Under-Determined Blind Source Separation

The Under-determined Blind Source Separation problem aims at estimating N source signals, with only a given set of M known mixtures, where M < N. The problem is solved by a two-stage approach. The rst stage is the estimation of the unknown mixing matrix. The contributions made unravel a more precise and accurate tool which directly relates to the initialization of the clustering algorithm. Di erent schemes such as segmentation, correlation and least square curve tting are used to take advantage of the sparsity of the sources. A signi cant addition involves applying linear transforms to produce a higher sparse domain. Further, the second stage is the sparse source recovery using a Matching Pursuit algorithm. The contributions involve a Matching Pursuit algorithm with di

Fault Feature Extraction for Reciprocating Compressors Based on Underdetermined Blind Source Separation

Entropy ◽

10.3390/e23091217 ◽

2021 ◽

Vol 23 (9) ◽

pp. 1217

Author(s):

Jindong Wang ◽

Xin Chen ◽

Haiyang Zhao ◽

Yanyang Li ◽

Zujian Liu

Keyword(s):

Blind Source Separation ◽

Hierarchical Clustering ◽

Source Separation ◽

Least Square Method ◽

Least Square ◽

Matrix Estimation ◽

Initial Cluster ◽

Mixing Matrix ◽

In practical engineering applications, the vibration signals collected by sensors often contain outliers, resulting in the separation accuracy of source signals from the observed signals being seriously affected. The mixing matrix estimation is crucial to the underdetermined blind source separation (UBSS), determining the accuracy level of the source signals recovery. Therefore, a two-stage clustering method is proposed by combining hierarchical clustering and K-means to improve the reliability of the estimated mixing matrix in this paper. The proposed method is used to solve the two major problems in the K-means algorithm: the random selection of initial cluster centers and the sensitivity of the algorithm to outliers. Firstly, the observed signals are clustered by hierarchical clustering to get the cluster centers. Secondly, the cosine distance is used to eliminate the outliers deviating from cluster centers. Then, the initial cluster centers are obtained by calculating the mean value of each remaining cluster. Finally, the mixing matrix is estimated with the improved K-means, and the sources are recovered using the least square method. Simulation and the reciprocating compressor fault experiments demonstrate the effectiveness of the proposed method.

A Novel Underdetermined Blind Source Separation Method and Its Application to Source Contribution Quantitative Estimation

Sensors ◽

10.3390/s19061413 ◽

2019 ◽

Vol 19 (6) ◽

pp. 1413 ◽

Cited By ~ 2

Author(s):

Jiantao Lu ◽

Wei Cheng ◽

Yanyang Zi

Keyword(s):

Blind Source Separation ◽

Quantitative Estimation ◽

Source Separation ◽

Estimation Method ◽

Least Square ◽

Source Contribution ◽

Time Frequency ◽

Source Contributions ◽

To identify the major vibration and radiation noise, a source contribution quantitative estimation method is proposed based on underdetermined blind source separation. First, the single source points (SSPs) are identified by directly searching the identical normalized time-frequency vectors of mixed signals, which can improve the efficiency and accuracy in identifying SSPs. Then, the mixing matrix is obtained by hierarchical clustering, and source signals can also be recovered by the least square method. Second, the optimal combination coefficients between source signals and mixed signals can be calculated based on minimum redundant error energy. Therefore, mixed signals can be optimally linearly combined by source signals via the coefficients. Third, the energy elimination method is used to quantitatively estimate source contributions. Finally, the effectiveness of the proposed method is verified via numerical case studies and experiments with a cylindrical structure, and the results show that source signals can be effectively recovered, and source contributions can be quantitatively estimated by the proposed method.

A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem

Circuits Systems and Signal Processing ◽

10.1007/s00034-018-0930-5 ◽

2018 ◽

Vol 38 (4) ◽

pp. 1889-1906 ◽

Cited By ~ 2

Author(s):

Fang Ye ◽

Jie Chen ◽

Lipeng Gao ◽

Wei Nie ◽

Qian Sun

Keyword(s):

Blind Source Separation ◽

Source Separation ◽

Estimation Algorithm ◽

Mixing Model ◽

Separation Problem ◽

Matrix Estimation ◽

Mixing Matrix ◽

Mixing Matrix Estimation

Blind Source Separation by Sparse Decomposition in a Signal Dictionary

Neural Computation ◽

10.1162/089976601300014385 ◽

2001 ◽

Vol 13 (4) ◽

pp. 863-882 ◽

Cited By ~ 476

Author(s):

Michael Zibulevsky ◽

Barak A. Pearlmutter

Keyword(s):

Blind Source Separation ◽

A Priori ◽

Source Separation ◽

Stage Separation ◽

Learned Dictionary ◽

Mixing Matrix ◽

Linear Mixtures ◽

Musical Sounds ◽

Source Signals ◽

Selection Of

The blind source separation problem is to extract the underlying source signals from a set of linear mixtures, where the mixing matrix is unknown. This situation is common in acoustics, radio, medical signal and image processing, hyperspectral imaging, and other areas. We suggest a two-stage separation process: a priori selection of a possibly overcomplete signal dictionary (for instance, a wavelet frame or a learned dictionary) in which the sources are assumed to be sparsely representable, followed by unmixing the sources by exploiting the their sparse representability. We consider the general case of more sources than mixtures, but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures. Experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques.

Mixing Matrix Estimation of Underdetermined Blind Source Separation based on Improved Density Clustering Algorithm

2019 8th Asia-Pacific Conference on Antennas and Propagation (APCAP) ◽

10.1109/apcap47827.2019.9471969 ◽

2019 ◽

Author(s):

Linyu Wang ◽

Gangyang Hou ◽

Jianhong Xiang

Keyword(s):

Blind Source Separation ◽

Clustering Algorithm ◽

Source Separation ◽

Matrix Estimation ◽

Mixing Matrix ◽

Mixing Matrix Estimation ◽

Density Clustering

Mixing Matrix Estimation of Underdetermined Blind Source Separation based on Improved Density Clustering Algorithm

2019 8th Asia-Pacific Conference on Antennas and Propagation (APCAP) ◽

10.1109/apcap47827.2019.9472130 ◽

2019 ◽

Author(s):

Linyu Wang ◽

Gangyang Hou ◽

Jianhong Xiang

Keyword(s):

Blind Source Separation ◽

Clustering Algorithm ◽

Source Separation ◽

Matrix Estimation ◽

Mixing Matrix ◽

Mixing Matrix Estimation ◽

Density Clustering

Mixing matrix estimation of MIMO radar based on adaptive hierarchical clustering algorithm for underdetermined blind source separation

2017 Progress in Electromagnetics Research Symposium - Fall (PIERS - FALL) ◽

10.1109/piers-fall.2017.8293549 ◽

2017 ◽

Cited By ~ 1

Author(s):

Jianhong Xiang ◽

Chen Li ◽

Qiang Guo

Keyword(s):

Blind Source Separation ◽

Hierarchical Clustering ◽

Clustering Algorithm ◽

Source Separation ◽

Mimo Radar ◽

Matrix Estimation ◽

Mixing Matrix ◽

Mixing Matrix Estimation ◽

Hierarchical Clustering Algorithm

A NEW ALGORITHM FOR THE UNDERDETERMINED BLIND SOURCE SEPARATION BASED ON SPARSE COMPONENT ANALYSIS

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001409006965 ◽

2009 ◽

Vol 23 (01) ◽

pp. 71-85 ◽

Cited By ~ 5

Author(s):

HAI-LIN LIU ◽

CHU-JUN YAO ◽

JIA-XUN HOU

Keyword(s):

Blind Source Separation ◽

Source Separation ◽

Spherical Coordinate ◽

Sparse Component Analysis ◽

Hyperplane Clustering ◽

The Matrix ◽

Mixing Matrix ◽

Normal Vectors ◽

For the purpose of estimating the mixing matrix under the nonstrictly sparse condition, this paper presents the algorithms to approximate the mixing matrix in two different situations in which the source vectors are 1-sparse and (m - 1)-sparse. When the source signals are 1-sparse, we use the generalized spherical coordinate transformation to convert the matrix of observation signals into the new one, which makes the process of estimating column A become the process of finding the center point of these new data. For the situation that source signals are (m - 1)-sparse, we propose a new algorithm for the underdetermined mixtures blind source separation based on hyperplane clustering. The algorithm firstly finds out the linearly independent vectors from the observations, and secondly determines all the normal vectors of hyperplanes by analyzing the number of observations that are in the same hyperplane. Finally, we identify the column vectors of the mixing matrix A by calculating the vectors which are orthogonal to the clustered normal vectors. These two new algorithms for estimating the mixing matrix are more suitable for the general cases as they have lower requirement for the sparsity of the observations.

A Novel Blind Source Separation Algorithm for Linear Mixture Signals

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.599-601.1357 ◽

2014 ◽

Vol 599-601 ◽

pp. 1357-1359

Author(s):

Wei Hua Liu ◽

Yun Zhang ◽

Ying Fu Chen ◽

Lei Wang ◽

Jian Cheng Liu

Keyword(s):

Cost Function ◽

Blind Source Separation ◽

Source Separation ◽

Separation Algorithm ◽

Mixing Matrix ◽

Separate Source ◽

Simulation Results ◽

The Cost ◽

A novel blind source separation (BSS) algorithm for linear mixture signals is proposed. It is shown that the property can be used to separate source signals by finding an un-mixing matrix that maximizes the cost function value of separated signals. Simulation results illustrate the efficiency and the good performance of the algorithm.