Hybrid Fuzzy C-Means Clustering Algorithm Oriented to Big Data Realms

Pérez-Ortega, Joaquín; Roblero-Aguilar, Sandra Silvia; Almanza-Ortega, Nelva Nely; Frausto–Solís, Juan; Zavala-Díaz, Crispín; Hernández, Yasmín; Landero-Nájera, Vanesa

doi:10.3390/axioms11080377

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…Expression (4) states that the membership degree of an object i to a cluster j must equal 1 if the object x i lies at the same position of centroid v j . Expression (5) declares that for each cluster j, the sum of the membership degrees of all the objects to cluster j must be greater than 0 and less than n (i.e., there may not be any centroid v j such that the sum of the membership degrees of all the objects to v j equals 0).…”

Section: Notationmentioning

confidence: 99%

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A New Criterion for Improving Convergence of Fuzzy C-Means Clustering

Pérez-Ortega,

Moreno-Calderón,

Roblero-Aguilar

et al. 2024

Axioms

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One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.

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Section: Notationmentioning

confidence: 99%

“…Some of them are the following: pattern recognition, image segmentation, data mining, medicine, taxonomy, and business, among others [3,4]. However, one of the limitations of data clustering is its high computational cost [5,6].…”

Section: Introductionmentioning

confidence: 99%

A New Criterion for Improving Convergence of Fuzzy C-Means Clustering

Pérez-Ortega,

Moreno-Calderón,

Roblero-Aguilar

et al. 2024

Axioms

Self Cite

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“…FCM [30] is an unsupervised affiliation-based clustering algorithm that uses an affiliation matrix U = {u ik } to represent the degree to which each object belongs to the corresponding class. The FCM objective function is:…”

Section: Fuzzy C-meansmentioning

confidence: 99%

“…To further illustrate the superiority of the AFC method, it is compared with K-means [37], FCM [30], hierarchical clustering (HC) [38], and DBSCAN [39] methods. Due to the lack of data labels, the results could not be evaluated quantitatively.…”

Section: Operational Risk Assessmentmentioning

confidence: 99%

Operational risk assessment for hydroelectric generating units using multi-head spatio-temporal attention and adaptive fuzzy clustering

Liu,

Xu,

Liu

et al. 2023

Meas. Sci. Technol.

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A novel operational risk assessment method for hydroelectric generating units (HGUs) is presented in this article. First, a multi-head spatio-temporal attention gated network (MSTAGN) is proposed to establish an operation risk benchmark model (ORBM) for HGUs to reveal the intricate relationship between performance and its multiple influencing factors. In particular, MSTAGN learns complex interaction relationships among multiple influencing factors in both temporal and spatial dimensions and automatically extracts important features. Then, a nonlinear mapping function is constructed to extract the deviation of the current measured performance parameters from the predicted baseline performance parameters as the operation risk degree (ORD). On this basis, an adaptive fuzzy clustering (AFC) algorithm is proposed to achieve a clear classification of the operating risk level for HGUs. The proposed method is applied in a HGU in Sichuan province, China. The results of comparative experiments demonstrate its viability and efficacy.

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“…Wang et al introduced an improved index for clustering validation based on the Silhouette index and the Calinski-Harabasz index [47]. A hybrid fuzzy c-means clustering algorithm was suggested in [48] and was essentially focused on big data problems. The Deep Possibilistic C-means Clustering Algorithm was recently introduced by Gu Y et al and was used on medical datasets [49].…”

Section: Introductionmentioning

confidence: 99%

FP-Conv-CM: Fuzzy Probabilistic Convolution C-Means

et al. 2023

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Soft computing models based on fuzzy or probabilistic approaches provide decision system makers with the necessary capabilities to deal with imprecise and incomplete information. Hybrid systems based on different soft computing approaches with complementary qualities and principles have also become popular. On the one hand, fuzzy logic makes its decisions on the basis of the degree of membership but gives no information on the frequency of an event; on the other hand, the probability informs us of the frequency of the event but gives no information on the degree of membership to a set. In this work, we propose a new measure that implements both fuzzy and probabilistic notions (i.e., the degree of membership and the frequency) while exploiting the ability of the convolution operator to combine functions on continuous intervals. This measure evaluates both the degree of membership and the frequency of objects/events in the design of decision support systems. We show, using concrete examples, the drawbacks of fuzzy logic and probability-based approaches taken separately, and we then show how a fuzzy probabilistic convolution measure allows the correction of these drawbacks. Based on this measure, we introduce a new clustering method named Fuzzy-Probabilistic-Convolution-C-Means (FP-Conv-CM). Fuzzy C-Means (FCM), Probabilistic K-Means (PKM), and FP-Conv-CM were tested on multiple datasets and compared on the basis of two performance measures based on the Silhouette metric and the Dunn’s Index. FP-Conv-CM was shown to improve on both metrics. In addition, FCM, PKM, and FP-Conv-CM were used for multiple image compression tasks and were compared based on three performance measures: Mean Square Error (MSE), Peak Signal-to-Noise Ratio (PSNR), and Structural SImilarity Index (SSIM). The proposed FP-Conv-CM method shows improvements in all these three measures as well.

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Hybrid Fuzzy C-Means Clustering Algorithm Oriented to Big Data Realms

Cited by 11 publications

References 26 publications

A New Criterion for Improving Convergence of Fuzzy C-Means Clustering

A New Criterion for Improving Convergence of Fuzzy C-Means Clustering

Operational risk assessment for hydroelectric generating units using multi-head spatio-temporal attention and adaptive fuzzy clustering

FP-Conv-CM: Fuzzy Probabilistic Convolution C-Means

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