Humoral-mediated clustering

The k-means clustering algorithm is a very classical clustering algorithm that is widely used because of its excellent efficiency and performance. The algorithm uses Euclidean distance to calculate the similarity between samples and iteratively updates the membership matrix to obtain clustering results. However, when k-means algorithm clusters datasets containing samples with intra-cluster distances greater than inter-cluster distances, errors often occur when partitioning the boundary samples, which eventually leads to unsatisfactory results. Moreover, although k-means algorithm makes the intra-cluster distance as small as possible, it neglects to maximize the inter-cluster distance, and eventually only finds the local optimal solution. Different from the existing k-means type algorithm, this paper proposes a similarity measure based on the impact factor, which determines the partitioning result by comparing the impact of samples on each cluster. And on the basis of the objective function of k-means algorithm, we combine the inter-cluster distance to solve the defects of local optimality that exist in k-means algorithm. In the paper, we theoretically analyze and prove the proposed method, and compare and analyze the clustering results of the algorithm with the class k-means algorithm on real datasets, and confirm that the proposed algorithm in this paper can effectively avoid the defects of the class k-means algorithm.

This work is an extension of our previous attempt to construct a spatial representation of 21 initial consonants in Thai by partitioning them into homogeneous clusters based on empirical measures of confusability and distance among phonemes. The measures were taken from perceptual identification performance of 28 listeners (seven full subjects) when stimuli were presented in noise. In present study, two methods of clustering, namely Multidimensional scaling analysis and k-means clustering were employed, yielding six different classifications and four perceptually relevant categories: intra-cluster short distance, intra-cluster long distance, inter-cluster short distance, and inter-cluster long distance. Another set of perceptual experiment (eight listeners; two full subjects) was carried out to verify the predictions. The findings reveal that the derived perceptual clusters and defined categories fit relatively well with the listeners' performance. Distinctive feature systems in phonological theory appear to provide some basis for the clustering of phonemes.

Genetic divergence among 32 Ashwagandha (Withania somnifera (L.) Dunal) accessions of different geographic origins was assessed using Mahalanobis D2 statistics. Observations revealed significant genotypic differences, and accordingly, genotypes were classified into six clusters. Cluster I was the largest, with twenty genotypes, followed by the cluster II, which has eight, and clusters III, IV, V, and VI contained only one most divergent genotype. The maximum divergence was observed between clusters II and III (D2 = 47.90), followed by clusters V and VI (D2 = 43.95), and clusters III and VI (D2 = 42.29). Cluster IV had the least inter-cluster distance (D2 = 22.82) with cluster VI. Clusters III, IV, V, and VI had only one genotype each, and hence, the intra-cluster distance was zero. The genotype of cluster V was unique as it had the highest values for fresh and dry root weight per plant, diameter and length of the main root, number of secondary roots per plant, number of berries per plant, and girth of stem with a high seed yield per plant. Cluster VI was desirable in respect of days to 50 per cent flowering and days to root harvest. Cluster II exhibited the highest value for height of plant and branches per plant. Cluster IV had the highest mean values for the number of seeds per berry. Thus, hybridization among these genotypes can generate desirable transgressive segregants. Aim of Studies: To assess the genetic divergen of Withania somnifera. Place and Duration of Study: Department of Horticulture, College of Agriculture, UAS, GKVK, Bengaluru from 2020-21 to 2021-22. Methodology: The genetic divergence between the genotypes in the population was estimated using formula D2= p (Yit - Yjt) and genetic divergence among 32 Ashwagandha (Withania somnifera (L.) Dunal) accessions of different geographic origins was assessed using Mahalanobis D2 statistics. Observations revealed significant genotypic differences, and accordingly. Results: Observations revealed significant genotypic differences, and accordingly, genotypes were classified into six clusters. Cluster I was the largest, with twenty genotypes, followed by the cluster II, which has eight, and clusters III, IV, V, and VI contained only one most divergent genotype. The maximum divergence was observed between clusters II and III (D2 = 47.90), followed by clusters V and VI (D2 = 43.95), and clusters III and VI (D2 = 42.29). Cluster IV had the least inter-cluster distance (D2 = 22.82) with cluster VI. Clusters III, IV, V, and VI had only one genotype each, and hence, the intra-cluster distance was zero. The genotype of cluster V was unique as it had the highest values for fresh and dry root weight per plant, diameter and length of the main root, number of secondary roots per plant, number of berries per plant, and girth of stem with a high seed yield per plant. Cluster VI was desirable in respect of days to 50 per cent flowering and days to root harvest. Cluster II exhibited the highest value for height of plant and branches per plant. Cluster IV had the highest mean values for the number of seeds per berry Conclusion of finding: Significant genetic divergence and complementarity for most features has been shown by the genotypes of clusters II and III and clusters V and VI. This could lead to significant genetic improvement for particular characters and their selection for new varieties.

Genetic divergence study among 45 brinjal genotypes was performed using Mahalanobsis D2 statistics to find prospective genotypes for use in a breeding programme. The genotypes were assessed for 11 traits and divided into twelve clusters based on Tocher’s method. Cluster I had the most genotypes (18), followed by cluster III (5), cluster V (4), cluster IV, VI and IX (3 each), cluster II, VII and X (2 each) and cluster VIII, XI and XII (1 each). The intracluster distances ranged between 0 and 1064.87. Cluster X has the largest intra-cluster distance (1064.87), followed by Cluster IV (831.08). Cluster VIII, XI, and XII had the smallest intra-cluster distance (0). The inter-cluster distances varied from 804.88 to 4758.26. The largest inter-cluster distance was between IX and XI (4758.26), followed by III and XII (3923.90), and the shortest distance was between cluster II and III (804.88). Genotypes from the cluster with a large inter-cluster distance could be selected as parents to produce superior F1 hybrids and segregants. The three characters, fruit length (29.70%), number of primary branches (18.89%), and plant height (14.55%), altogether account for 63.14% of overall divergence. As a result, the combination of those traits could be exploited to develop superior varieties with higher yields.

A novel validity index with dynamic cut-off for determining true clusters

An enormous amount of microarray data has been generated and archived for a large variety of biological studies such as gene expression. In order to analyze gene expression data, many clustering algorithms have been proposed, but very few techniques have been developed to evaluate those clustering algorithms. A clustering evaluation method is used to find the degree of similarity between members of the same clusters and members of different clusters. We propose a new clustering evaluation technique F-Statistics Algorithm for Clustering Evaluation (FACE), which uses both inter-cluster and intracluster distances, and can be used to improve performance of clustering methods. We describe and evaluate FACE in the context of bioinformatics clustering by comparison with existing evaluation measurements on a set of yeast data. Results show that FACE is more stable and makes better conclusions.

In an effort to achieve improved classifier accuracy, extensive research has been conducted in classifier ensembles. Very recently, cluster ensembles have emerged. It is well known that off-the-shelf clustering methods may discover different structures in a given set of data. This is because each clustering algorithm has its own bias resulting from the optimization of different criteria. Furthermore, there is no ground truth against which the clustering result can be validated. Thus, no cross-validation technique can be carried out to tune input parameters involved in the clustering process. As a consequence, the user is not equipped with any guidelines for choosing the proper clustering method for a given dataset. Cluster ensembles offer a solution to challenges inherent to clustering arising from its ill-posed nature. Cluster ensembles can provide more robust and stable solutions by leveraging the consensus across multiple clustering results, while averaging out emergent spurious structures that arise due to the various biases to which each participating algorithm is tuned. In this chapter, we discuss the problem of combining multiple weighted clusters, discovered by a locally adaptive algorithm (Domeniconi, Papadopoulos, Gunopulos, & Ma, 2004) which detects clusters in different subspaces of the input space. We believe that our approach is the first attempt to design a cluster ensemble for subspace clustering (Al-Razgan & Domeniconi, 2006). Recently, several subspace clustering methods have been proposed (Parsons, Haque, & Liu, 2004). They all attempt to dodge the curse of dimensionality which affects any algorithm in high dimensional spaces. In high dimensional spaces, it is highly likely that, for any given pair of points within the same cluster, there exist at least a few dimensions on which the points are far apart from each other. As a consequence, distance functions that equally use all input features may not be effective. Furthermore, several clusters may exist in different subspaces comprised of different combinations of features. In many real-world problems, some points are correlated with respect to a given set of dimensions, while others are correlated with respect to different dimensions. Each dimension could be relevant to at least one of the clusters. Global dimensionality reduction techniques are unable to capture local correlations of data. Thus, a proper feature selection procedure should operate locally in input space. Local feature selection allows one to embed different distance measures in different regions of the input space; such distance metrics reflect local correlations of data. In (Domeniconi, Papadopoulos, Gunopulos, & Ma, 2004) we proposed a soft feature selection procedure (called LAC) that assigns weights to features according to the local correlations of data along each dimension. Dimensions along which data are loosely correlated receive a small weight, which has the effect of elongating distances along that dimension. Features along which data are strongly correlated receive a large weight, which has the effect of constricting distances along that dimension. Thus the learned weights perform a directional local reshaping of distances which allows a better separation of clusters, and therefore the discovery of different patterns in different subspaces of the original input space.

Genetic divergence among 44 genotypes of Indian mustard was estimated using Mahalanobis' D2 statistics and total of 14 clusters were formed in timely sown condition and 7 clusters in late sown condition. Cluster I had maximum number of genotypes (27) in timely sown condition followed by cluster IV with 4 genotypes and cluster XIV with 2 genotypes all the other clusters viz. Cluster II, III, V, VI, VII, VIII, IX, X, XI, XII and XIII had one genotype each in them. In late sown condition out of 7 clusters formed Cluster I had maximum (34) number of genotypes followed by cluster II and cluster IV with 4 & 2 genotypes respectively while cluster III, V, VI and VII had one genotype each. Inter Cluster distance was observed highest between cluster IX and Cluster XIV (458.52) followed by cluster VIII and cluster XIV (367.37) and cluster II cluster XIV having a distance of 334.49 in timely sown condition. Larger distances between the clusters suggest more genetic diversity between the genotypes present in them which mean genotypes present in these clusters can be used as parents in breeding programmes. In late sown condition Cluster VI and Cluster VII showed highest maximum distance of 1138.26 followed by clusters II and VII exhibiting a distance of 1125.53 and cluster IV and Cluster VII at a distance of 679.73 in late sown condition. Intra cluster distance showed a maximum distance in cluster I (149.87) followed by cluster II (149.34). Four clusters Cluster III, V, VI and VII showed a intra cluster distance of zero in late sown condition. Cluster I and cluster II can be used in breeding programmes owing to their large intra cluster distance. In timely sown condition Cluster XIV (100.18) followed by cluster IV & cluster I showed a distance of 92.19 & 81.36 respectively. All the other clusters showed an intra cluster distance of zero, showing no intra cluster diversity. Therefore, it was concluded that more emphasis should be given on cluster VI for selecting genotypes as parents for crossing with the genotypes of cluster I which may produce new recombinants with desired traits.

Fuzzy clustering has emerged as a powerful technique for analyzing complex, uncertain, and high-dimensional data across diverse application domains, including pattern recognition, bioinformatics, image analysis, and decision support systems. Unlike classical clustering, which assigns each data instance to a single cluster, fuzzy clustering allows partial membership, thereby capturing inherent ambiguity in real-world datasets. This review provides a comprehensive examination of heuristic-based fuzzy clustering algorithms. We begin by outlining the fundamental concepts of clustering, fuzzy set theory, and the principles of fuzzy clustering. Subsequently, we discuss the evolution of core algorithms, including Fuzzy C-Means (FCM) and Possibilistic C-Means (PCM), and highlight significant modifications derived from altering distance metrics, objective functions, and optimization strategies. Particular emphasis is placed on heuristic and metaheuristic enhancements—such as genetic algorithms, particle swarm optimization, and artificial immune systems—that address the limitations of classical approaches, including sensitivity to initialization, susceptibility to noise and outliers, and premature convergence. Recent contributions in hybrid fuzzy clustering are also reviewed, with attention to their strengths, weaknesses, and potential applications. Finally, we synthesize insights from the literature to categorize the persistent disadvantages of existing methods and identify promising directions for future research, including adaptive fuzzifiers, noise-resilient models, and integration with evolutionary computation. This study not only consolidates advances in heuristic-based fuzzy clustering but also provides guidance for researchers aiming to design more robust, scalable, and application-driven clustering algorithms.

Recently, there has been a surge in the development of robust norm distance-based linear discriminant analysis (LDA) techniques, which have garnered significant attention in the field of feature extraction. However, a persistent issue that has yet to be resolved is that the successful suppression of outliers may inadvertently impede the accurate discrimination of normal points. To solve this problem, we, in this article, study a novel robust LDA measured by double capped $L_{p}$ -norm distance (CLD) metrics with min constraints (DCLDA) to learn robust discriminant projections, in which normal points and outliers are separately treated. To be specific, it takes a double capped $L_{p}$ -norm with "Min" constraints in the proposed model to measure the distances for between- and within-class dispersions. The proposed model effectively ensures accurate discrimination of normal points by $L_{p}$ -norm, while also eliminating the exaggerated effect of outliers that may arise from larger $p$ values. The resulted objective is not trivial because of its nonconvexity and nonsmoothness. As one of the major contributions of this article, we introduce a new reformulation that provides an objective problem theoretically equivalent to the original. By this reformulation, we develop an effective iterative algorithm to solve the proposed model. The algorithm is proven to be convergent through rigorous theoretical analysis. Extensive experiments were conducted on several real-world datasets across different image classification tasks to showcase the effectiveness of the proposed method.

Ensemble learning for anomaly detection has been barely studied, due to difficulty in acquiring ground truth and the lack of inherent objective functions. In contrast, ensemble approaches for classification and clustering have been studied and effectively used for long. Our work taps into this gap and builds a new ensemble approach for anomaly detection, with application to event detection in temporal graphs as well as outlier detection in no-graph settings. It handles and combines multiple heterogeneous detectors to yield improved and robust performance. Importantly, trusting results from all the constituent detectors may deteriorate the overall performance of the ensemble, as some detectors could provide inaccurate results depending on the type of data in hand and the underlying assumptions of a detector. This suggests that combining the detectors selectively is key to building effective anomaly ensembles—hence “less is more”. In this paper we propose a novel ensemble approach called SELECT for anomaly detection, which automatically and systematically selects the results from constituent detectors to combine in a fully unsupervised fashion. We apply our method to event detection in temporal graphs and outlier detection in multi-dimensional point data (no-graph), where SELECT successfully utilizes five base detectors and seven consensus methods under a unified ensemble framework. We provide extensive quantitative evaluation of our approach for event detection on five real-world datasets (four with ground truth events), including Enron email communications, RealityMining SMS and phone call records, New York Times news corpus, and World Cup 2014 Twitter news feed. We also provide results for outlier detection on seven real-world multi-dimensional point datasets from UCI Machine Learning Repository. Thanks to its selection mechanism, SELECT yields superior performance compared to the individual detectors alone, the full ensemble (naively combining all results), an existing diversity-based ensemble, and an existing weighted ensemble approach.

The density peaks clustering (DPC) algorithm can identify clusters with various shapes and densities in the underlying dataset. However, the DPC algorithm cannot exactly find the true quantity of clustering centers when computing the local density, and it is difficult to handle non-convex datasets. Moreover, the DPC algorithm is difficult to identify boundary points and outliers without a reasonable allocation strategy when dealing with low-density points. To solve these limitations, a novel deviation density peaks clustering (DeDPC) algorithm is proposed. First, the local deviation of the spatial distance of datasets with different structures is utilised to replace the local density to generate a more reasonable clustering center decision graph. Second, a threshold is defined to further divide and process low-density points. Finally, outliers in low-density points can be accurately found to accurately cluster the dataset. To evaluate the performance of the DeDPC algorithm, experiments are conducted on synthetic and real-world datasets and the DeDPC is compared with other clustering methods. The DeDPC is also applied to medical image segmentation to further demonstrate its capability for medical image processing. The simulation results show that the DeDPC method has good validity and utility for both non-convex datasets and medical image segmentation.

Density Peak Clustering (DPC) is a widely used clustering method that automatically identifies cluster centers based on local density and distance metrics. However, DPC tends to converge to local optimal solutions when processing datasets with uneven density distributions. This paper proposes DPC-DIST, an improved algorithm that addresses this limitation through a geometric distribution coefficient δ . By incorporating spatial distribution characteristics into density calculations, DPC-DIST effectively prevents convergence to suboptimal solutions. Comprehensive experiments on six benchmark datasets (Wine, Iris, Seeds, Blobs, R15, R3) demonstrate that DPC-DIST consistently outperforms the original DPC, K-means++, and spectral clustering algorithms. Significant improvements were observed in high-dimensional data processing, with 9.3 % increase in Silhouette Coefficient and 47.7 % improvement in Calinski-Harabasz Score on the Wine dataset. The algorithm shows particular advantages in facility location optimization and logistics planning applications, demonstrating its practical value for real-world scenarios.

In this study, six types of arrhythmia beats observed in ECG signals have been analysed by using clustering methods. A set of morphological properties and windowed raw ECG data are used as feature vectors in clustering algorithms. Purpose of the analysis is to see if the examined arrhytmia types form natural groups in the feature spaces. The performances of the clustering algorithms are tested by different distance metrics and algorithms. The results are examined based on the average sensitivity, specificity, selectivity and accuracy of the classifier. The results show that k-means clustering technique with the distance parameter set at cosine values by using the windowed raw data features give better results. Results also show that analyzed arrythmia types do not form distinct clusters in examined feature spaces. On the other hand, in some cases very high specificity results are observed for some arrythmia types. That means suggested features could be quite useful in elimination processes in hierarchic classifiers.

In this current study, a comprehensive examination encompassing 72 distinct rice genotypes from the Germplasm collection was conducted. Notable checks, Sarjoo-52, NDR-2065, and MTU-7029, exhibited a broad spectrum of variations in multiple traits during the kharif season of 2022. The assessment, conducted at CRS Masodha of Acharya Narendra Deva University of Agriculture and Technology, Narendra Nagar (Kumarganj), Ayodhya, involved a meticulously designed experiment with 8 blocks and 11 plots each. The parameters under scrutiny included days to 50% flowering, days to maturity, plant height, panicle length, number of productive tillers per plant, flag leaf area, fertile spikelet per panicle, spikelet fertility percentage per panicle, biological yield, harvest index, 1000-grain weight, and grain yield. Employing non-hierarchical Euclidean cluster analysis, the 72 genotypes were classified into 11 clusters. Cluster (IX) exhibited the highest number of entries (9), followed by clusters (V), (VIII), and (XI) with 8 entries each. Clusters (I), (VI), and (VII) comprised 7 entries each, while clusters (II), (III), and (IV) contained 6 entries each, and cluster (X) had only 3 entries. Noteworthy intra-cluster and inter-cluster distances were observed, with cluster (X) displaying the highest intra-cluster distance (27.97) and cluster (I) exhibiting the lowest (3.88). The maximum inter-cluster distance was noted between cluster (X) and cluster (IV) (36.24), while the minimum inter-cluster distance was observed between cluster (VII) and cluster (VI) (12.516). Lines from distinct clusters demonstrating high-performance traits in the desired direction may be considered as potential parental choices for future breeding programs.