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Identifiability Conditions and Subspace Clustering in Sparse BSS [chapter]

Pando Georgiev, Fabian Theis, Anca Ralescu
Independent Component Analysis and Signal Separation  
We develop a subspace clustering algorithm, which is a generalization of the k-plane clustering algorithm, and is suitable for separation of sparse mixtures with bigger sparsity (i.e. when the number of  ...  The latter confirms the new identifiability conditions which require less hyperplanes in the data for full recovery of the sources and the mixing matrix.  ...  Identifiability Conditions The following identifiability conditions are extension and refinement of those in [5] .  ... 
doi:10.1007/978-3-540-74494-8_45 dblp:conf/ica/GeorgievTR07 fatcat:tgggez37xnfgnf7nond6bu4cha

Blind Source Separation of Linear Mixtures with Singular Matrices [chapter]

Pando Georgiev, Fabian J. Theis
2004 Lecture Notes in Computer Science  
A sufficient condition for solving this problem is that the level of sparsity of S is bigger than m − rank(A) in sense that the number of zeros in each column of S is bigger than m − rank(A).  ...  We consider the Blind Source Separation problem of linear mixtures with singular matrices and show that it can be solved if the sources are sufficiently sparse.  ...  by sparse BSS methods.  ... 
doi:10.1007/978-3-540-30110-3_16 fatcat:ogxs6e5ltffs7fyhpszd3vtkmq

Sparse Component Analysis and Blind Source Separation of Underdetermined Mixtures

P. Georgiev, F. Theis, A. Cichocki
2005 IEEE Transactions on Neural Networks  
In this letter, we solve the problem of identifying matrices S and A knowing only their multiplication X = AS, under some conditions, expressed either in terms of A and sparsity of S (identifiability conditions  ...  ), or in terms of X (sparse component analysis (SCA) conditions).  ...  ACKNOWLEDGMENT The authors would like to thank the reviewers for their useful hints and constructive comments throughout the reviewing process.  ... 
doi:10.1109/tnn.2005.849840 pmid:16121741 fatcat:pnawsb6fhfgr7nq2mf6a4ikjpq

An efficient K-SCA based unerdetermined channel identification algorithm for online applications

Ehsan Eqlimi, Bahador Makkiabadi
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
In a sparse component analysis problem, under some nonstrict conditions on sparsity of the sources, called k-SCA, we are able to estimate both mixing system ( ) and sparse sources ( ) uniquely.  ...  Furthermore, to accelerate the process, we integrate the "subspaces clustering" and "channel clustering" stages in an online scenario to estimate the mixing matrix columns as the mixture vectors are received  ...  In 2005 Georgiev et al [2, 3] proposed k-sparse component analysis (k-SCA) algorithm to solve the Underdetermined BSS (UBSS) that assumes the source signals are ( x +1) sparse i.e. there are at most  ... 
doi:10.1109/eusipco.2015.7362867 dblp:conf/eusipco/EqlimiM15 fatcat:6mlac2kqajg2jhtbt3aq7j5ouu

Mixing matrix estimation in UBSS based on homogeneous polynomials

Bin Nong, Weihong Fu
2018 IET Signal Processing  
First, the observed signal subspaces (hyperplanes) are identified by polynomial fitting, differentiation, and spectral clustering.  ...  Then, the intersection lines between clustering planes are estimated by using normal vectors of each subspace, which are finally proved to be column vectors of the mixing matrix up to scaling and ordering  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (61201134) and the 111 project (B08038). References  ... 
doi:10.1049/iet-spr.2018.5207 fatcat:nkz3m6eee5cjhe2ax7t55276c4

Sparse Component Analysis Using Time-Frequency Representations for Operational Modal Analysis

Shaoqian Qin, Jie Guo, Changan Zhu
2015 Sensors  
The K-hyperline clustering algorithm is used to identify the direction vectors of the hyperlines and then the mixing matrix is calculated.  ...  Sparse component analysis (SCA) has been widely used for blind source separation(BSS) for many years.  ...  Author Contributions Qin and Guo provided the initial idea and conception; Qin implemented the software and conducted the numerical simulation; Guo carried out the experimental validation; Qin and Guo  ... 
doi:10.3390/s150306497 pmid:25789492 pmcid:PMC4435134 fatcat:6duqo3pqyjhpxf6juzu7bkjw3e

Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain

Abdeldjalil Aissa-El-Bey, Nguyen Linh-Trung, Karim Abed-Meraim, Adel Belouchrani, Yves Grenier
2007 IEEE Transactions on Signal Processing  
The separation can still be achieved thanks to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values.  ...  The first uses quadratic timefrequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD.  ...  Subspace projection allows us to identify at any point the sources present, and hence, to estimate the corresponding TFD values of these sources.  ... 
doi:10.1109/tsp.2006.888877 fatcat:ht3ddlrzxncwvomot53gmdu3fi

A bilinear algorithm for sparse representations

Pando Georgiev, Panos Pardalos, Fabian Theis
2007 Computational optimization and applications  
m × m submatrices of A are nonsingular, and S is sparse in sense that each column of S has at least n − m + 1 zero elements.  ...  We consider the following sparse representation problem: represent a given matrix X ∈ IR m×N as a multiplication X = AS of two matrices A ∈ IR m×n (m n < N ) and S ∈ IR n×N , under requirements that all  ...  Matrix identification We describe conditions in the sparse BSS problem under which we can identify the mixing matrix uniquely up to permutation and scaling of the columns.  ... 
doi:10.1007/s10589-007-9043-y fatcat:d2j4g7cp2rcifepq2qomosssri

The discriminative functional mixture model for a comparative analysis of bike sharing systems

Charles Bouveyron, Etienne Côme, Julien Jacques
2015 Annals of Applied Statistics  
It is based on a functional mixture model that allows the clustering of the data in a discriminative functional subspace.  ...  This work was motivated by interest in analyzing and comparing several European BSSs to identify common operating patterns in BSSs and to propose practical solutions to avoid potential issues.  ...  The authors would like to thank the editors and the reviewers for their meaningful comments, which have greatly contributed to improving the manuscript.  ... 
doi:10.1214/15-aoas861 fatcat:x3xaxurc3zbzpbkrro6e4exwzi

Sparse Coding for Convolutive Blind Audio Source Separation [chapter]

Maria G. Jafari, Samer A. Abdallah, Mark D. Plumbley, Mike E. Davies
2006 Lecture Notes in Computer Science  
In this paper, we address the convolutive blind source separation (BSS) problem with a sparse independent component analysis (ICA) method, which uses ICA to find a set of basis vectors from the observed  ...  data, followed by clustering to identify the original sources.  ...  The subspaces corresponding to the original sources are then identified using clustering techniques. In [7] , manual clustering was used.  ... 
doi:10.1007/11679363_17 fatcat:ektxmk2kunamnk6d4r6m6qlo5m

Underdetermined Blind Source Separation Based on Subspace Representation

SangGyun Kim, C.D. Yoo
2009 IEEE Transactions on Signal Processing  
His research interests are in the application of statistical signal processing and machine learning to neural and multimedia signals. Dr.  ...  Kim is a member of the IEEE, the Institute of Electrical Engineers of Korea (IEEK), and the Acoustical Society of Korea (ASK).  ...  In [23] , the underdetermined BSS problem is transformed to a complete BSS problem by generating latent mixture to maximize its conditional probability without regard to any optimality condition.  ... 
doi:10.1109/tsp.2009.2017570 fatcat:hlasrgikynfqnjzpqj3hwep4gy

Blind Separation of Underdetermined Convolutive Mixtures Using Their Time–Frequency Representation

Abdeldjalil Aissa-El-Bey, Karim Abed-Meraim, Yves Grenier
2007 IEEE Transactions on Audio, Speech, and Language Processing  
In that case, the separation can be achieved thanks to subspace projection which allows us to identify the active sources and to estimate their corresponding time-frequency distribution (TFD) values.  ...  Finally, numerical performance evaluations and comparisons of the proposed methods are provided highlighting their effectiveness.  ...  Subspace projection allows us to identify at any point the active sources, and then to estimate their corresponding TFD values.  ... 
doi:10.1109/tasl.2007.898455 fatcat:qq35dsqxnjfk3g6hze6523qmsu

A simple closed-form solution for overdetermined blind separation of locally sparse quasi-stationary sources

Xiao Fu, Wing-Kin Ma
2012 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The ideas in the existing BSS works often focus on exploiting the time-varying statistics characteristics of quasi-stationary sources, through various kinds of formulations and optimization methods.  ...  Blind source separation (BSS) under this scenario has drawn much attention, motivated by applications such as speech and audio separation.  ...  As a result, we can derive a sufficient condition [i.e., (15)] under which U1:K is aligned to the subspace spanned by H; such an alignment also assures that U1:KU T 1:K G = 0.  ... 
doi:10.1109/icassp.2012.6288401 dblp:conf/icassp/FuM12a fatcat:b2ujinacgvcxhifsavzuvazbye

Output-only modal identification with limited sensors using sparse component analysis

Yongchao Yang, Satish Nagarajaiah
2013 Journal of Sound and Vibration  
The developed SCA method reveals the essence of modal expansion that the monotone modal responses with disjoint sparsest representations in frequency domain naturally cluster in the directions of the mode  ...  Blind source separation (BSS) based methods have been shown to be efficient and powerful to perform output-only modal identification.  ...  If the system responses are fed as mixtures into the BSS model, then the target of output-only identifying Φ and q(t) in Eq. (2) can be solved by blind recovery of A and s(t) using those BSS techniques  ... 
doi:10.1016/j.jsv.2013.04.004 fatcat:vv7x5ip57nghbdpz3ngptdojte

A Novel Underdetermined Source Recovery Algorithm Based on k-Sparse Component Analysis

Ehsan Eqlimi, Bahador Makkiabadi, Nasser Samadzadehaghdam, Hassan Khajehpour, Fahimeh Mohagheghian, Saeid Sanei
2018 Circuits, systems, and signal processing  
Assuming the sources are at most (m − 1)-sparse where m is the number of mixtures, the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection  ...  Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation (UBSS) in array signal processing applications.  ...  The condition k m − 1 is very promising in comparison to k m.  ... 
doi:10.1007/s00034-018-0910-9 fatcat:koyyqv64dbh7naygqw67m2ighy
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