{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T22:06:53Z","timestamp":1682374013463},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,10,8]],"date-time":"2014-10-08T00:00:00Z","timestamp":1412726400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Semi-symmetric three-way arrays are essential tools in blind source separation (BSS) particularly in independent component analysis (ICA). These arrays can be built by resorting to higher order statistics of the data. The canonical polyadic (CP) decomposition of such semi-symmetric three-way arrays allows us to identify the so-called mixing matrix, which contains the information about the intensities of some latent source signals present in the observation channels. In addition, in many applications, such as the magnetic resonance spectroscopy (MRS), the columns of the mixing matrix are viewed as relative concentrations of the spectra of the chemical components. Therefore, the two loading matrices of the three-way array, which are equal to the mixing matrix, are nonnegative. Most existing CP algorithms handle the symmetry and the nonnegativity separately. Up to now, very few of them consider both the semi-nonnegativity and the semi-symmetry structure of the three-way array. Nevertheless, like all the methods based on line search, trust region strategies, and alternating optimization, they appear to be dependent on initialization, requiring in practice a multi-initialization procedure. In order to overcome this drawback, we propose two new methods, called <jats:inline-formula>\n              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                <mml:msubsup>\n                  <mml:mrow>\n                    <mml:mtext>JD<\/mml:mtext>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mtext>LU<\/mml:mtext>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mo>+<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:msubsup>\n              <\/mml:math>\n            <\/jats:inline-formula> and <jats:inline-formula>\n              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                <mml:msubsup>\n                  <mml:mrow>\n                    <mml:mtext>JD<\/mml:mtext>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mtext>QR<\/mml:mtext>\n                  <\/mml:mrow>\n                  <mml:mrow>\n                    <mml:mo>+<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:msubsup>\n              <\/mml:math>\n            <\/jats:inline-formula>, to solve the problem of CP decomposition of semi-nonnegative semi-symmetric three-way arrays. Firstly, we rewrite the constrained optimization problem as an unconstrained one. In fact, the nonnegativity constraint of the two symmetric modes is ensured by means of a square change of variable. Secondly, a Jacobi-like optimization procedure is adopted because of its good convergence property. More precisely, the two new methods use LU and QR matrix factorizations, respectively, which consist in formulating high-dimensional optimization problems into several sequential polynomial and rational subproblems. By using both LU and QR matrix factorizations, we aim at studying the influence of the used matrix factorization. Numerical experiments on simulated arrays emphasize the advantages of the proposed methods especially the one based on LU factorization, in the presence of high-variance model error and of degeneracies such as bottlenecks. A BSS application on MRS data confirms the validity and improvement of the proposed methods.<\/jats:p>","DOI":"10.1186\/1687-6180-2014-150","type":"journal-article","created":{"date-parts":[[2014,10,8]],"date-time":"2014-10-08T01:05:13Z","timestamp":1412730313000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations"],"prefix":"10.1186","volume":"2014","author":[{"given":"Lu","family":"Wang","sequence":"first","affiliation":[]},{"given":"Laurent","family":"Albera","sequence":"additional","affiliation":[]},{"given":"Amar","family":"Kachenoura","sequence":"additional","affiliation":[]},{"given":"Huazhong","family":"Shu","sequence":"additional","affiliation":[]},{"given":"Lotfi","family":"Senhadji","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,10,8]]},"reference":[{"key":"751_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/0470012110","volume-title":"Multi-way Analysis: Applications in the Chemical Sciences","author":"A Smilde","year":"2004","unstructured":"Smilde A, Bro R, Geladi P: Multi-way Analysis: Applications in the Chemical Sciences. Wiley, West Sussex; 2004."},{"issue":"8","key":"751_CR2","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1109\/TSP.2013.2238534","volume":"61","author":"ALF de Almeida","year":"2013","unstructured":"de Almeida ALF, Favier G, Ximenes LR: Space-time-frequency (STF) MIMO communication systems with blind receiver based on a generalized PARATUCK2 model. IEEE Trans. Signal Process 2013, 61(8):1895-1909.","journal-title":"IEEE Trans. Signal Process"},{"issue":"3","key":"751_CR3","doi-asserted-by":"publisher","first-page":"844","DOI":"10.1016\/j.neuroimage.2007.04.041","volume":"37","author":"M De Vos","year":"2007","unstructured":"De Vos M, Vergult A, De Lathauwer L, De Clercq W, Van Huffel S, Dupont P, Palmini A, Van Paesschen W: Canonical decomposition of ictal scalp EEG reliably detects the seizure onset zone. Neuroimage 2007, 37(3):844-854. 10.1016\/j.neuroimage.2007.04.041","journal-title":"Neuroimage"},{"key":"751_CR4","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1002\/cem.1236","volume":"23","author":"P Comon","year":"2009","unstructured":"Comon P, Luciani X, de Almeida ALF: Tensor decompositions, alternating least squares and other tales. J. Chemometr 2009, 23: 393-405. 10.1002\/cem.1236","journal-title":"J. Chemometr"},{"issue":"3","key":"751_CR5","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/BF02289464","volume":"31","author":"LR Tucker","year":"1966","unstructured":"Tucker LR: Some mathematical notes on three-mode factor analysis. Psychometrika 1966, 31(3):279-311. 10.1007\/BF02289464","journal-title":"Psychometrika"},{"issue":"4","key":"751_CR6","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1137\/S0895479896305696","volume":"21","author":"L De Lathauwer","year":"2000","unstructured":"De Lathauwer L, De Moor B, Vandewalle J: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl 2000, 21(4):1253-1278. 10.1137\/S0895479896305696","journal-title":"SIAM J. Matrix Anal. Appl"},{"issue":"2","key":"751_CR7","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/0024-3795(77)90069-6","volume":"18","author":"JB Kruskal","year":"1977","unstructured":"Kruskal JB: Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Lin. Algebra Appl 1977, 18(2):98-138.","journal-title":"Lin. Algebra Appl"},{"issue":"1","key":"751_CR8","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1002\/sapm192761164","volume":"6","author":"FL Hitchcock","year":"1927","unstructured":"Hitchcock FL: The expression of a tensor or a polyadic as a sum of products. J. Math. Phys 1927, 6(1):164-189.","journal-title":"J. Math. Phys"},{"key":"751_CR9","doi-asserted-by":"publisher","DOI":"10.1002\/9780470238004","volume-title":"Applied Multiway Data Analysis","author":"PM Kroonenberg","year":"2008","unstructured":"Kroonenberg PM: Applied Multiway Data Analysis. Wiley, Hoboken; 2008."},{"issue":"8","key":"751_CR10","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1109\/78.852018","volume":"48","author":"ND Sidiropoulos","year":"2000","unstructured":"Sidiropoulos ND, Bro R, Giannakis GB: Parallel factor analysis in sensor array processing. IEEE Trans. Signal Process 2000, 48(8):2377-2388. 10.1109\/78.852018","journal-title":"IEEE Trans. Signal Process"},{"issue":"2","key":"751_CR11","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/j.sigpro.2005.12.014","volume":"87","author":"ALF de Almeida","year":"2007","unstructured":"de Almeida ALF, Favier G, Motab JCM: PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization. Signal Process 2007, 87(2):337-351. 10.1016\/j.sigpro.2005.12.014","journal-title":"Signal Process"},{"issue":"5","key":"751_CR12","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1109\/LSP.2013.2248149","volume":"20","author":"ALF de Almeida","year":"2013","unstructured":"de Almeida ALF, Favier G: Double Khatri-Rao space-time-frequency coding using semi-blind PARAFAC based receiver. IEEE Signal Process. Lett 2013, 20(5):471-474.","journal-title":"IEEE Signal Process. Lett"},{"key":"751_CR13","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.laa.2004.05.007","volume":"391","author":"L Albera","year":"2004","unstructured":"Albera L, Ferr\u00e9ol A, Comon P, Chevalier P: Blind identification of overcomplete mixtures of sources (BIOME). Lin. Algebra Appl 2004, 391: 3-30.","journal-title":"Lin. Algebra Appl"},{"issue":"11","key":"751_CR14","doi-asserted-by":"publisher","first-page":"5720","DOI":"10.1109\/TSP.2010.2062179","volume":"58","author":"F R\u00f6emer","year":"2010","unstructured":"R\u00f6emer F, Haardt M: Tensor-based channel estimation and iterative refinements for two-way relaying with multiple antennas and spatial reuse. IEEE Trans. Signal Process 2010, 58(11):5720-5735.","journal-title":"IEEE Trans. Signal Process"},{"issue":"1","key":"751_CR15","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0167-9473(94)90132-5","volume":"18","author":"RA Harshman","year":"1994","unstructured":"Harshman RA, Lundy ME: PARAFAC: parallel factor analysis. Comput. Stat. Data Anal 1994, 18(1):39-72. 10.1016\/0167-9473(94)90132-5","journal-title":"Comput. Stat. Data Anal"},{"issue":"2","key":"751_CR16","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1137\/110843587","volume":"33","author":"A Uschmajew","year":"2012","unstructured":"Uschmajew A: Local convergence of the alternating least squares algorithm for canonical tensor approximation. SIAM. J. Matrix Anal. Appl 2012, 33(2):639-652. 10.1137\/110843587","journal-title":"SIAM. J. Matrix Anal. Appl"},{"issue":"3","key":"751_CR17","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1137\/06065577","volume":"30","author":"M Rajih","year":"2008","unstructured":"Rajih M, Comon P, Harshman RA: Enhanced line search: a novel method to accelerate PARAFAC. SIAM J. Matrix Anal. Appl 2008, 30(3):1128-1147. 10.1137\/06065577","journal-title":"SIAM J. Matrix Anal. Appl"},{"issue":"2","key":"751_CR18","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1002\/cem.1335","volume":"25","author":"E Acar","year":"2011","unstructured":"Acar E, Dunlavy DM, Kolda TG: A scalable optimization approach for fitting canonical tensor decompositions. J. Chemometr 2011, 25(2):67-86. 10.1002\/cem.1335","journal-title":"J. Chemometr"},{"issue":"9","key":"751_CR19","doi-asserted-by":"publisher","first-page":"2722","DOI":"10.1016\/j.sigpro.2013.02.016","volume":"93","author":"F R\u00f6emer","year":"2013","unstructured":"R\u00f6emer F, Haardt M: A semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations (SECSI). Signal Process 2013, 93(9):2722-2738. 10.1016\/j.sigpro.2013.02.016","journal-title":"Signal Process"},{"key":"751_CR20","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/j.chemolab.2013.12.009","volume":"132","author":"X Luciani","year":"2014","unstructured":"Luciani X, Albera L: Canonical polyadic decomposition based on joint eigenvalue decomposition. Chemometr. Intell. Lab 2014, 132: 152-167.","journal-title":"Chemometr. Intell. Lab"},{"issue":"3","key":"751_CR21","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF02310791","volume":"35","author":"JD Carroll","year":"1970","unstructured":"Carroll JD, Chang J-J: Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika 1970, 35(3):283-319. 10.1007\/BF02310791","journal-title":"Psychometrika"},{"issue":"2","key":"751_CR22","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1016\/j.csda.2004.08.005","volume":"50","author":"F Husson","year":"2006","unstructured":"Husson F, Pag\u00e9s J: INDSCAL model: geometrical interpretation and methodology. Comput. Stat. Data Anal 2006, 50(2):358-378. 10.1016\/j.csda.2004.08.005","journal-title":"Comput. Stat. Data Anal"},{"issue":"7","key":"751_CR23","doi-asserted-by":"publisher","first-page":"1545","DOI":"10.1109\/TSP.2002.1011195","volume":"50","author":"A Yeredor","year":"2002","unstructured":"Yeredor A: Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation. IEEE Trans. Signal Process 2002, 50(7):1545-1553. 10.1109\/TSP.2002.1011195","journal-title":"IEEE Trans. Signal Process"},{"key":"751_CR24","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1137\/S0895479893259546","volume":"17","author":"JF Cardoso","year":"1996","unstructured":"Cardoso JF, Souloumiac A: Jacobi angles for simultaneous diagonalization. SIAM J. Matrix Anal. Appl 1996, 17: 161-164. 10.1137\/S0895479893259546","journal-title":"SIAM J. Matrix Anal. Appl"},{"key":"751_CR25","first-page":"777","volume":"5","author":"A Ziehe","year":"2004","unstructured":"Ziehe A, Laskov P, Nolte G, Muller K-R: A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation. J. Mach. Learn. Res 2004, 5: 777-800.","journal-title":"J. Mach. Learn. Res"},{"key":"751_CR26","volume-title":"ICA 2006, Springer LNCS 3889","author":"B Afsari","year":"2006","unstructured":"Afsari B: Simple LU and QR based non-orthogonal matrix joint diagonalization. In ICA 2006, Springer LNCS 3889. Charleston, SC, USA; 5\u20138 March 2006."},{"key":"751_CR27","first-page":"2773","volume-title":"Proc. ICASSP \u201801","author":"AJ Van der Veen","year":"2001","unstructured":"Van der Veen AJ: Joint diagonalization via subspace fitting techniques. In Proc. ICASSP \u201801. Salt Lake, City, UT; 7\u201311 May 2001:2773-2776."},{"issue":"9","key":"751_CR28","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1109\/LSP.2005.853046","volume":"12","author":"A Yeredor","year":"2005","unstructured":"Yeredor A: On using exact joint diagonalization for noniterative approximate joint diagonalization. IEEE Signal Process. Lett 2005, 12(9):645-648.","journal-title":"IEEE Signal Process. Lett"},{"issue":"9","key":"751_CR29","doi-asserted-by":"publisher","first-page":"3270","DOI":"10.1109\/TSP.2006.877673","volume":"54","author":"R Vollgraf","year":"2006","unstructured":"Vollgraf R, Obermayer K: Quadratic optimization for simultaneous matrix diagonalization. IEEE Trans. Signal Process 2006, 54(9):3270-3278.","journal-title":"IEEE Trans. Signal Process"},{"issue":"5","key":"751_CR30","doi-asserted-by":"publisher","first-page":"1803","DOI":"10.1109\/TSP.2006.889983","volume":"55","author":"XL Li","year":"2007","unstructured":"Li XL, Zhang XD: Nonorthogonal joint diagonalization free of degenerate solution. IEEE Trans. Signal Process 2007, 55(5):1803-1814.","journal-title":"IEEE Trans. Signal Process"},{"issue":"6","key":"751_CR31","doi-asserted-by":"publisher","first-page":"2222","DOI":"10.1109\/TSP.2009.2016997","volume":"57","author":"A Souloumiac","year":"2009","unstructured":"Souloumiac A: Nonorthogonal joint diagonalization by combining Givens and hyperbolic rotations. IEEE Trans. Signal Process 2009, 57(6):2222-2231.","journal-title":"IEEE Trans. Signal Process"},{"issue":"7","key":"751_CR32","doi-asserted-by":"publisher","first-page":"3457","DOI":"10.1109\/TSP.2011.2141667","volume":"59","author":"XF Xu","year":"2011","unstructured":"Xu XF, Feng DZ, Zheng WX: A fast algorithm for nonunitary joint diagonalization and its application to blind source separation. IEEE Trans. Signal Process 2011, 59(7):3457-3463.","journal-title":"IEEE Trans. Signal Process"},{"issue":"1","key":"751_CR33","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1109\/TSP.2011.2171682","volume":"60","author":"G Chabriel","year":"2012","unstructured":"Chabriel G, Barr\u00e8re J: A direct algorithm for nonorthogonal approximate joint diagonalization. IEEE Trans. Signal Process 2012, 60(1):39-47.","journal-title":"IEEE Trans. Signal Process"},{"issue":"3","key":"751_CR34","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1109\/MSP.2014.2298045","volume":"31","author":"G Chabriel","year":"2014","unstructured":"Chabriel G, Kleinsteuber M, Moreau E, Shen H, Tichavsk\u00fd P, Yeredor A: Joint matrices decompositions and blind source separation: A survey of methods, identification, and applications. IEEE Signal Process. Mag 2014, 31(3):34-43.","journal-title":"IEEE Signal Process. Mag"},{"issue":"6755","key":"751_CR35","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1038\/44565","volume":"401","author":"DD Lee","year":"1999","unstructured":"Lee DD, Seung HS: Learning the parts of objects by non-negative matrix factorization. Nature 1999, 401(6755):788-791. 10.1038\/44565","journal-title":"Nature"},{"issue":"12","key":"751_CR36","doi-asserted-by":"publisher","first-page":"3001","DOI":"10.1364\/JOSAA.25.003001","volume":"25","author":"Q Zhang","year":"2008","unstructured":"Zhang Q, Wang H, Plemmons RJ, Pauca VP: Tensor methods for hyperspectral data analysis: a space object material identification study. J. Opt. Soc. Am. A. Opt. Image Sci. Vis 2008, 25(12):3001-3012. 10.1364\/JOSAA.25.003001","journal-title":"J. Opt. Soc. Am. A. Opt. Image Sci. Vis"},{"issue":"9","key":"751_CR37","doi-asserted-by":"publisher","first-page":"2159","DOI":"10.1016\/j.sigpro.2011.03.006","volume":"91","author":"J-P Royer","year":"2011","unstructured":"Royer J-P, Thirion-Moreau N, Comon P: Computing the polyadic decomposition of nonnegative third order tensors. Signal Process 2011, 91(9):2159-2171. 10.1016\/j.sigpro.2011.03.006","journal-title":"Signal Process"},{"key":"751_CR38","doi-asserted-by":"publisher","DOI":"10.1002\/9780470747278","volume-title":"Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation","author":"A Cichocki","year":"2009","unstructured":"Cichocki A, Zdunek R, Phan AH, Amari S: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, West Sussex; 2009."},{"issue":"3","key":"751_CR39","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1109\/MSP.2014.2298891","volume":"31","author":"GX Zhou","year":"2014","unstructured":"Zhou GX, Cichocki A, Zhao Q, Xie SL: Nonnegative matrix and tensor factorizations : an algorithmic perspective. IEEE Signal Process. Mag 2014, 31(3):54-65.","journal-title":"IEEE Signal Process. Mag"},{"issue":"1","key":"751_CR40","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.laa.2014.02.001","volume":"450","author":"J Coloigner","year":"2014","unstructured":"Coloigner J, Karfoul A, Albera L, Comon P: Line search and trust region strategies for canonical decomposition of semi-nonnegative semi-symmetric 3rd order tensors. Lin. Algebra Appl 2014, 450(1):334-374.","journal-title":"Lin. Algebra Appl"},{"issue":"8","key":"751_CR41","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1109\/LSP.2013.2267797","volume":"20","author":"L Wang","year":"2013","unstructured":"Wang L, Albera L, Kachenoura A, Shu HZ, Senhadji L: Nonnegative joint diagonalization by congruence based on LU matrix factorization. IEEE Signal Process. Lett 2013, 20(8):807-810.","journal-title":"IEEE Signal Process. Lett"},{"key":"751_CR42","first-page":"449","volume-title":"SAM\u201914, Proceedings of the Eighth IEEE Sensor Array and Multichannel Signal Processing Workshop","author":"L Wang","year":"2014","unstructured":"Wang L, Albera L, Kachenoura A, Shu HZ, Senhadji L: CP decomposition of semi-nonnegative semi-symmetric tensors based on QR matrix factorization. In SAM\u201914, Proceedings of the Eighth IEEE Sensor Array and Multichannel Signal Processing Workshop. A Coruna, Spain; 22\u201325 June 2014:449-452."},{"issue":"3","key":"751_CR43","doi-asserted-by":"publisher","first-page":"1148","DOI":"10.1137\/060655997","volume":"30","author":"B Afsari","year":"2008","unstructured":"Afsari B: Sensitivity analysis for the problem of matrix joint diagonalization. SIAM J. Matrix Anal. Appl 2008, 30(3):1148-1171. 10.1137\/060655997","journal-title":"SIAM J. Matrix Anal. Appl"},{"issue":"2","key":"751_CR44","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1109\/97.554471","volume":"4","author":"M Wax","year":"1997","unstructured":"Wax M, Sheinvald J: A least-squares approach to joint diagonalization. IEEE Signal Process. Lett 1997, 4(2):52-53.","journal-title":"IEEE Signal Process. Lett"},{"issue":"6","key":"751_CR45","doi-asserted-by":"publisher","first-page":"3022","DOI":"10.1109\/TSP.2007.893974","volume":"55","author":"S D\u00e9gerine","year":"2007","unstructured":"D\u00e9gerine S, Kane E: A comparative study of approximate joint diagonalization algorithms for blind source separation in presence of additive noise. IEEE Trans. Signal Process 2007, 55(6):3022-3031.","journal-title":"IEEE Trans. Signal Process"},{"issue":"5","key":"751_CR46","doi-asserted-by":"publisher","first-page":"1673","DOI":"10.1109\/TSP.2006.889469","volume":"55","author":"EM Fadaili","year":"2007","unstructured":"Fadaili EM, Thirion-Moreau N, Moreau E: Nonorthogonal joint diagonalization\/zero diagonalization for source separation based on time-frequency distributions. IEEE Trans. Signal Process 2007, 55(5):1673-1687.","journal-title":"IEEE Trans. Signal Process"},{"issue":"2","key":"751_CR47","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1109\/78.554307","volume":"45","author":"A Belouchrani","year":"1997","unstructured":"Belouchrani A, Abed-Meraim K, Cardoso JF, Moulines E: A blind source separation technique using second-order statistics. IEEE Trans. Signal Process 1997, 45(2):434-444. 10.1109\/78.554307","journal-title":"IEEE Trans. Signal Process"},{"key":"751_CR48","doi-asserted-by":"publisher","first-page":"1837","DOI":"10.1137\/S089547980035689X","volume":"22","author":"DT Pham","year":"2001","unstructured":"Pham DT: Joint approximate diagonalization of positive definite Hermitian matrices. SIAM J. Matrix Anal. Appl 2001, 22: 1837-1848.","journal-title":"SIAM J. Matrix Anal. Appl"},{"issue":"3","key":"751_CR49","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1109\/TSP.2008.2009271","volume":"57","author":"P Tichavsk\u00fd","year":"2009","unstructured":"Tichavsk\u00fd P, Yeredor A: Fast approximate joint diagonalization incorporating weight matrices. IEEE Trans. Signal Process 2009, 57(3):878-891.","journal-title":"IEEE Trans. Signal Process"},{"key":"751_CR50","volume-title":"Optimality computation and interpretation of nonnegative matrix factorizations","author":"M Chu","year":"2004","unstructured":"Chu M, Diele F, Plemmons R, Ragni S: Optimality computation and interpretation of nonnegative matrix factorizations. Technical report, Wake Forest University 2004"},{"key":"751_CR51","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719512","volume-title":"Matrix Analysis and Applied Linear Algebra","author":"CD Meyer","year":"2000","unstructured":"Meyer CD: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia; 2000."},{"key":"751_CR52","volume-title":"Multirate Systems and Filter Banks","author":"PP Vaidyanathan","year":"1993","unstructured":"Vaidyanathan PP: Multirate Systems and Filter Banks. PTR Prentice Hall, United States; 1993."},{"key":"751_CR53","first-page":"81","volume-title":"SAM\u201914, Proceedings of the Eighth IEEE Sensor Array and Multichannel Signal Processing Workshop","author":"L Wang","year":"2014","unstructured":"Wang L, Kachenoura A, Albera L, Karfoul A, Shu HZ, Senhadji L: Nonnegative compression for semi-nonnegative independent component analysis. In SAM\u201914, Proceedings of the Eighth IEEE Sensor Array and Multichannel Signal Processing Workshop. A Coruna, Spain; 22\u201325 June 2014:81-84."},{"issue":"3","key":"751_CR54","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0165-1684(94)90029-9","volume":"36","author":"P Comon","year":"1994","unstructured":"Comon P: Independent component analysis, a new concept? Signal Process 1994, 36(3):287-314. 10.1016\/0165-1684(94)90029-9","journal-title":"Signal Process"},{"issue":"3","key":"751_CR55","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1109\/TNN.2003.810616","volume":"14","author":"MD Plumbley","year":"2003","unstructured":"Plumbley MD: Algorithms for nonnegative independent component analysis. IEEE Trans. Neural Netw 2003, 14(3):534-543. 10.1109\/TNN.2003.810616","journal-title":"IEEE Trans. Neural Netw"},{"issue":"2","key":"751_CR56","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1137\/07069239X","volume":"30","author":"H Kim","year":"2008","unstructured":"Kim H, Park H: Nonnegative matrix factorization based on alternating nonnegativity constrained least squares and active set method. SIAM J. Matrix Anal. Appl 2008, 30(2):713-730. 10.1137\/07069239X","journal-title":"SIAM J. Matrix Anal. Appl"},{"key":"751_CR57","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/B978-0-12-374726-6.00010-2","volume-title":"Handbook of Blind Source Separation, ed. by P Comon, C Jutten,","author":"De Lathauwer","year":"2010","unstructured":"De Lathauwer: Algebraic methods after prewhitening. In Handbook of Blind Source Separation, ed. by P Comon, C Jutten,. Elsevier, Oxford; 2010:155-177. Chap. 5"},{"issue":"5","key":"751_CR58","doi-asserted-by":"publisher","first-page":"1361","DOI":"10.2337\/db09-0916","volume":"60","author":"DE Befroy","year":"2011","unstructured":"Befroy DE, Shulman GI: Magnetic resonance spectroscopy studies of human metabolism. Diabetes 2011, 60(5):1361-1369. 10.2337\/db09-0916","journal-title":"Diabetes"},{"key":"751_CR59","volume-title":"S\u00e9paration de sources non-n\u00e9gatives: application au traitement des signaux de spectroscopie","author":"S Moussaoui","year":"2005","unstructured":"Moussaoui S: S\u00e9paration de sources non-n\u00e9gatives: application au traitement des signaux de spectroscopie. PhD thesis, Universit\u00e9 Henri Poincar\u00e9, (2005)"},{"key":"751_CR60","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1016\/B978-0-12-374726-6.00023-0","volume-title":"Handbook of Blind Source Separation ed. by P Comon, C Jutten,","author":"L Albera","year":"2010","unstructured":"Albera L, Comon P, Parra LC, Karfoul A, Kachenoura A, Senhadji L: Biomedical applications. In Handbook of Blind Source Separation ed. by P Comon, C Jutten,. Elsevier, Oxford; 2010:737-777. Chap. 18"}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2014-150.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/1687-6180-2014-150\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2014-150.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T10:57:54Z","timestamp":1630580274000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/1687-6180-2014-150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,8]]},"references-count":60,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["751"],"URL":"https:\/\/doi.org\/10.1186\/1687-6180-2014-150","relation":{},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,8]]},"assertion":[{"value":"31 March 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2014","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 October 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"150"}}