Combining Multiple Clusterings of Chemical Structures Using Cumulative Voting-Based Aggregation Algorithm

Consensus clustering methods are motivated by the success of combining multiple classifiers in many areas. In this paper, graph-based consensus clustering is used to improve the quality of chemical compound clustering by enhancing the robustness, novelty, consistency and stability of individual clusterings. For this purpose, Hyper-Graph Partitioning Algorithm (HGPA) [1], was applied. The clustering is evaluated based on the ability to separate actives from inactives molecules in each cluster and the results were compared with the Ward's clustering method. The chemical dataset MDL Drug Data Report (MDDR) database has been used for experiments. The MDL Drug Data Report (MDDR) database consists of 102516 molecules. For the experiments, the dataset DS1 was chosen from the MDDR database. This dataset has been used for many virtual screening experiments [2-4]. The dataset DS1contains 10 heterogeneous activity classes (8568 molecules). For the clustering experiments, two 2D fingerprint descriptors will be used which are developed by Scitegic's Pipeline Pilot [5]. These are 120-bit ALOGP and 1024-bit extended connectivity fingerprints (ECFP_4). The results were evaluated based on the effectiveness of the methods to separate actives from non-actives molecules using QPI- (for quality partition index) measure, which was devised by Varin et al. [6]. As defined by [7], an active cluster as a non-singleton cluster for which the percentage of active molecules in the cluster is greater than the percentage of active molecules in the dataset as a whole. Let p be the number of actives in active clusters, q the number of inactives in active clusters, r the number of actives in inactive clusters (i.e., clusters that are not active clusters) and s the number of singleton actives. The high value occurs when the actives are clustered tightly together and separated from the inactive molecules. Then the quality partition index, QPI, is defined to be: QPI=pp+q+r+s (1) Then, the results will be compared with Ward's individual clustering method, the standard clustering method for chemoinformatics applications. The generation process has been done by multiple run of K-means algorithms, each with random initialization of cluster centroids. The number of partitions generated in this step is ranged between n = 5 to n = 50, with 5-times step. Then, all the generated partitions were combined using HGPA to obtain the consensus partition. This process is done for each fingerprint (ALOGP and ECFP_4). The mean of QPI values are averaged over the ten activity classes of the datasets. Tables ​Tables1,1, ​,22 show the effectiveness of MDDR dataset clustering using ALOGP and ECFP_4 fingerprints. The best PQI value of consensus clustering methods for each column has been bold-faced for ease of reference. Table 1 Effectivenss of clustering of high diverse MDDR dataset: ALOGP Fingerprint. Table 2 Effectivenss of clustering of high diverse MDDR dataset: ECFP_4 Fingerprint. Visual inspection of the results enables comparisons to be made between the effectiveness of clustering of MDDR datasets and Ward's method, the best of choice clustering method for chemoinformatics applications. In addition, ten times of consensus clustering, for each fingerprint were observed in order to study the effectiveness of consensus clustering with different ensemble sizes. The results show that HGPA consensus clustering gives robust and novel result when K-means algorithm is run 20-50 times using ALOGP. The performance of consensus clustering outperforms the Wards' method. For consensus of dataset which represented by ECFP_4 fingerprint, the best QPI values of consensus clustering are obtained from ensembles of size n = 20-50. The performance of consensus clustering gives robust results which are better than overall performance of individual clusterings. The values of QPI in both datasets for consensus clustering are close to the Wards method. The consensus clustering, HGPA, provide stable clusters by decreasing the sensitivity to noise and outliers. The average percentages of singleton clusters of individual clusterings compared with consensus clustering for both fingerprints. The results show that consensus clustering partition the datasets with average percentage of singleton equal to zero, which is much better than individual clusterings and Wards' method. For example, 16.72% of molecules of DS1 are clustered as singletons when Wards method is applied on ALOGP fingerprint with number of clusters equal to 1000 clusters. Finally we conclude that graph-based consensus clustering can improve the effectiveness of chemical compounds clustering. The performance of consensus clustering is more robust, novel, stable, consistent, and out-perform Wards' method in case of using ALOGP fingerprint. By using ECFP_4 fingerprint, consensus clustering methods provide more robust, stable, and consistent clustering and close to the Wards clustering results. The experiments reported here suggest that graph-based consensus clustering can improve the quality of individual clustering by using the efficient algorithm, K-means algorithm, to generate the ensemble with size (20-50) for both structurally diverse chemical datasets.

Patient stratification or disease subtyping is crucial for precision medicine and personalized treatment of complex diseases. The increasing availability of high-throughput molecular data provides a great opportunity for patient stratification. Many clustering methods have been employed to tackle this problem in a purely data-driven manner. Yet, existing methods leveraging high-throughput molecular data often suffers from various limitations, e.g. noise, data heterogeneity, high dimensionality or poor interpretability. Here we introduced an Entropy-based Consensus Clustering (ECC) method that overcomes those limitations all together. Our ECC method employs an entropy-based utility function to fuse many basic partitions to a consensus one that agrees with the basic ones as much as possible. Maximizing the utility function in ECC has a much more meaningful interpretation than any other consensus clustering methods. Moreover, we exactly map the complex utility maximization problem to the classic K -means clustering problem, which can then be efficiently solved with linear time and space complexity. Our ECC method can also naturally integrate multiple molecular data types measured from the same set of subjects, and easily handle missing values without any imputation. We applied ECC to 110 synthetic and 48 real datasets, including 35 cancer gene expression benchmark datasets and 13 cancer types with four molecular data types from The Cancer Genome Atlas. We found that ECC shows superior performance against existing clustering methods. Our results clearly demonstrate the power of ECC in clinically relevant patient stratification. The Matlab package is available at http://scholar.harvard.edu/yyl/ecc . yunfu@ece.neu.edu or yyl@channing.harvard.edu. Supplementary data are available at Bioinformatics online.

Quantifying the similarity of molecules is considered one of the major tasks in virtual screening. There are many similarity measures that have been proposed for this purpose, some of which have been derived from document and text retrieving areas as most often these similarity methods give good results in document retrieval and can achieve good results in virtual screening. In this work, we propose a similarity measure for ligand-based virtual screening, which has been derived from a text processing similarity measure. It has been adopted to be suitable for virtual screening; we called this proposed measure the Adapted Similarity Measure of Text Processing (ASMTP). For evaluating and testing the proposed ASMTP we conducted several experiments on two different benchmark datasets: the Maximum Unbiased Validation (MUV) and the MDL Drug Data Report (MDDR). The experiments have been conducted by choosing 10 reference structures from each class randomly as queries and evaluate them in the recall of cut-offs at 1% and 5%. The overall obtained results are compared with some similarity methods including the Tanimoto coefficient, which are considered to be the conventional and standard similarity coefficients for fingerprint-based similarity calculations. The achieved results show that the performance of ligand-based virtual screening is better and outperforms the Tanimoto coefficients and other methods.

Consensus clustering provides a framework to ensemble multiple clustering results to obtain a consensus and robust result. Most existing consensus clustering methods usually apply all data to ensemble learning, whereas ignoring the side effects caused by some difficult or unreliable instances. To tackle this problem, we propose a novel self-paced consensus clustering method to gradually involve instances from more reliable to less reliable ones into the ensemble learning. We first construct an initial bipartite graph from the multiple base clustering results, where the nodes represent the instances and clusters and the edges indicate that an instance belongs to a cluster. Then, we learn a structured bipartite graph from the initial one by self-paced learning, i.e., we automatically decide the reliability of each edge and involves the edges into graph learning in order of their reliability. At last, we obtain the final consensus clustering result from the learned bipartite graph. The extensive experimental results demonstrate the effectiveness and superiority of the proposed method.

Virtual screening (VS) is a computational practice applied in drug discovery research. VS is popularly applied in a computer-based search for new lead molecules based on molecular similarity searching. In chemical databases similarity searching is used to identify molecules that have similarities to a user-defined reference structure and is evaluated by quantitative measures of intermolecular structural similarity. Among existing approaches, 2D fingerprints are widely used. The similarity of a reference structure and a database structure is measured by the computation of association coefficients. In most classical similarity approaches, it is assumed that the molecular features in both biological and non-biologically-related activity carry the same weight. However, based on the chemical structure, it has been found that some distinguishable features are more important than others. Hence, this difference should be taken consideration by placing more weight on each important fragment. The main aim of this research is to enhance the performance of similarity searching by using multiple descriptors. In this paper, a deep learning method known as deep belief networks (DBN) has been used to reweight the molecule features. Several descriptors have been used for the MDL Drug Data Report (MDDR) dataset each of which represents different important features. The proposed method has been implemented with each descriptor individually to select the important features based on a new weight, with a lower error rate, and merging together all new features from all descriptors to produce a new descriptor for similarity searching. Based on the extensive experiments conducted, the results show that the proposed method outperformed several existing benchmark similarity methods, including Bayesian inference networks (BIN), the Tanimoto similarity method (TAN), adapted similarity measure of text processing (ASMTP) and the quantum-based similarity method (SQB). The results of this proposed multi-descriptor-based on Stack of deep belief networks method (SDBN) demonstrated a higher accuracy compared to existing methods on structurally heterogeneous datasets.

ObjectiveCluster analysis of spatio-temporal event-related potential (ERP) data is a promising tool for exploring the measurement time window of ERPs. However, even after preprocessing, the remaining noise can result in uncertain cluster maps followed by unreliable time windows while clustering via conventional clustering methods. MethodsWe designed an ensemble deep clustering pipeline to determine a reliable time window for the ERP of interest from temporal concatenated grand average ERP data. The proposed pipeline includes semi-supervised deep clustering methods initialized by consensus clustering and unsupervised deep clustering methods with end-to-end architectures. Ensemble clustering from those deep clusterings was used by the designed adaptive time window determination to estimate the time window. ResultsAfter applying simulated and real ERP data, our method successfully obtained the time window for identifying the P3 components (as the interest of both ERP studies) while additional noise (e.g., adding 20 dB to −5 dB white Gaussian noise) was added to the prepared data. ConclusionCompared to the state-of-the-art clustering methods, a superior clustering performance was yielded from both ERP data. Furthermore, more stable and precise time windows were elicited as the noise increased. SignificanceOur study provides a complementary understanding of identifying the cognitive process using deep clustering analysis to the existing studies. Our finding suggests that deep clustering can be used to identify the ERP of interest when the data is imperfect after preprocessing.

Ligand flexibility is an important problem in molecular docking and virtual screening. To address this challenge, we investigate a hierarchical pre-organization of multiple conformations of small molecules. Such organization of pre-calculated conformations removes the exploration of ligand conformational space from the docking calculation and allows for concise representation of what can be thousands of conformations. The hierarchy also recognizes and prunes incompatible conformations early in the calculation, eliminating redundant calculations of fit. We investigate the method by docking the MDL Drug Data Report (MDDR), an annotated database of 100,000 molecules, into apo and holo forms of seven unrelated targets. This annotated database allows us to track the ranking of tens to hundreds of annotated ligands in each of the docking systems. The binding sites and database are prepared in an automated fashion in an attempt to remove some human bias from the calculations. Many thousands of explicit and implicit ligand conformations may be docked in calculations not much longer than required for single conformer docking. As long as internal energies are not considered, recombination with the hierarchy is additive as the number of degrees of freedom is increased. Molecules with even millions of conformations can be docked in a few minutes on a single desktop computer.

A molecular equivalence number (meqnum) classifies a molecule with respect to a class of structural features or topological shapes such as its cyclic system or its set of functional groups. Meqnums can be used to organize molecular structures into nonoverlapping, yet highly relatable classes. We illustrate the construction of some different types of meqnums and present via examples some methods of comparing diverse chemical libraries based on meqnums. In the examples we compare a library which is a random sample from the MDL Drug Data Report (MDDR) with a library which is a random sample from the Available Chemical Directory (ACD). In our analyses, we discover some interesting features of the topological shape of a molecule and its set of functional groups that are strongly linked with compounds occurring in the MDDR but not in the ACD. We also illustrate the utility of molecular equivalence indices in delineating the structural domain over which an SAR conclusion is valid.

A molecular equivalence number (meqnum) classifies a molecule with respect to a class of structural features or topological shapes such as its cyclic system or its set of functional groups. Meqnums can be used to organize molecular structures into nonoverlapping, yet highly relatable classes. We illustrate the construction of some different types of meqnums and present via examples some methods of comparing diverse chemical libraries based on meqnums. In the examples we compare a library which is a random sample from the MDL Drug Data Report (MDDR) with a library which is a random sample from the Available Chemical Directory (ACD). In our analyses, we discover some interesting features of the topological shape of a molecule and its set of functional groups that are strongly linked with compounds occurring in the MDDR but not in the ACD. We also illustrate the utility of molecular equivalence indices in delineating the structural domain over which an SAR conclusion is valid.

In recent years, nonalcoholic fatty liver disease (NAFLD) has become a more serious public health issue worldwide. This study strived to investigate the molecular mechanism of pathogenesis of NAFLD and explore promising diagnostic and therapeutic targets for NAFLD. Raw data from GSE130970 were downloaded from the Gene Expression Omnibus database. We used the dataset to analyze the expression levels of cuproptosis-related genes in NAFLD patients and healthy controls to identify the differentially expressed cuproptosis-related genes (DECRGs). The relationship and potential mechanism between DECRGs and clinicopathological factors were examined by enrichment analysis and two consensus clustering methods. We screened key DECRGs based on Random Forest (RF), and then verified the key DECRGs in NAFLD patients, high-fat diet (HFD)-fed mice, and palmitic acid-induced AML12 cells. ROC analysis showed good diagnostic function of DECRGs in normal and NAFLD liver tissue. Two consensus clusters indicated the important role of cuproptosis in the development of NAFLD. We screened for key DECRGs (DLD, DLAT) based on RF and found a close relationship between the DECRGs and clinicopathological factors. We collected clinical blood samples to verify the differences in gene expression levels by qPCR. In addition, we further verified the expression levels of DLD and DLAT in HFD mice and AML12 cells, which showed the same results. This study provides a novel perspective on the pathogenesis of NAFLD. We identified two cuproptosis-related genes that are closely related to NAFLD. These genes may play a significant role in the molecular pathogenesis of NAFLD, which may be useful to make progress in the diagnosis and treatment of NAFLD.

Clustering is one of the major tasks in data mining. However, selecting an algorithm to cluster a dataset is a difficult task, especially if there is no prior knowledge on the structure of the data. Consensus clustering methods can be used to combine multiple base clusterings into a new solution that provides better partitioning. In this work, we present a new consensus clustering method based on detecting clustering patterns by mining frequent closed itemset. Instead of generating one consensus, this method both generates multiple consensuses based on varying the number of base clusterings, and links these solutions in a hierarchical representation that eases the selection of the best clustering. This hierarchical view also provides an analysis tool, for example to discover strong clusters or outlier instances.

BackgroundThe Pubchem Database is a large-scale resource for chemical information, containing millions of chemical compound activities derived by high-throughput screening (HTS). The ability to extract characteristic substructures from such enormous amounts of data is steadily growing in importance. Compounds with shared basic active structures (BASs) exhibiting G-protein coupled receptor (GPCR) activity and repeated dose toxicity have been mined from small datasets. However, the mining process employed was not applicable to large datasets owing to a large imbalance between the numbers of active and inactive compounds. In most datasets, one active compound will appear for every 1000 inactive compounds. Most mining techniques work well only when these numbers are similar.ResultsThis difficulty was overcome by sampling an equal number of active and inactive compounds. The sampling process was repeated to maintain the structural diversity of the inactive compounds. An interactive KNIME workflow that enabled effective sampling and data cleaning processes was created. The application of the cascade model and subsequent structural refinement yielded the BAS candidates. Repeated sampling increased the ratio of active compounds containing these substructures. Three samplings were deemed adequate to identify all of the meaningful BASs. BASs expressing similar structures were grouped to give the final set of BASs. This method was applied to HIV integrase and protease inhibitor activities in the MDL Drug Data Report (MDDR) database and to procaspase-3 activators in the PubChem BioAssay database, yielding 14, 12, and 18 BASs, respectively.ConclusionsThe proposed mining scheme successfully extracted meaningful substructures from large datasets of chemical structures. The resulting BASs were deemed reasonable by an experienced medicinal chemist. The mining itself requires about 3 days to extract BASs with a given physiological activity. Thus, the method described herein is an effective way to analyze large HTS databases.

Pharmacologically active molecules can provide remedies for a range of different illnesses and infections. Therefore, the search for such bioactive molecules has been an enduring mission. As such, there is a need to employ a more suitable, reliable, and robust classification method for enhancing the prediction of the existence of new bioactive molecules. In this paper, we adopt a recently developed combination of different boosting methods (Adaboost) for the prediction of new bioactive molecules. We conducted the research experiments utilizing the widely used MDL Drug Data Report (MDDR) database. The proposed boosting method generated better results than other machine learning methods. This finding suggests that the method is suitable for inclusion among the in silico tools for use in cheminformatics, computational chemistry and molecular biology.

QuestionsWhich clustering algorithms are most effective according to different cluster validity evaluators? Which distance or dissimilarity measure is most suitable for clustering algorithms?LocationHyrcanian forest, Iran (Asia), Virginia region forest, United States (North America), beech forests, Ukraine (Europe).MethodsWe tested 25 clustering algorithms with nine vegetation data sets comprised of three real data sets and six simulated data sets exhibiting different cluster separation values. The clustering algorithms included both hierarchical and non‐hierarchical partitioning. Five evaluators were employed on each cluster solution to evaluate different clustering algorithms. Algorithms were ranked from best to worst on each clustering evaluator for each data set.ResultsThe comparison revealed that the OPTSIL initiated from a Flexible‐β (−0.25) solution achieved particularly good performance. We also found that Ward's method and Flexible‐β (−0.1) implementations were accurate. K‐means with Hellinger distance was superior to Partitioning Around Medoids (PAM) algorithms. Accordance between distance measures and clustering algorithms was also observed. Bray–Curtis dissimilarity combined with a range of clustering algorithms was successful in most cases. Bray–Curtis dissimilarity proved superior to other distance measures for heterogeneous data sets.ConclusionsAll in all, the results demonstrate that choosing the most suitable method before clustering is critical for achieving maximally interpretable clusters. The complexity of vegetation data sets makes this issue even more important. The choice of distance measure had more effect than the choice of clustering method on the quality of results. Our results illustrate that OPTSIL Flexible‐β (−0.1) and OPTPART could prove superior to alternative conventional clustering algorithms when internal evaluation criteria are used to optimize clustering.

Purpose. To evaluate the relationship between the shape of horseshoe tear and the localization of vitreoretinal tractions (VRT) using methods of the peripheral vitreoretinal interface visualization and classify horseshoe tears by shape for surgical planning. Material and methods. We studied horseshoe tears parameters of 52 patients (52 eyes). The localization of VRT was determined by wide-field OCT, the horseshoe tear shape was determined as the ratio of length to width of the tear (l/b) by multispectral laser scanning. The ratio of the obtained data was evaluated by the Spearman correlation analysis. We used Ward's method of hierarchical clustering to classify the horseshoe tears by shape. The obtained data were used to perform YAG- laser excision of the vitreoretinal adhesion zone in patients with rhegmatogenous retinal detachment as part of the combined microinvasive laser-surgical technology. Results. The l/b ratio ranged from 1/4 to 3/1. A strong negative correlation has been revealed between the horseshoe tear shape and the fixation of vitreoretinal tractions (rs -0.95; p <0.05). Horseshoe tears were identified in 4 groups using Ward's method of clustering. Each group corresponded to a specific localization of VRT. The extension of VRT beyond the tear was associated with a high risk of rhegmatogenous retinal detachment. Conclusion. A significant correlation has been found between the studied factors confirm the possibility of using data on the horseshoe tear shape for an approximate evaluation of vitreoretinal adhesion localization. The obtained data allows to determine the exact VRT excision zone when performing combined laser-surgical technology without the need for preoperative wide-field OCT. Key words: rhegmatogenous retinal detachment, wide-field OCT, horseshoe tear, vitreoretinal traction, YAG – laser retinotomy.