Evaluation of Partitioning Around Medoids Algorithm with Various Distances on Microarray Data

Clustering is the most common method for organizing unlabeled data into its natural groups (called clusters), based on similarity (in some sense or another) among data objects. The Partitioning Around Medoids (PAM) algorithm belongs to the partitioning-based methods of clustering widely used for objects categorization, image analysis, bioinformatics and data compression, but due to its high time complexity, the PAM algorithm cannot be used with large datasets or in any embedded or real-time application. In this work, we propose a simple and scalable parallel architecture for the PAM algorithm to reduce its running time. This architecture can easily be implemented either on a multi-core processor system to deal with big data or on a reconfigurable hardware platform, such as FPGA and MPSoCs, which makes it suitable for real-time clustering applications. Our proposed model partitions data equally among multiple processing cores. Each core executes the same sequence of tasks simultaneously on its respective data subset and shares intermediate results with other cores to produce results. Experiments show that the computational complexity of the PAM algorithm is reduced exponentially as we increase the number of cores working in parallel. It is also observed that the speedup graph of our proposed model becomes more linear with the increase in number of data points and as the clusters become more uniform. The results also demonstrate that the proposed architecture produces the same results as the actual PAM algorithm, but with reduced computational complexity.

Quantum computing is a promising paradigm that can provide viable solutions to high-complexity problems. The $k$-medoids algorithm is a powerful clustering method ubiquitously used in data mining, image processing, pattern recognition, etc. The core of $k$-medoids algorithm is to perform cluster assignment and center update, which are time-consuming for large data sets. A\"{\i}meur et al. proposed a quantum $k$-medoids algorithm [A\"{\i}meur, Brassard, and Gambs, Mach. Learn. 90, 261 (2013)] by quantizing the center update. Nevertheless, it has a query complexity $O({N}^{3/2})$ for one iteration, which is computationally expensive for a large $N$ where $N$ is the number of points. In this paper, we propose a complete quantum algorithm for $k$-medoids algorithm. Specifically, in cluster assignment, we devise a quantum subroutine to calculate the Manhattan distance between any two points and then assign all points to the closest center in parallel, which is faster than what is achievable classically. In center update, for a cluster, we use parallel amplitude estimation to calculate the average distance of each point to all the others. It makes our algorithm polynomially faster than the algorithm of A\"{\i}meur et al., whose sum of distances of each point to all the others is computed by adding the distances one by one. Our quantum $k$-medoids algorithm, with time complexity $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{O}({N}^{1/2})$, achieves a polynomial speedup in $N$ compared to the existing one.

This paper presents a new coherency identification method for dynamic reduction of a power system. To achieve dynamic reduction, coherency-based equivalence techniques divide generators into groups according to coherency, and then aggregate them. In order to minimize the changes in the dynamic response of the reduced equivalent system, coherency identification of the generators should be clearly defined. The objective of the proposed coherency identification method is to determine the optimal coherent groups of generators with respect to the dynamic response, using the Partitioning Around Medoids (PAM) algorithm. For this purpose, the coherency between generators is first evaluated from the dynamic simulation time response, and in the proposed method this result is then used to define a dissimilarity index. Based on the PAM algorithm, the coherent generator groups are then determined so that the sum of the index in each group is minimized. This approach ensures that the dynamic characteristics of the original system are preserved, by providing the optimized coherency identification. To validate the effectiveness of the technique, simulated cases with an IEEE 39-bus test system are evaluated using PSS/E. The proposed method is compared with an existing coherency identification method, which uses the K-means algorithm, and is found to provide a better estimate of the original system.

One hundred and sixty-eight genotypes of cotton from the same growing region were used as a germplasm group to study the validity of different genetic distances in constructing cotton core subset. Mixed linear model approach was employed to unbiasedly predict genotypic values of 20 traits for eliminating the environmental effect. Six commonly used genetic distances (Euclidean, standardized Euclidean, Mahalanobis, city block, cosine and correlation distances) combining four commonly used hierarchical cluster methods (single distance, complete distance, unweighted pair-group average and Ward's methods) were used in the least distance stepwise sampling (LDSS) method for constructing different core subsets. The analyses of variance (ANOVA) of different evaluating parameters showed that the validities of cosine and correlation distances were inferior to those of Euclidean, standardized Euclidean, Mahalanobis and city block distances. Standardized Euclidean distance was slightly more effective than Euclidean, Mahalanobis and city block distances. The principal analysis validated standardized Euclidean distance in the course of constructing practical core subsets. The covariance matrix of accessions might be ill-conditioned when Mahalanobis distance was used to calculate genetic distance at low sampling percentages, which led to bias in small-sized core subset construction. The standardized Euclidean distance is recommended in core subset construction with LDSS method.

The security and integrity of computer systems and networks highly depend on malware detection. In the realm of malware detection, the K-Nearest Neighbors (KNN) algorithm is a well-liked and successful machine learning algorithm. However, the choice of an acceptable distance metric parameter has a significant impact on the KNN algorithm's performance. This study tries to improve malware detection by adjusting the KNN algorithm's distance metric parameter. The distance metric greatly influences the similarity or dissimilarity between instances in the feature space. The KNN algorithm for malware detection can be more accurate and effective by carefully choosing or modifying the distance metric. This paper analyzes multiple distance metrics, including Minkowski distance, Manhattan distance, and Euclidean distance. These metrics account for the traits of malware samples while capturing various aspects of similarity. The effectiveness of the KNN algorithm is evaluated using the MalMem-2022 malware dataset, and the results are broken down into these three-distance metrics. The experimental findings show that, among the three distance metric parameters, the Euclidean and Minkowski distance metric parameters considerably produced the best outcomes with binary classification. While with multiclass classification, the KNN algorithm has achieved the highest outcomes using Manhattan distance.

Over the last decades, glaciers across the Andes have been strongly affected by a loss of mass and surface areas. This increases risks of water scarcity for the Andean population and ecosystems. However, the factors controlling glacier changes in terms of surface area and mass loss remain poorly documented at watershed scale across the Andes. Using machine learning methods (Least Absolute Shrinkage and Selection Operator, known as LASSO), we explored climatic and morphometric variables that explain the spatial variance of glacier surface area variations in 35 watersheds (1980–2019), and of glacier mass balances in 110 watersheds (2000–2018), with data from 2,500 to 21,000 glaciers, respectively, distributed between 8 and 55°S in the Andes. Based on these results and by applying the Partitioning Around Medoids (PAM) algorithm we identified new glacier clusters. Overall, spatial variability of climatic variables presents a higher explanatory power than morphometric variables with regards to spatial variance of glacier changes. Specifically, the spatial variability of precipitation dominates spatial variance of glacier changes from the Outer Tropics to the Dry Andes (8–37°S) explaining between 49 and 93% of variances, whereas across the Wet Andes (40–55°S) the spatial variability of temperature is the most important climatic variable and explains between 29 and 73% of glacier changes spatial variance. However, morphometric variables such as glacier surface area show a high explanatory power for spatial variance of glacier mass loss in some watersheds (e.g., Achacachi with r2 = 0.6 in the Outer Tropics, Río del Carmen with r2 = 0.7 in the Dry Andes). Then, we identified a new spatial framework for hydro-glaciological analysis composed of 12 glaciological zones, derived from a clustering analysis, which includes 274 watersheds containing 32,000 glaciers. These new zones better take into account different seasonal climate and morphometric characteristics of glacier diversity. Our study shows that the exploration of variables that control glacier changes, as well as the new glaciological zones calculated based on these variables, would be very useful for analyzing hydro-glaciological modelling results across the Andes (8–55°S).

Typology of German sheep farms - Differences in structure, characteristics, challenges and the provision of goods and services

Good inspections are crucial for managing risk and making decisions about facility maintenance. This paper proposes a method using the partitioning around medoids (PAM) algorithm to ensure that the inspector inspects a diverse set of components which maximize the information about the facility. We compares a number of different metrics by which to cluster the components using PAM, and evaluated the effectiveness of the clustering using Bayesian ANOVA testing.

The aim of the current paper is to revisit the performance of spectral clustering algorithms for water distribution networks. In the literature, there have been attempts to introduce improved algorithms based on graph theory. We focus on a class of these algorithms that applies the concepts of the spectral clustering approach. We assess the performance of spectral clustering algorithms on a wider range of water network types (i.e. large, medium, and small sized networks) using a wider range of clustering methods (both partitioning and hierarchical) and performance indicators. Our findings suggest that partitioning methods, such as k-means are not consistently efficient in all types of networks. Nonetheless, the Partitioning Around Medoids (PAM) algorithm shows a relatively good performance according to modularity, while the internal indices of k-means and hierarchical clustering algorithms are more efficient. Stability indices show that PAM and CLARA algorithms are more efficient.

This paper compares the performance of three clustering algorithms on the task of outlier's detection. The goal is to illustrate that better clustering indicates better detection of outliers. k-means (KM), Bisecting k-means (BKM) and the partitioning around medoids (PAM) algorithms are each combined with the clustering-based outliers detection (Find CBLOF) method. Undertaken experimental results over four gene expression datasets where outliers are presented show that the clustering solutions of the PAM algorithm enable the Find CBLOF algorithm to discover more outliers than those of both the k-means and the bisecting k-means algorithms. The main reason for this is that PAM provides better clustering quality than that of the other two clustering algorithms on the tested datasets measured by external and internal quality measures.

BackgroundThe TNM staging system is based on three anatomic prognostic factors: Tumor, Lymph Node and Metastasis. However, cancer is no longer considered an anatomic disease. Therefore, the TNM should be expanded to accommodate new prognostic factors in order to increase the accuracy of estimating cancer patient outcome. The ensemble algorithm for clustering cancer data (EACCD) by Chen et al. reflects an effort to expand the TNM without changing its basic definitions. Though results on using EACCD have been reported, there has been no study on the analysis of the algorithm. In this report, we examine various aspects of EACCD using a large breast cancer patient dataset. We compared the output of EACCD with the corresponding survival curves, investigated the effect of different settings in EACCD, and compared EACCD with alternative clustering approaches.ResultsUsing the basic T and N definitions, EACCD generated a dendrogram that shows a graphic relationship among the survival curves of the breast cancer patients. The dendrograms from EACCD are robust for large values of m (the number of runs in the learning step). When m is large, the dendrograms depend on the linkage functions.The statistical tests, however, employed in the learning step have minimal effect on the dendrogram for large m. In addition, if omitting the step for learning dissimilarity in EACCD, the resulting approaches can have a degraded performance. Furthermore, clustering only based on prognostic factors could generate misleading dendrograms, and direct use of partitioning techniques could lead to misleading assignments to clusters.ConclusionsWhen only the Partitioning Around Medoids (PAM) algorithm is involved in the step of learning dissimilarity, large values of m are required to obtain robust dendrograms, and for a large m EACCD can effectively cluster cancer patient data.

Performance analysis of clustering techniques over microarray data: A case study

Instance-based learning techniques use a set of stored training instances to classify new examples. The most common such learning technique is the nearest neighbor method, in which new instances are classified according to the closest training instance. A critical element of any such method is the metric used to determine distance between instances. Euclidean distance is by far the most commonly used metric; no one, however, has systematically considered whether a different metric, such as Manhattan distance, might perform equally well on naturally occurring data sets. Some evidence from psychological research indicates that Manhattan distance might be preferable in some circumstances. This paper examines three different distance metrics and presents experimental comparisons using data from three domains: malignant cancer classification, heart disease diagnosis, and diabetes prediction. The results of these studies indicate that the Manhattan distance metric works works quite well, although not better than the Euclidean metric that has become a standard for machine learning experiments. Because the nearest neighbor technique provides a good benchmark for comparisons with other learning algorithms, the results below include a number of such comparisons, which show that nearest neighbor, using any distance metric, compares quite well to other machine learning techniques.

Recommendation systems (RSs) are tools for interacting with large and complex information spaces. They provide a personalized view of such spaces, prioritizing items likely to be of interest to the user. The main objective of RSs is to tool up users with desired items that meet their preferences. A major problem in RSs is called: “cold-start”; it is a potential problem called so in computer-based information systems which comprises a degree of automated data modeling. Particularly, it concerns the issue in which the system cannot draw any inferences nor have it yet gathered sufficient information about users or items. Since RSs performance is substantially limited by cold-start users and cold-start items problems; this research study takes the route for a major aim to attenuate users’ cold-start problem. Still in the process of researching, sundry studies have been conducted to tackle this issue by using clustering techniques to group users according to their social relations, their ratings or both. However, a clustering technique disregards a variety of users’ tastes. In this case, the researcher has adopted the overlapping technique as a tool to deal with the clustering technique’s defects. The advantage of the overlapping technique excels over others by allowing users to belong to multi-clusters at the same time according to their behavior in the social network and ratings feedback. On that account, a novel overlapping method is presented and applied. This latter is executed by using the partitioning around medoids (PAM) algorithm to implement the clustering, which is achieved by means of exploiting social relations and confidence values. After acquiring users’ clusters, the average distances are computed in each cluster. Thereafter, a content comparison is made regarding the distances between every user and the computed distances of the clusters. If the comparison result is less than or equal to the average distance of a cluster, a new user is added to this cluster. The singular value decomposition plus (SVD[Formula: see text]) method is then applied to every cluster to compute predictions values. The outcome is calculated by computing the average of mean absolute error (MAE) and root mean square error (RMSE) for every cluster. The model is tested by two real world datasets: Ciao and FilmTrust. Ultimately, findings have exhibited a great deal of insights on how the proposed model outperformed a number of the state-of-the-art studies in terms of prediction accuracy.

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.