Part of Jung JY, Bae J. Workflow clustering method based on process similarity. CAS Our analysis also shows that the application of weights can have a major impact on the clustering solution obtained by partitioning or hierarchical classification algorithms. ik The myExperiment dataset of 100 workflows (generated using the Taverna workflow platform) and their respective classes. } can be defined as follows: Finally, an individual global workflow support of the workflow w i Still considering the Rand index as a measure of classification effectiveness, we confirmed that for the Armadillo dataset, having more tasks in the workflow generally leads to better classification results regardless of the criterion (CH, Silhouette or logSS) used to select the optimal number of clusters (p<0.01; Figure3a). Some other useful clustering information can be extracted from workflows beside the number or type of tasks, input and output port of tasks and connections between tasks. Panel (a) reports the PS matrix computed for the set of the five bioinformatics workflows presented in Figure1 (a support value of 1.0 in the diagonal indicates that the corresponding element was always singleton in its class, whereas a support value of 1.0 in a non-diagonal position indicates that the two corresponding elements were always grouped together); panels (b) and (c) illustrate the distributions of the global individual PSG index obtained for the 120 workflows from the Armadillo dataset for the k-means and k-medoids partitioning algorithms, respectively. Commun Stat Theory. Language-based methods rely on the text mining of workflow metadata and the use of keyword similarity measures [6,23]. The detailed results of hierarchical clustering are presented as well. The four types of workflow encoding examined in this study were compared using the weighted versions of k-means and k-medoids partitioning algorithms. The Calinski-Harabasz, Silhouette and logSS clustering indices were considered. additive trees) by running the Fitch, Kitsch and Neighbor programs from the PHYLIP package [36]. J Comp Interdisc Sci. it defines the diagonal elements of the support matrix in Figure9a): where S Panel (a) illustrates the effect of the encoding type for both unweighted (first two bars) and weighted (last four bars) encodings; panel (b) - the effect of the applied hierarchical clustering algorithm; panel (c) - the effect of the distance measure. Hartigan JA.

The Creative Commons Public Domain Dedication waiver (https://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. This type of workflow encoding, which is similar to the N-gram encoding of Wombacher and Li [21], preserves the essential structural information without carrying out lengthy graph theory methods aimed at the determining the distance matrix between workflows. Experiment datasets ( This classification is shown for four weighted and four unweighted workflow encoding types (I, II, III and IV) discussed in this article, the cosine and Euclidean distances and four different hierarchical clustering algorithms (Fitch, Kirsch, NJ and UPGMA). workflows; they are represented by the matrix columns) and m variables (i.e.

The general trend which can be observed in this simulation for all four encoding schemes is that the increase in the number of workflow tasks leads to the increase in the value of RI in the case of the Calinski-Harabasz and Silhouette indices and, in a slighter extent, in the case of logSS. my Biometrika. The average Robinson and Foulds topological distance ( SEM) was used to measure clustering performances. Berlin Heidelberg: Springer; 2006. p. 37989. Thus, the tasks annotated with the word HGT received the weight of 1.0, whereas all the other tasks received the weight of 0.1. In this study, we define and evaluate four workflow encoding schemes which can be used for regrouping workflows either containing similar tasks, or having similar execution times, or using similar keywords (or meta-data), or having similar workflow structures. Los Alamitos: IEEE Computer Society; 2013. p. 18895. =120). The cluster c, for which d(i, c)=b(i) can be considered the neighbor of i. Google Scholar. Hennig C. Cluster-wise assessment of cluster stability. Terms and Conditions, To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Classification of hierarchical workflow clustering strategies for the computational methods corresponding to specific keywords); the weight of 0.1 is given to the variables corresponding to the remaining tasks. $$,$$ s(k)=\left[{\displaystyle \sum_{i=1}^{n_k}\frac{b(i)-a(i)}{ \max \left(a(i),b(i)\right)}}\right]/{n}_k. ij

J Multivar Anal. Makarenkov V, Legendre P. Optimal variable weighting for ultrametric and additive trees and K-means partitioning: Methods and software. The latter work focuses on the recognition of the strongest clustering by permuting the rows of the proportion matrix in order to obtain its block-diagonal form that maximizes the within-block co-occurrences [47]. [20], who found that workflow task connectivity information does not necessarily bring an additional advantage to the workflow clustering process. All authors listed contributed to and approved the final manuscript. Cookies policy. The applied weights can be defined by the user through the introduction of specific keywords characterizing certain tasks; the corresponding tasks weight can be given following the presence or absence of these keywords in the methods annotations. However, using only the presence-absence data in the workflow representation discards structural information characterizing the dataflow. 2008;13:7717. (i=1, , n) can be computed as follows: The first of the two main terms in the numerators of Equations13 and 14 contains a maximum that accounts for the proportion of times two workflows appear, or do not appear, in the same class over multiple random starts. is the vector representing workflow i in cluster k. When the Calinski-Harabasz criterion is considered, the number of clusters corresponding to its highest value is selected as the optimal one. In: OConner L, editor. This is mainly due to a greater sparseness of data corresponding to encodings of Types III and IV. The overall PSG support (Equation13) for these workflows was found to be 0.90, while the individual global workflow supports (Equation14) were as follows: PSG(W1)=0.98, PSG(W2)=0.85, PSG(W3)=0.81, PSG(W4)=1.0 and PSG(W5)=0.85. In addition, we also introduced the global pairwise support index, PSG, allowing one to estimate the global support of the proposed clustering solution as well as the global support of individual elements (i.e. Evaluation of the resulting partitioning as a function of a distance measure, showed that the cosine distance performed significantly better than the Euclidean distance (the average RI of 0.68 vs 0.61, and p<0.001; see Figures3c, 4c and 5b). J Graph Algorithms Appl. The most commonly used distances in the framework of k-means partitioning are the Euclidean distance, Manhattan distance and Minkowski distance. Hennig [44] proposed a method, based on the Jaccard coefficient, for assessing the support of individual clusters of the obtained partitioning solution using a bootstrap resampling. Grigori D, Corrales JC, Bouzeghoub M, Gater A. To investigate whether the workflow structural information can provide a better workflow classification compared to the presence-absence and occurrence encodings, we represented the five workflows from Figure1 as connected directed graphs and encoded them into a pair-of-tasks format (see encoding of type III in Table1). We first evaluated the performances of the basic encoding scheme (Type I, see Figure2a), consisting of a binary presence-absence matrix accompanied by the weights proportional to the tasks running times. In Third Workshop on Workflows in Support of Large-Scale Science: 17 November 2008; Austin, TX. Article Centre-Ville, Montreal, QC, H3C 3J7, Canada, You can also search for this author in workflow W4 in Figure9a). objects, taxa, or workflows in our study) characterized by m variables (i.e. [20] and Kastner et al. Privacy The time complexity of the Fitch and Kitsch algorithms is O(n New York: ACM; 2008. p. 9. Google Scholar. Statistics such as the average task execution time, the size of transmitted data, the success or failure of each task as well as the selected tasks parameters can be also taken into account when clustering workflows [23,27]. is assigned to a singleton class in the partition P In language-based approaches, string distance measures, such as the Hamming or Levenshtein distances, can be applied to assess dissimilarities between workflows [22]. When the performances of the four hierarchical clustering algorithms were considered, no significant difference between the corresponding average RF distances was found (Figure8b). The keyword used for encodings of types II and IV was HGT (standing for horizontal gene transfer). Our second simulation was carried out using both the Armadillo and myExperiment datasets, the weighted k-means and k-medoids partitioning algorithms and the cosine and Euclidean distances. m In this study, we defined and tested through simulations four workflow encoding schemes combined with specific weighting strategies characteristic for bioinformatics projects. $$,$$ {\displaystyle \sum_i{\displaystyle \sum_j\frac{{\left({\delta}_{ij}-{d}_{ij}\right)}^2}{d_{ij}^p}}}\to \min . For example, simulation studies, which are now a must for statistical validation of new bioinformatics methods and software, are frequently carried out using the available workflow platforms.

Felsenstein J. Inferring phylogenies. In this section, we discuss the results obtained using the hierarchical clustering methods in the framework of workflow clustering. Tamura K, Peterson D, Peterson N, Stecher G, Nei M, Kumar S. MEGA5: molecular evolutionary genetics analysis using maximum likelihood, evolutionary distance, and maximum parsimony methods. An examination of procedures for determining the number of clusters in a data set. Silva V, Chirigati F, Maia K, Ogasawara E, Oliveira D, Braganholo V, et al. Our findings, based on the analysis of 220 real-life bioinformatics workflows generated by the Armadillo [8] and Taverna [4] WfMS, suggest that the weighted cosine distance in association with the k-medoids partitioning algorithm and the presence-absence workflow encoding provided the highest values of the Rand index among all compared clustering strategies. Visualization of the resulting classifications trees in Figures6 and 7 was carried out with the program Mega5 [43]. New York: Wiley; 1975. Summarizing the results obtained for the Armadillo and myExperiment datasets, we can notice that the best hierarchical classification was found using the Fitch algorithm with the weighted cosine distance and encoding of Type I.

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