Underdetermined mixing matrix estimation based on joint density-based clustering algorithms
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Underdetermined mixing matrix estimation based on joint density-based clustering algorithms Xuan-sen He 1,2 & Fan He 3 & Li Xu 1 Received: 15 January 2020 / Revised: 12 August 2020 / Accepted: 19 October 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
In underdetermined blind source separation (UBSS), the estimation of the mixing matrix is crucial because it directly affects the performance of UBSS. To improve the estimation accuracy, this paper proposes a joint clustering analysis method based on density based spatial clustering of applications with noise (DBSCAN) and clustering by fast search and find of density peaks (CFSFDP). In the reprocessing, the observed signals in the time domain are transformed into sparse signals in the frequency domain through a short time Fourier transform (STFT), and single-source-point (SSP) detection is used to enhance the linear clustering characteristic of signals. In addition, to facilitate the use of density-based clustering analysis, mirroring mapping is used to transform the linear clustering into compact clustering on the positive half unit circle (or sphere). For the estimation of the underdetermined mixing matrix (UMM), the DBSCAN algorithm is first used to search for high-density data points, and automatically find the number of clusters and the cluster centers; then, the CFSFDP algorithm is used to search the density peaks of the data clusters, so as to further modify the cluster centers. Because each cluster center corresponds to a column vector of the mixing matrix, the proposed algorithm can estimate the UMM through cluster analysis. The simulation results show that the proposed algorithm can not only improve the estimation accuracy of the UMM, but also provide a more robust estimator. In addition, the joint clustering method also makes up for the shortcomings of the CFSFDP algorithm that requires human intervention. Keywords Underdetermined blind source separation (UBSS) . Mixing matrix estimation . Singlesource-point (SSP) detection . Density based spatial clustering of applications with noise (DBSCAN) . Clustering by fast search and find of density peaks (CFSFDP)
* Xuan-sen He [email protected] Extended author information available on the last page of the article
Multimedia Tools and Applications
1 Introduction Blind source separation (BSS) [10, 11, 15, 38] aims to estimate an unobserved vector of M sources s(t)∈RM from N observations of their mixtures x(t)∈RN without any prior knowledge of the mixing system. In the noise-free case, the linear instantaneous BSS model can be expressed as x(t) = As(t), where A∈RN × M is the mixing matrix. To reveal the hidden factors that underlie the sets of measurements or the observed signals, independent component analysis (ICA) [1, 24, 26, 46] is one of the most widely used techniques for BSS. In general, the number of sources is equal to the number of observed signals, N = M, the mixture is said to be determined since the mixing matrix is square matrix. In practice, however, N ≠ M is a fr
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