correlation matrix

Clustering is one of the fundamental tools in data analysis and data mining, enabling the extraction of hidden and meaningful structures from large datasets by grouping data based on intrinsic similarities. However, selecting optimal clusters in conventional clustering algorithms poses challenges, especially when clusters are dense or heterogeneous. In this study, a novel genetic algorithm-based method is proposed to identify the most stable clusters in ensemble clustering. By leveraging cluster stability criteria and a correlation matrix, the proposed approach improves the accuracy and stability of the final clustering results. The proposed method involves generating initial partitions of the data using six different clustering algorithms. Next, the Fisher criterion is applied to identify more stable clusters. These selected clusters are then evaluated and optimized using a genetic algorithm to construct an optimized correlation matrix. This matrix is subsequently fed into a hierarchical clustering algorithm, which produces the final consensus clustering. The proposed method was tested on standard datasets. Results demonstrated improvements of 12% and 5% in NMI and ARI metrics, respectively, compared to previous methods. The use of a genetic algorithm enabled the identification of clusters with higher stability and diversity, reducing the impact of noise and increasing the accuracy of the final clustering. Moreover, the method outperformed individual base clustering algorithms in providing more precise clustering results. Due to its ability to enhance the accuracy and stability of clustering, the proposed method holds potential for applications in domains such as big data analysis, machine learning, and information retrieval. The use of the Fisher criterion for selecting stable clusters and genetic algorithms for optimization are among the strengths of this research. This method not only preserves diversity among clusters but also significantly enhances clustering accuracy. Future studies could explore the combination of this approach with more advanced algorithms to assess its applicability to more complex datasets.

Data clustering is one of the main steps in data mining, which is responsible for exploring hidden patterns in non-tagged data. Due to the complexity of the problem and the weakness of the basic clustering methods, most studies today are guided by clustering ensemble methods. Diversity in primary results is one of the most important factors that can affect the quality of the final results. Also, the quality of the initial results is another factor that affects the quality of the results of the ensemble. Both factors have been considered in recent research on ensemble clustering. Here, a new framework for improving the efficiency of clustering has been proposed, which is based on the use of a subset of primary clusters, and the proposed method answers the above questions and ambiguities. The selection of this subset plays a vital role in the efficiency of the assembly. Since evolutionary intelligent algorithms have been able to solve the majority of complex engineering problems, this paper also uses these intelligent methods to select subsets of primary clusters. This selection is done using three intelligent methods (genetic algorithm, simulation annealing and particle swarm optimization). In this paper a clustering ensemble method is proposed which is based on a subset of primary clusters. The main idea behind this method is using more stable clusters in the ensemble. The stability is applied as a goodness measure of the clusters. The clusters which satisfy a threshold of this measure are selected to participate in the ensemble. For combining the chosen clusters, a co-association based consensus function is applied. A new EAC based method which is called Extended Evidence Accumulation Clustering, EEAC, is proposed for constructing the Co-association Matrix from the subset of clusters. Experimental results on several standard datasets with normalized mutual information evaluation, Fisher and accuracy criteria compared to Alizadeh, Azimi, Berikov, CLWGC, RCESCC, KME, CFSFDP, DBSCAB, NSC and Chen methods show the significant improvement of the proposed method in comparison with other ones.

Some of important issues in acoustic echo cancellation (AEC) using adaptive filters are the sparseness of the acoustic path impulse responses and strong dependency of the convergence performance of adaptive algorithm to the eigenvalue spread of the input signal correlation matrix. These issues result in a performance degradation of the adaptive AEC systems. In this paper, to improve the performance of the LMS/Newton adaptive algorithm in AEC, the matrix inverse computation is modified. To this end, the matrix inversion lemma is employed such that the contribution of the matrix inverse in the weight update is initially high and as a result, the dependency of the adaptive algorithm to the eigenvalue spread is low during the initial convergence. In addition, for the step-size adjustment, an improved proportionate method is applied such that during the convergence, the contribution of those weights having higher amplitudes in the adaptation process is gradually varied to become identical at the end of convergence. The proposed adaptive proportionate method, results in both convergence rate and steady-state performance improvement for identification of sparse acoustic impulse responses. Simulation results using a colored speech-like signal shows the steady-state misalignment of the proposed algorithm is typically 6.5 dB lower than that of the LMS/Newton algorithm. Moreover, the convergence of the proposed algorithm is typically 3.6 sec faster than that of the PNLMS algorithm, to achieve a misalignment of -17 dB. Theoretical misalignment analyses in the transient and steady state are presented and verified with simulation results.