Rand Index Research Articles

Enhancement of K-means clustering in big data based on equilibrium optimizer algorithm

Abstract Data mining’s primary clustering method has several uses, including gene analysis. A set of unlabeled data is divided into clusters using data features in a clustering study, which is an unsupervised learning problem. Data in a cluster are more comparable to one another than to those in other groups. However, the number of clusters has a direct impact on how well the K-means algorithm performs. In order to find the best solutions for these real-world optimization issues, it is necessary to use techniques that properly explore the search spaces. In this research, an enhancement of K-means clustering is proposed by applying an equilibrium optimization approach. The suggested approach adjusts the number of clusters while simultaneously choosing the best attributes to find the optimal answer. The findings establish the usefulness of the suggested method in comparison to existing algorithms in terms of intra-cluster distances and Rand index based on five datasets. Through the results shown and a comparison of the proposed method with the rest of the traditional methods, it was found that the proposal is better in terms of the internal dimension of the elements within the same cluster, as well as the Rand index. In conclusion, the suggested technique can be successfully employed for data clustering and can offer significant support.

A multi-objective evolutionary algorithm with decomposition and the information feedback for high-dimensional medical data

High-dimensional medical data often leads to a phenomenon known as the ”curse of dimensionality,” which causes additional memory and high training costs, as well as degrading the generalization capacity of learning algorithms. To address this issue, a multi-objective evolutionary algorithm that integrates decomposition and the information feedback model (IFMMOEAD) is proposed for high-dimensional medical data. This algorithm not only considers the number of selected features, but also classification accuracy and correlation measures of features when feature dimensionality reduction is executed. The property of IFMMOEAD is first verified by standard benchmarks DTLZ1–DTLZ7. Then, it is used to develop machine learning algorithms for thirty-five high-dimensional cancer gene expression data sets, showing excellent potential for high-dimensional medical machine learning. Finally, the IFMMOEAD is applied to empirical clinical data of multiple myeloma, significantly outperforming existing algorithms in terms of normalized mutual information and adjusted rand index metrics. We suggest that this algorithm could be implemented in medical information systems as a promising technique for high-dimensional medical problems.

A Maximum-Entropy Fuzzy Clustering Approach for Cancer Detection When Data Are Uncertain

(1) Background: Cancer is a leading cause of death worldwide and each year, approximately 400,000 children develop cancer. Early detection of cancer greatly increases the chances for successful treatment, while screening aims to identify individuals with findings suggestive of specific cancer or pre-cancer before they have developed symptoms. Precise detection, however, often mainly relies on human experience and this could suffer from human error and error with a visual inspection. (2) Methods: The research of statistical approaches to analyze the complex structure of data is increasing. In this work, an entropy-based fuzzy clustering technique for interval-valued data (EFC-ID) for cancer detection is suggested. (3) Results: The application on the Breast dataset shows that EFC-ID performs better than the conventional FKM in terms of AUC value (EFC-ID = 0.96, FKM = 0.88), sensitivity (EFC-ID = 0.90, FKM = 0.64), and specificity (EFC-ID = 0.93, FKM = 0.92). Furthermore, the application on the Multiple Myeloma data shows that EFC-ID performs better than the conventional FKM in terms of Chi-squared (EFC-ID = 91.64, FKM = 88.26), Accuracy rate (EFC-ID = 0.71, FKM = 0.60), and Adjusted Rand Index (EFC-ID = 0.33, FKM = 0.21). (4) Conclusions: In all cases, the proposed approach has shown good performance in identifying the natural partition and the advantages of the use of EFC-ID have been detailed illustrated.

Complet+: a computationally scalable method to improve completeness of large-scale protein sequence clustering.

A major challenge for clustering algorithms is to balance the trade-off between homogeneity, i.e., the degree to which an individual cluster includes only related sequences, and completeness, the degree to which related sequences are broken up into multiple clusters. Most algorithms are conservative in grouping sequences with other sequences. Remote homologs may fail to be clustered together and instead form unnecessarily distinct clusters. The resulting clusters have high homogeneity but completeness that is too low. We propose Complet+, a computationally scalable post-processing method to increase the completeness of clusters without an undue cost in homogeneity. Complet+ proves to effectively merge closely-related clusters of protein that have verified structural relationships in the SCOPe classification scheme, improving the completeness of clustering results at little cost to homogeneity. Applying Complet+ to clusters obtained using MMseqs2's clusterupdate achieves an increased V-measure of 0.09 and 0.05 at the SCOPe superfamily and family levels, respectively. Complet+ also creates more biologically representative clusters, as shown by a substantial increase in Adjusted Mutual Information (AMI) and Adjusted Rand Index (ARI) metrics when comparing predicted clusters to biological classifications. Complet+ similarly improves clustering metrics when applied to other methods, such as CD-HIT and linclust. Finally, we show that Complet+ runtime scales linearly with respect to the number of clusters being post-processed on a COG dataset of over 3 million sequences. Code and supplementary information is available on Github: https://github.com/EESI/Complet-Plus.

VoomSOM: voom-based Self-Organizing Maps for Clustering RNASequencing Data

Background: Due to overdispersion in the RNA-Seq data and its discrete structure, clustering samples based on gene expression profiles remains a challenging problem, and several clustering approaches have been developed so far. However, there is no “gold standard” strategy for clustering RNA-Seq data, so alternative approaches are needed. Objective: In this study, we presented a new clustering approach, which incorporates two powerful methods, i.e., voom and self-organizing maps, into the frequently used clustering algorithms such as kmeans, k-medoid and hierarchical clustering algorithms for RNA-seq data clustering. Methods: We first filter and normalize the raw RNA-seq count data. Then to transform counts into continuous data, we apply the voom method, which outputs the log-cpm matrix and sample quality weights. After the voom transformation, we apply the SOM algorithm to log-cpm values to get the codebook used in the downstream analysis. Next, we calculate the weighted distance matrices using the sample quality weights obtained from voom transformation and codebooks from the SOM algorithm. Finally, we apply k-means, k-medoid and hierarchical clustering algorithms to cluster samples. Results: The performances of the presented approach and existing methods are compared over simulated and real datasets. The results show that the new clustering approach performs similarly or better than other methods in the Rand index and adjusted Rand index. Since the voom method accurately models the observed mean-variance relationship of RNA-seq data and SOM is an efficient algorithm for modeling high dimensional data, integrating these two powerful methods into clustering algorithms increases the performance of clustering algorithms in overdispersed RNA-seq data. Conclusion: The proposed algorithm, voomSOM, is an efficient and novel clustering approach that can be applied to RNA-Seq data clustering problems.

Clustering heterogeneous categorical data using enhanced mini batch K-means with entropy distance measure

<span lang="EN-US">Clustering methods in data mining aim to group a set of patterns based on their similarity. In a data survey, heterogeneous information is established with various types of data scales like nominal, ordinal, binary, and Likert scales. A lack of treatment of heterogeneous data and information leads to loss of information and scanty decision-making. Although many similarity measures have been established, solutions for heterogeneous data in clustering are still lacking. The recent entropy distance measure seems to provide good results for the heterogeneous categorical data. However, it requires many experiments and evaluations. This article presents a proposed framework for heterogeneous categorical data solution using a mini batch k-means with entropy measure (MBKEM) which is to investigate the effectiveness of similarity measure in clustering method using heterogeneous categorical data. Secondary data from a public survey was used. The findings demonstrate the proposed framework has improved the clustering’s quality. MBKEM outperformed other clustering algorithms with the accuracy at 0.88, v-measure (VM) at 0.82, adjusted rand index (ARI) at 0.87, and Fowlkes-Mallow’s index (FMI) at 0.94. It is observed that the average minimum elapsed time-varying for cluster generation, </span><em><span lang="EN-US">k</span></em><span lang="EN-US"> at 0.26 s. In the future, the proposed solution would be beneficial for improving the quality of clustering for heterogeneous categorical data problems in many domains.</span>

Random Feature-Based Collaborative Kernel Fuzzy Clustering for Distributed Peer-to-Peer Networks

Kernel clustering has the ability to get the inherent nonlinear structure of the data. But the high computational complexity and the unknown representation of the kernel space make it unavailable for the data clustering in distributed peer-to-peer (P2P) networks. To solve this issue, we propose a new series of random feature-based collaborative kernel clustering algorithms in this article. In the most basic algorithm, each node in a distributed P2P network first maps its data into a low-dimensional random feature space with the approximation of the given kernel by using the random Fourier feature mapping method. Then, each node independently searches the clusters with its local data and the collaborative knowledge from its neighbor nodes, and the distributed clustering is performed among all network nodes until reaching the global consensus result, i.e., all nodes have the same cluster centers. In addition, an improved version is designed with assignment of feature weights, which is optimized by the maximum-entropy technique to extract important features for the cluster identification. What’s more, to relief the impact of different kernel functions and related parameters on clustering results, the combination of multiple kernels rather than a single kernel is adopted for the low-dimensional approximation, and the optimized weights are assigned to provide the guidance on the choice of the kernels and their parameters and discover significant features at the same time. Experiments on synthetic and real-world datasets show that the proposed methods achieve similar and even better results than the traditional kernel clustering methods on various performance metrics, including the average classification rate, the average normalized mutual information, and the average adjusted rand index. More importantly, the low-dimensional random features approximated to kernels and the distributed clustering mechanism adopted in these methods bring the greatly lower temporal complexity.

Research Highlights.

Research Highlights.

Design of Metaheuristic Optimization Algorithms for Deep Learning Model for Secure IoT Environment

Because of the rise in the number of cyberattacks, the devices that make up the Internet of Things (IoT) environment are experiencing increased levels of security risks. In recent years, a significant number of centralized systems have been developed to identify intrusions into the IoT environment. However, due to diverse requirements of IoT devices such as dispersion, scalability, resource restrictions, and decreased latency, these strategies were unable to achieve notable outcomes. The present paper introduces two novel metaheuristic optimization algorithms for optimizing the weights of deep learning (DL) models, use of DL may help in the detection and prevention of cyberattacks of this nature. Furthermore, two hybrid DL classifiers, i.e., convolutional neural network (CNN) + deep belief network (DBN) and bidirectional long short-term memory (Bi-LSTM) + gated recurrent network (GRU), were designed and tuned using the already proposed optimization algorithms, which results in ads to improved model accuracy. The results are evaluated against the recent approaches in the relevant field along with the hybrid DL classifier. Model performance metrics such as accuracy, rand index, f-measure, and MCC are used to draw conclusions about the model’s validity by employing two distinct datasets. Regarding all performance metrics, the proposed approach outperforms both conventional and cutting-edge methods.

An efficient entropy based dissimilarity measure to cluster categorical data

Clustering is an unsupervised learning technique that discovers intrinsic groups based on proximity between data points. Therefore, the performance of clustering techniques mainly relies on the proximity measures used to compute the (dis)similarity between the data objects. In general, it is relatively easier to compute the distance between numerical data points as numerical operations can directly be applied to values along features. However, for categorical datasets, computing the (dis)similarity between the data objects becomes a non-trivial problem. Therefore, in this paper, we propose a new distance metric based on the information theoretic approach to compute the dissimilarity between categorical data points. We compute entropy along each feature to capture the intra-attribute statistical information, based on which significance of attributes are decided during clustering. The proposed measure is free from any domain-dependent parameters and also does not rely on the distribution of data points. Experiment is conducted over diversified benchmark data sets, considering six competing proximity measures with three popular clustering algorithms and the clustering results are compared in terms of RI (Rand Index), ARI (Adjusted Rand Index), CA (Clustering Accuracy) and Cluster Discrimination Matrix (CDM). Over 85 percent of the data sets, the clustering accuracy of the proposed metric embedded with K-Mode and Weighted K-Mode outperforms its counterparts. Approximately, 0.2951 s is needed by the proposed metric to cluster a data set having 10,000 data points with 8 attributes and 2 clusters on a standard desktop machine. Overall, experimental results demonstrate the efficacy of the proposed metric to handle complex real datasets of different characteristics.

United States Federal Emergency Management Agency regional clustering by disaster exposure: a new paradigm for disaster response.

The Federal Emergency Management Agency (FEMA) divides the United States (US) into ten standard regions to promote local partnerships and priorities. These divisions, while longstanding, do not adequately address known hazard risk as reflected in past federal disaster declarations. From FEMA's inception in 1979 until 2020, the OpenFEMA dataset reports 4127 natural disaster incidents declared by 53 distinct state-level jurisdictions, listed by disaster location, type, and year. An unsupervised spectral clustering (SC) algorithm was applied to group these jurisdictions into regions based on affinity scores assigned to each pair of jurisdictions accounting for both geographic proximity and historical disaster exposures. Reassigning jurisdictions to ten regions using the proposed SC algorithm resulted in an adjusted Rand index (ARI) of 0.43 when compared with the existing FEMA regional structure, indicating little similarity between the current FEMA regions and the clustering results. Reassigning instead into six regions substantially improved cluster quality with a maximized silhouette score of 0.42, compared to a score of 0.34 for ten regions. In clustering US jurisdictions not only by geographic proximity but also by the myriad hazards faced in relation to one another, this study demonstrates a novel method for FEMA regional allocation and design that may ultimately improve FEMA disaster specialization and response.

EGRC-Net: Embedding-Induced Graph Refinement Clustering Network.

Existing graph clustering networks heavily rely on a predefined yet fixed graph, which can lead to failures when the initial graph fails to accurately capture the data topology structure of the embedding space. In order to address this issue, we propose a novel clustering network called Embedding-Induced Graph Refinement Clustering Network (EGRC-Net), which effectively utilizes the learned embedding to adaptively refine the initial graph and enhance the clustering performance. To begin, we leverage both semantic and topological information by employing a vanilla auto-encoder and a graph convolution network, respectively, to learn a latent feature representation. Subsequently, we utilize the local geometric structure within the feature embedding space to construct an adjacency matrix for the graph. This adjacency matrix is dynamically fused with the initial one using our proposed fusion architecture. To train the network in an unsupervised manner, we minimize the Jeffreys divergence between multiple derived distributions. Additionally, we introduce an improved approximate personalized propagation of neural predictions to replace the standard graph convolution network, enabling EGRC-Net to scale effectively. Through extensive experiments conducted on nine widely-used benchmark datasets, we demonstrate that our proposed methods consistently outperform several state-of-the-art approaches. Notably, EGRC-Net achieves an improvement of more than 11.99% in Adjusted Rand Index (ARI) over the best baseline on the DBLP dataset. Furthermore, our scalable approach exhibits a 10.73% gain in ARI while reducing memory usage by 33.73% and decreasing running time by 19.71%. The code for EGRC-Net will be made publicly available at https://github.com/ZhihaoPENG-CityU/EGRC-Net.

Application of machine learning to associative scRNA-seq data gene expression and alternative polyadenylation sites clustering

Cell type identification is a vital step in the analysis of scRNA-seq data. Transcriptome subtype pivotal information such as alternative polyadenylation (APA) obtained from standard scRNA-seq data can also provide valid clues for cell type identification with no alteration of experimental techniques or increased experimental costs. Furthermore, using multimodal analysis techniques and their methods, more confident cell type identification results can be obtained. For that purpose, we constructed a workflow framework: On five different scRNA-seq datasets, 18 methods based on machine learning that have not yet been applied to identify cell types by association APA and single-cell gene expression fusion were compared with three single-cell clustering methods, and compared these method against the advanced method scLAPA based on similarity network fusion (SNF). In our experiments, we used the adjusted Rand index (ARI) as a metric. We found that unsupervised methods like WMSC and supervised methods like MOGONET have more robust and excellent results in associating APA with single-cell gene expression clustering than methods based only on single-cell gene expression clustering and advanced scLAPA methods.

Effective Customer Review Analysis Using Combined Capsule Networks with Matrix Factorization Filtering

Nowadays, commercial transactions and customer reviews are part of human life and various business applications. The technologies create a great impact on online user reviews and activities, affecting the business process. Customer reviews and ratings are more helpful to the new customer to purchase the product, but the fake reviews completely affect the business. The traditional systems consume maximum time and create complexity while analyzing a large volume of customer information. Therefore, in this work optimized recommendation system is developed for analyzing customer reviews with minimum complexity. Here, Amazon Product Kaggle dataset information is utilized for investigating the customer review. The collected information is analyzed and processed by batch normalized capsule networks (NCN). The network explores the user reviews according to product details, time, price purchasing factors, etc., ensuring product quality and ratings. Then effective recommendation system is developed using a butterfly optimized matrix factorization filtering approach. Then the system’s efficiency is evaluated using the Rand Index, Dunn index, accuracy, and error rate.

Unsupervised Learning-based New Seed-Expanding Approach using Influential Nodes for Community Detection in Social Networks

Several recent studies focus on community structure due to its importance in analyzing and understanding complex networks. Communities are groups of nodes highly connected with themselves and not much connected to the rest of the network. Community detection helps us to understand the properties of the dynamic process within a network. In this paper, we propose a novel seed-centric approach based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) and k-means algorithm to find communities in a social network. TOPSIS is used to find the seeds within this network using the benefits of multiple measure centralities. The use of a single centrality to determine seeds within a network, like in classical algorithms of community detection, doesn’t succeed in the majority of cases to reach the best selection of seeds. Therefore, we consider all centrality metrics as a multi-attribute of TOPSIS and we rank nodes based on the TOPSIS’ relative closeness. The Top-K nodes extracted from TOPSIS will be considered as seeds in the proposed approach. Afterwards, we apply the k-means algorithm using these seeds as starting centroids to detect and construct communities within a social network. The proposed approach is tested on Facebook ego network and validated on the famous dataset having the ground-truth community structure Zachary karate club. Experimental results on Facebook ego network show that the dynamic k-means provides reasonable communities in terms of distribution of nodes. These results are confirmed using Zachary karate club. Two detected communities are detected with higher normalized mutual information NMI and Adjusted Rand Index ARI compared to other seed centric algorithms such as Yasca, LICOD, etc. The proposed method is effective, feasible, and provides better results than other available state-of-the-art community detection algorithms.

An intelligent extraction approach of feature information from three-dimensional DAD chromatogram for integrated quality control of traditional Chinese medicines: Gardenia jasminoides root as an example.

Traditional Chinese medicine (TCM) fingerprinting, which has the characteristics of holism and ambiguity, is a conventional strategy for the holistic quality control of TCMs. However, the fingerprinting of TCMs at the current stage generally adopts a single wavelength or few wavelengths, lacking the effective utilization of diode-array detector (DAD) chromatogram data. This study proposes an intelligent extraction approach of feature information from a three-dimensional DAD chromatogram to establish a novel bar-form-diagram (BFD) for integrated quality control of TCMs. The BFD was automatically established by the chromatographic and spectral information of a complex hybrid system in a DAD chromatogram. This covered the peak areas of target compositions at the optimal absorption wavelength. Taking 27 batches of Gardenia jasminoides root as samples, the BFD combined with chemometrics was applied for assessing the quality of samples completely, which improved the accuracy of origin classification using hierarchical cluster analysis, principal component analysis, soft independent modeling of class analogy and orthogonal partial least squares discriminant analysis. Single-wavelength fingerprinting and BFD used 23 and 38 common peaks as variables respectively, and the adjusted rand index results of the single wavelength and BFD were 0.559 and 0.819, respectively. Compared with the ergodic methods of each single wavelength, the peak recognition method in this study improved the operation speed from 180 s to 4 s and the computational complexity. The established BFD approach performed more abundant characteristic information of chemical components of TCMs and more accurate origin classification ability, and it had great advantages in the overall quality control of TCMs.

An Efficient Method to Accurately Cluster Large Number of High Dimensional Facial Images

Accurately clustering large, high dimensional datasets is a challenging problem in unsupervised learning. K-means is considered to be a fast, widely used and accurate centroid based data partitioning algorithm for spherical datasets. However, its non-determinism and heavy dependence on the selection of initial cluster centers along with vulnerability to noise make it a poor candidate for clustering large datasets with high dimensionality. To overcome these, we develop a novel, nature inspired, centroid based clustering algorithm, inspired from the principles of particle physics. Our method ensures that the convergence to local optima and non-deterministic outputs are avoided. We experiment the method on large datasets of human face images. Besides, our method addresses the problem of outliers and presence of not well-separated data in these datasets. We use a deep learning model for extracting facial features into a vector of 128 dimensions. We validate the quality and accuracy of our methods using different statistical parameters like <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f-measure, accuracy, error rate, average in group proportion and normalized cluster size rand index</i> . These evaluations show that our method exhibits better accuracy and quality in clustering large face image datasets, in comparison with other existing mechanisms. The strength of our algorithms is more visible as the size of the dataset grows.

Distribution preserving-based deep semi-NMF for data representation

The semi-nonnegative matrix factorization (Semi-NMF) is a promising soft K-means clustering technique. Deep Semi-NMF, which stacks one-layer Semi-NMF into multi-layer, is able to learn the hierarchical projections and can obtain the deep hidden representations according to the unknown attributes of the given data. On the other hand, the inherent structure of the each data cluster can be described by the distribution of the intraclass data. Then one hopes to learn the new deep hidden representations which can preserve the intrinsic structures embedded in the original data space perfectly. Here seamlessly integrating the benefits of the Deep Semi-NMF and the distribution preserving strategy, we propose a novel distribution preserving-based deep semi-nonnegative matrix factorization method (DPNMF) to achieve this goal. In DPNMF, by maintaining the consistency of two distributions that can approximate the manifold structures, we can seek the deep hidden features which reveal the original intrinsic structures. As a result, the manifold structures in the raw data are well preserved in the new feature space. We also devise an adaptive projected Barzilai-Borwein method to optimize the proposed constrained objective function efficiently. The experimental results on the several real-world datasets show that the proposed DPNMF can achieve advantageous clustering performance in terms of accuracy (ACC), normalized mutual information (NMI), and adjusted rand index (ARI).

Subtyping of Campylobacter coli isolated from raw poultry meat in retail markets using amplified intergenic locus polymorphism - A novel rapid subtyping method

In order to provide more phylogenetic information of Campylobacter coli in large-scale epidemiological investigation, this work was undertaken to develop a novel genotyping method based on amplified intergenic locus polymorphism (AILP), by using pulsed-field gel electrophoresis (PFGE; using SmaI enzymes) as control. Eleven pairs of primers were selected to type C. coli strains for this purpose. A total of 68 C. coli isolates recovered from 51 retail raw chicken and 37 retail raw duck were subtyped. The Simpson's index of diversity (SID) of AILP and PFGE, as well as the adjusted Rand index (AR) and the adjusted Wallace coefficient (AW) between AILP and PFGE, were calculated. The new AILP method differentiated 68 C. coli isolates into 55 different subtypes (SID = 0.993), compared with 46 different profiles obtained from PFGE (SID = 0.980). The SID value of the AILP method was improved with the increasing number of primers, and a combination of 7 loci was selected as the optimal combination. The congruent analysis of the AILP method and PFGE showed moderate congruence between the two methods (AR = 0.462). The AW indicated that if AILP data is the available one can confidently predict the PFGE cluster. The results of this study showed that the AILP method had higher discrimination than PFGE and also allowed for significant reduction in time and cost.

DiviK: divisive intelligent K-means for hands-free unsupervised clustering in big biological data

BackgroundInvestigating molecular heterogeneity provides insights into tumour origin and metabolomics. The increasing amount of data gathered makes manual analyses infeasible—therefore, automated unsupervised learning approaches are utilised for discovering tissue heterogeneity. However, automated analyses require experience setting the algorithms’ hyperparameters and expert knowledge about the analysed biological processes. Moreover, feature engineering is needed to obtain valuable results because of the numerous features measured.ResultsWe propose DiviK: a scalable stepwise algorithm with local data-driven feature space adaptation for segmenting high-dimensional datasets. The algorithm is compared to the optional solutions (regular k-means, spatial and spectral approaches) combined with different feature engineering techniques (None, PCA, EXIMS, UMAP, Neural Ions). Three quality indices: Dice Index, Rand Index and EXIMS score, focusing on the overall composition of the clustering, coverage of the tumour region and spatial cluster consistency, are used to assess the quality of unsupervised analyses. Algorithms were validated on mass spectrometry imaging (MSI) datasets—2D human cancer tissue samples and 3D mouse kidney images. DiviK algorithm performed the best among the four clustering algorithms compared (overall quality score 1.24, 0.58 and 162 for d(0, 0, 0), d(1, 1, 1) and the sum of ranks, respectively), with spectral clustering being mostly second. Feature engineering techniques impact the overall clustering results less than the algorithms themselves (partial eta ^2 effect size: 0.141 versus 0.345, Kendall’s concordance index: 0.424 versus 0.138 for d(0, 0, 0)).ConclusionsDiviK could be the default choice in the exploration of MSI data. Thanks to its unique, GMM-based local optimisation of the feature space and deglomerative schema, DiviK results do not strongly depend on the feature engineering technique applied and can reveal the hidden structure in a tissue sample. Additionally, DiviK shows high scalability, and it can process at once the big omics data with more than 1.5 mln instances and a few thousand features. Finally, due to its simplicity, DiviK is easily generalisable to an even more flexible framework. Therefore, it is helpful for other -omics data (as single cell spatial transcriptomic) or tabular data in general (including medical images after appropriate embedding). A generic implementation is freely available under Apache 2.0 license at https://github.com/gmrukwa/divik.