projection (UMAP). UMAP seeks to capture both local and global structures in high-dimensional data. We then use Gaussian mixture models to identify clusters in the embedded data and use the adjusted Rand index (ARI) to establish stability in the discovery of these clusters. This technique is applied to five common clinical chief complaints from a real-world ED EHR dataset, describing the emergent properties of discovered clusters. We observe clinically-relevant cluster attributes, suggesting that visual embeddings of EHR data using non-linear dimensionality reduction is a promising approach to reveal data-driven patient phenotypes. In the five chief complaints, we find between 2 and 6 clusters, with the peak mean pairwise ARI between subsequent training iterations to range from 0.35 to 0.74.

The Initialization of Flexible K-Medoids Partitioning Method Using a Combination of Deviation and Sum of Variable Values

This research proposed a new algorithm for clustering datasets using the Flexible K-Medoids Partitioning Method. The procedure is divided into two phases, selecting the initial medoids and determining the partitioned dataset. The initial medoids are selected based on the block representation of a combination of the sum and deviation of the variable values. The relative positions of the objects will be separated when the sum of the values of the p variables is different even though these objects have the same variance. The objects are selected flexibly from each block as the initial medoids to construct the initial groups. This process ensures that any identical objects will be in the same group. The candidate of final medoids is determined randomly by selecting objects from each initial group. Then, the final medoids were identified based on the combination of objects that produces the minimum value of the total deviation within the cluster. The proposed method overcomes the empty group that may arise in a simple and fast k-medoids algorithm. In addition, it overcomes identical objects in the different groups that may occur in the initialization of the simple k-medoids algorithm. Furthermore, the artificial data and six real datasets, namely iris, ionosphere, soybean small, primary tumor, heart disease case 1 and zoo were used to evaluate this method, and the results were compared with other algorithms based on the initial and final groups' performance. The experiment results showed that the proposed method ensures that no initial groups are empty. For real datasets, the adjusted Rand index and clustering accuracy of the final groups of the new algorithm outperforms the other methods.

CLUSTERING SURGEMES USING PROTOTYPES FROM ROBOTIC KINEMATIC INFORMATION

Training a surgeon to be skilled and competent to perform a given surgical procedure is essential in providing a high quality of care and reducing the risk of complications. However, existing training techniques limit us from conducting in-depth analyses of surgical motions to evaluate these skills accurately. We develop a method to identify the gestures by applying unsupervised methods to cluster the surgical activities learned directly from raw kinematic data. We design an unsupervised method to determine the surgical motions in a Suturing procedure based on predefined surgical gestures. The first step is to find the prototypes by clustering the surgemes of the expert surgeon from all the same expert trials. Then, we map the other surgeons surgemes to the nearest representative of the prototypes and report the clustering accuracy by employing the rand index technique. We utilize four techniques in our proposed unsupervised approach for gesture clustering based on Hierarchical and FCM algorithms. In addition, we highlight the advantages of representing time series data before clustering in terms of computation time saving and system complexity reduction, respectively.

Evaluation and Comparison of Spatial Clustering for Solar Irradiance Time Series

This work exposes an innovative clustering method of solar radiation stations, using static and dynamic parameters, based on multi-criteria analysis for future objectives to make the forecasting of the solar resource easier. The innovation relies on a characterization of solar irradiation from both a quantitative point of view and a qualitative one (variability of the intermittent sources). Each of the 76 Spanish stations studied is firstly characterized by static parameters of solar radiation distributions (mean, standard deviation, skewness, and kurtosis) and then by dynamic ones (Hurst exponent and forecastability coefficient, which is a new concept to characterize the “difficulty” to predict the solar radiation intermittence) that are rarely used, or even never used previously, in such a study. A redundancy analysis shows that, among all the explanatory variables used, three are essential and sufficient to characterize the solar irradiation behavior of each site; thus, in accordance with the principle of parsimony, only the mean and the two dynamic parameters are used. Four clustering methods were applied to identify geographical areas with similar solar irradiation characteristics at a half-an-hour time step: hierarchical, k-means, k-medoids, and spectral cluster. The achieved clusters are compared with each other and with an updated Köppen–Geiger climate classification. The relationship between clusters is analyzed according to the Rand and Jaccard Indexes. For both cases (five and three classes), the hierarchical clustering algorithm is the closest to the Köppen classification. An evaluation of the clustering algorithms’ performance shows no interest in implementing k-means and spectral clustering simultaneously since the results are similar by more than 90% for three and five classes. The recommendations for operating a solar radiation clustering are to use k-means or hierarchical clustering based on mean, Hurst exponent, and forecastability parameters.

Unsupervised segmentation of hyperspectral remote sensing images with superpixels

In this paper, we propose an unsupervised method for hyperspectral remote sensing image segmentation. The method exploits the mean-shift clustering algorithm that takes as input a preliminary hyperspectral superpixels segmentation together with the spectral pixel information. The proposed method does not require the number of segmentation classes as input parameter, and it does not exploit any a-priori knowledge about the type of land-cover or land-use to be segmented (e.g. water, vegetation, building etc.). Experiments on Salinas, SalinasA, Pavia Center and Pavia University datasets are carried out. Performance are measured in terms of normalized mutual information, adjusted Rand index and F1-score. Results demonstrate the validity of the proposed method in comparison with the state of the art.

Evaluation of effect based on different typing methods in Escherichia coli

Objective: To evaluate the typing and clinical application effect based on clustered regularly interspaced short palindromic repeats (CRISPRs), serotype, and Multilocus Sequence Typing (MLST). Methods: The spacers, serotype and sequence type (ST) were obtained with CRISPRsFinder, SeroTypeFinder and MLST. PCR was used to amplify the CRISPRs, and the spacers were used to predict serotype and ST, then comparing with the serotype and ST. Results: We defined the I-E CRISPR/Cas as CT-Ⅰ, I-F CRISPR/Cas as CT-Ⅱ, and only CRISPR3-4 as CT-Ⅲ. We designated each unique arrangement spacer profile as a unique CRISPRs type. A total of 79 CT types, 76 serotypes, and 66 STs were identified. The CRISPRs typing was the most discriminating, with the Simpson index of 0.936, having the highest correlation with serology with the adjusted Rand index of 0.908. The CRISPRs type could divide the same serotype (ST) into two subtypes [O157∶H7(ST11), O104∶H4(ST678), and O26∶H11(ST21)]. The detection rates of CRISPR1, CRISPR2, CRISPR3, CRISPR4, and CRISPR3-4 were 81.1%, 94.5%, 1.4%, 1.4%, and 4.6%, with the accuracy rate of 95.0% and 100.0% according to the spacers to forecast O157∶H7 (ST11) and ST131. Conclusion: Based on the CRISPRs spacer, this method can be used as an essential molecular typing for E.coli, as it presents a good typing and clinical application effect.

Learning discriminative and structural samples for rare cell types with deep generative model.

Cell types (subpopulations) serve as bio-markers for the diagnosis and therapy of complex diseases, and single-cell RNA-sequencing (scRNA-seq) measures expression of genes at cell level, paving the way for the identification of cell types. Although great efforts have been devoted to this issue, it remains challenging to identify rare cell types in scRNA-seq data because of the few-shot problem, lack of interpretability and separation of generating samples and clustering of cells. To attack these issues, a novel deep generative model for leveraging the small samples of cells (aka scLDS2) is proposed by precisely estimating the distribution of different cells, which discriminate the rare and non-rare cell types with adversarial learning. Specifically, to enhance interpretability of samples, scLDS2 generates the sparse faked samples of cells with $\ell _1$-norm, where the relations among cells are learned, facilitating the identification of cell types. Furthermore, scLDS2 directly obtains cell types from the generated samples by learning the block structure such that cells belonging to the same types are similar to each other with the nuclear-norm. scLDS2 joins the generation of samples, classification of the generated and truth samples for cells and feature extraction into a unified generative framework, which transforms the rare cell types detection problem into a classification problem, paving the way for the identification of cell types with joint learning. The experimental results on 20 datasets demonstrate that scLDS2 significantly outperforms 17 state-of-the-art methods in terms of various measurements with 25.12% improvement in adjusted rand index on average, providing an effective strategy for scRNA-seq data with rare cell types. (The software is coded using python, and is freely available for academic https://github.com/xkmaxidian/scLDS2).

Fuzzy Cluster Analysis for Interval Data Based on the Overlap Distance

This article builds the fuzzy clustering algorithm for interval data (FCAI). In the proposed algorithm, we use the overlap distance as a criterion to cluster for interval data. The FCAI can determine not only the suitable number of clusters, the elements in each cluster but also the probability of assigning the elements to the established clusters at the same time. In addition, we also consider the convergence of the proposed algorithm by the theory and illustrated it by the numerical examples. The FCAI is applied well in image recognition, a problem with many challenges nowadays. Using the Grey Level Co-occurrence matrices (GLCMs), we propose a novel texture extraction approach to generate featured intervals. The complex computations of the FCAI can be performed conveniently and efficiently by the established Matlab program. We utilize the corrected rand indexes (CR) to find the suitable number of clusters while a partition entropy (PE) and partition coefficients (PC) are applied to argue the quality of fuzzy clusters. As a result, the experiments on the data sets having different characteristics and elements show the reasonableness of the proposed algorithm and its advantages in comparison to the existing ones. Regarding our best knowledge, it has also shown potential in the real application of this study.

SECEDO: SNV-based subclone detection using ultra-low coverage single-cell DNA sequencing.

MotivationSeveral recently developed single-cell DNA sequencing technologies enable whole-genome sequencing of thousands of cells. However, the ultra-low coverage of the sequenced data (<0.05× per cell) mostly limits their usage to the identification of copy number alterations in multi-megabase segments. Many tumors are not copy number-driven, and thus single-nucleotide variant (SNV)-based subclone detection may contribute to a more comprehensive view on intra-tumor heterogeneity. Due to the low coverage of the data, the identification of SNVs is only possible when superimposing the sequenced genomes of hundreds of genetically similar cells. Thus, we have developed a new approach to efficiently cluster tumor cells based on a Bayesian filtering approach of relevant loci and exploiting read overlap and phasing.ResultsWe developed Single Cell Data Tumor Clusterer (SECEDO, lat. ‘to separate’), a new method to cluster tumor cells based solely on SNVs, inferred on ultra-low coverage single-cell DNA sequencing data. We applied SECEDO to a synthetic dataset simulating 7250 cells and eight tumor subclones from a single patient and were able to accurately reconstruct the clonal composition, detecting 92.11% of the somatic SNVs, with the smallest clusters representing only 6.9% of the total population. When applied to five real single-cell sequencing datasets from a breast cancer patient, each consisting of 2000 cells, SECEDO was able to recover the major clonal composition in each dataset at the original coverage of 0.03×, achieving an Adjusted Rand Index (ARI) score of 0.6. The current state-of-the-art SNV-based clustering method achieved an ARI score of 0, even after merging cells to create higher coverage data (factor 10 increase), and was only able to match SECEDOs performance when pooling data from all five datasets, in addition to artificially increasing the sequencing coverage by a factor of 7. Variant calling on the resulting clusters recovered more than twice as many SNVs as would have been detected if calling on all cells together. Further, the allelic ratio of the called SNVs on each subcluster was more than double relative to the allelic ratio of the SNVs called without clustering, thus demonstrating that calling variants on subclones, in addition to both increasing sensitivity of SNV detection and attaching SNVs to subclones, significantly increases the confidence of the called variants.Availability and implementationSECEDO is implemented in C++ and is publicly available at https://github.com/ratschlab/secedo. Instructions to download the data and the evaluation code to reproduce the findings in this paper are available at: https://github.com/ratschlab/secedo-evaluation. The code and data of the submitted version are archived at: https://doi.org/10.5281/zenodo.6516955.Supplementary information Supplementary data are available at Bioinformatics online.

Understanding the Adjusted Rand Index and Other Partition Comparison Indices Based on Counting Object Pairs

In unsupervised machine learning, agreement between partitions is commonly assessed with so-called external validity indices. Researchers tend to use and report indices that quantify agreement between two partitions for all clusters simultaneously. Commonly used examples are the Rand index and the adjusted Rand index. Since these overall measures give a general notion of what is going on, their values are usually hard to interpret. The goal of this study is to provide a thorough understanding of the adjusted Rand index as well as many other partition comparison indices based on counting object pairs. It is shown that many overall indices based on the pair-counting approach can be decomposed into indices that reflect the degree of agreement on the level of individual clusters. The decompositions (1) show that the overall indices can be interpreted as summary statistics of the agreement on the cluster level, (2) specify how these overall indices are related to the indices for individual clusters, and (3) show that the overall indices are affected by cluster size imbalance: if cluster sizes are unbalanced these overall measures will primarily reflect the degree of agreement between the partitions on the large clusters, and will provide much less information on the agreement on smaller clusters. Furthermore, the value of Rand-like indices is determined to a large extent by the number of pairs of objects that are not joined in either of the partitions.

Improved K‐means algorithm for clustering non‐spherical data

AbstractAs one of the commonly used data mining algorithms, K‐means has the advantage of fast clustering speed, but the disadvantage is that it is less effective for clustering non‐spherical data. An improved K‐means algorithm (IK‐means) is proposed to enhance clustering efficiency for non‐spherical data. The original dataset is clustered into a relatively larger number of high‐density sub‐clusters, and the final result is obtained by merging connected sub‐clusters respectively. The connectivity among sub‐clusters is evaluated by the sub‐clusters density and the nearest distance class between sub‐clusters. By testing on University of California, Irvine(UCI) datasets and several other artificial simulation datasets, the comparison of proposed IK‐means algorithm against DBSCAN, KGFCM shows its clustering capability for data of arbitrary shape. The clustering Adjusted Rand Index (ARI) value for 72,000 sizes data is 24% higher than DBSCAN, and 95.2% higher than KGFCM. For larger datasets, the IK‐means algorithm is faster than DBSCAN and KGFCM.

Similarity-based Partitions on Pre-ordered Sets

Objective: To determine partitions of subsets where a preorder relation and a similarity relation coexist. Each partition-set represents a class of elements that reflects the variety of the whole set, so the similarity relation can be considered to reduce the size of large sets and to handle them more easily. We look at the minimal partitions originated by the similarity relation and compare them using well-established methods. Methods: A precise definition of the notion of similarity is proposed by unifying two pieces of relevant literature. The similarity-based partitions are mainly compared by using a method called the Rand index and a new method for the subset similarity index. Results: Looking at the minimal partitions originated by the similarity relation and comparing them using well-established methods, we observed that from an aseptic point of view, there are no essential differences between any of them. Conclusion: Comparing partitions produced by different methods is an important issue in clustering when comparing results obtained using different methods, parameters or initializations. When the sole objective is the variety offered by the sets in question, any smallest similarity-based partitions can be used to handle large sets. If it becomes necessary to consider the quality of the elements contained in those large sets, then one of them must be chosen specifically.

The impact of public health emergency governance based on artificial intelligence

Abstract To optimize the data clustering effect of public health emergencies, an application research on social governance ability under public health emergencies based on artificial intelligence is proposed. First, the firefly optimization algorithm is used to collect the information data of the social governance ability of public health emergencies, establish a unified format, and save it. Then, artificial intelligence technology is used to mine the correlation of clustering data, and on this basis, a learning model integrating global structure information and local structure information is established. Finally, the social governance model under public health emergencies is established. The experimental results show that the design method has high clustering accuracy, regularization cross index, and adjusted rand index (ARI) index. This shows that the design method can improve the social governance ability of data fusion clustering and improve the social governance ability.

Axon Tracing and Centerline Detection using Topologically-Aware 3D U-Nets.

As advances in microscopy imaging provide an ever clearer window into the human brain, accurate reconstruction of neural connectivity can yield valuable insight into the relationship between brain structure and function. However, human manual tracing is a slow and laborious task, and requires domain expertise. Automated methods are thus needed to enable rapid and accurate analysis at scale. In this paper, we explored deep neural networks for dense axon tracing and incorporated axon topological information into the loss function with a goal to improve the performance on both voxel-based segmentation and axon centerline detection. We evaluated three approaches using a modified 3D U-Net architecture trained on a mouse brain dataset imaged with light sheet microscopy and achieved a 10% increase in axon tracing accuracy over previous methods. Furthermore, the addition of centerline awareness in the loss function outperformed the baseline approach across all metrics, including a boost in Rand Index by 8%.

An Evaluative Measure of Clustering Methods Incorporating Hyperparameter Sensitivity

Clustering algorithms are often evaluated using metrics which compare with ground-truth cluster assignments, such as Rand index and NMI. Algorithm performance may vary widely for different hyperparameters, however, and thus model selection based on optimal performance for these metrics is discordant with how these algorithms are applied in practice, where labels are unavailable and tuning is often more art than science. It is therefore desirable to compare clustering algorithms not only on their optimally tuned performance, but also some notion of how realistic it would be to obtain this performance in practice. We propose an evaluation of clustering methods capturing this ease-of-tuning by modeling the expected best clustering score under a given computation budget. To encourage the adoption of the proposed metric alongside classic clustering evaluations, we provide an extensible benchmarking framework. We perform an extensive empirical evaluation of our proposed metric on popular clustering algorithms over a large collection of datasets from different domains, and observe that our new metric leads to several noteworthy observations.

A neighbour-similarity based community discovery algorithm

Discovery of communities in a network is a non-trivial task. Recently, many similarity functions have been introduced to cluster nodes of the same type, but tightness relationship between the nodes inside the clusters always remained as an issue. Another important issue is that for some difficult cases like selecting a community for a node that equally belongs to more than one community which may create an ambiguity in determining the node’s best-fit community remain unaddressed in many community discovery algorithms. A single wrong prediction about a node’s community may lead to an incorrect prediction for other nodes, resulting in a poor community structure. To address such issues, a Neighbour Based Community Detection(NBCD) algorithm based on two novel similarity measures using a similarity parameter α and a set of ground rules are proposed in this work. The similarity parameter α provides a choice for the user to select the tightness of the nodes within the communities. The NBCD algorithm is a two-step process: one is community detection and the next is node shifting. Extensive experiments are carried out on real-world benchmark data sets and artificial networks to assess the performance of the proposed algorithm. NBCD algorithm is compared with several recent and state-of-the-art community discovery algorithms. Normalized Mutual Information(NMI), Adjusted Mutual Information(AMI), Adjusted Rand Index(ARI), F-measure and Modularity are used as the performance measures. Experimental results prove that the proposed algorithm, NBCD, performs well with respect to all the performance measures and performs better than the other community detection algorithms considered.

Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)

BackgroundData transformations are commonly used in bioinformatics data processing in the context of data projection and clustering. The most used Euclidean metric is not scale invariant and therefore occasionally inappropriate for complex, e.g., multimodal distributed variables and may negatively affect the results of cluster analysis. Specifically, the squaring function in the definition of the Euclidean distance as the square root of the sum of squared differences between data points has the consequence that the value 1 implicitly defines a limit for distances within clusters versus distances between (inter-) clusters.MethodsThe Euclidean distances within a standard normal distribution (N(0,1)) follow a N(0,sqrt{2}) distribution. The EDO-transformation of a variable X is proposed as EDO= X/(sqrt{2}cdot s) following modeling of the standard deviation s by a mixture of Gaussians and selecting the dominant modes via item categorization. The method was compared in artificial and biomedical datasets with clustering of untransformed data, z-transformed data, and the recently proposed pooled variable scaling.ResultsA simulation study and applications to known real data examples showed that the proposed EDO scaling method is generally useful. The clustering results in terms of cluster accuracy, adjusted Rand index and Dunn’s index outperformed the classical alternatives. Finally, the EDO transformation was applied to cluster a high-dimensional genomic dataset consisting of gene expression data for multiple samples of breast cancer tissues, and the proposed approach gave better results than classical methods and was compared with pooled variable scaling.ConclusionsFor multivariate procedures of data analysis, it is proposed to use the EDO transformation as a better alternative to the established z-standardization, especially for nontrivially distributed data. The “EDOtrans” R package is available at https://cran.r-project.org/package=EDOtrans.