LEADER 05410nam 2200709 450 001 9910139216203321 005 20221206095039.0 010 $a1-118-09774-2 010 $a1-283-10079-7 010 $a9786613100795 010 $a0-470-63828-1 010 $a0-470-63827-3 024 7 $a10.1002/9780470638286 035 $a(CKB)2560000000058231 035 $a(EBL)661690 035 $a(SSID)ssj0000471627 035 $a(PQKBManifestationID)11300768 035 $a(PQKBTitleCode)TC0000471627 035 $a(PQKBWorkID)10429306 035 $a(PQKB)11056311 035 $a(MiAaPQ)EBC661690 035 $a(CaBNVSL)mat05732789 035 $a(IDAMS)0b000064814ebff9 035 $a(IEEE)5732789 035 $a(PPN)264394453 035 $a(OCoLC)739118460 035 $a(EXLCZ)992560000000058231 100 $a20151221d2011 uy 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNeural-based orthogonal data fitting $ethe EXIN neural networks /$fGiansalvo Cirrincione, Maurizio Cirrincione 210 1$aHoboken, New Jersey :$cWiley,$dc2010. 210 2$a[Piscataqay, New Jersey] :$cIEEE Xplore,$d[2011] 215 $a1 online resource (278 p.) 225 1 $aAdaptive and learning systems for signal processing, communications and control series ;$v38 300 $aDescription based upon print version of record. 311 $a0-471-32270-9 320 $aIncludes bibliographical references (p. 227-237) and index. 327 $aForeword -- Preface -- 1 The Total Least Squares Problems -- 1.1 Introduction -- 1.2 Some TLS Applications -- 1.3 Preliminaries -- 1.4 Ordinary Least Squares Problems -- 1.5 Basic TLS Problem -- 1.6 Multidimensional TLS Problem -- 1.7 Nongeneric Unidimensional TLS Problem -- 1.8 Mixed OLS-TLS Problem -- 1.9 Algebraic Comparisons Between TLS and OLS -- 1.10 Statistical Properties and Validity -- 1.11 Basic Data Least Squares Problem -- 1.12 The Partial TLS Algorithm -- 1.13 Iterative Computation Methods -- 1.14 Rayleigh Quotient Minimization Non Neural and Neural Methods -- 2 The MCA EXIN Neuron -- 2.1 The Rayleigh Quotient -- 2.2 The Minor Component Analysis -- 2.3 The MCA EXIN Linear Neuron -- 2.4 The Rayleigh Quotient Gradient Flows -- 2.5 The MCA EXIN ODE Stability Analysis -- 2.6 Dynamics of the MCA Neurons -- 2.7 Fluctuations (Dynamic Stability) and Learning Rate -- 2.8 Numerical Considerations -- 2.9 TLS Hyperplane Fitting -- 2.10 Simulations for the MCA EXIN Neuron -- 2.11 Conclusions -- 3 Variants of the MCA EXIN Neuron -- 3.1 High-Order MCA Neurons -- 3.2 The Robust MCA EXIN Nonlinear Neuron (NMCA EXIN) -- 3.3 Extensions of the Neural MCA -- 4 Introduction to the TLS EXIN Neuron -- 4.1 From MCA EXIN to TLS EXIN -- 4.2 Deterministic Proof and Batch Mode -- 4.3 Acceleration Techniques -- 4.4 Comparison with TLS GAO -- 4.5 A TLS Application: Adaptive IIR Filtering -- 4.6 Numerical Considerations -- 4.7 The TLS Cost Landscape: Geometric Approach -- 4.8 First Considerations on the TLS Stability Analysis -- 5 Generalization of Linear Regression Problems -- 5.1 Introduction -- 5.2 The Generalized Total Least Squares (GeTLS EXIN) Approach -- 5.3 The GeTLS Stability Analysis -- 5.4 Neural Nongeneric Unidimensional TLS -- 5.5 Scheduling -- 5.6 The Accelerated MCA EXIN Neuron (MCA EXIN+) -- 5.7 Further Considerations -- 5.8 Simulations for the GeTLS EXIN Neuron -- 6 The GeMCA EXIN Theory -- 6.1 The GeMCA Approach -- 6.2 Analysis of Matrix K -- 6.3 Analysis of the Derivative of the Eigensystem of GeTLS EXIN. 327 $a6.4 Rank One Analysis Around the TLS Solution -- 6.5 The GeMCA Spectra -- 6.6 Qualitative Analysis of the Critical Points of the GeMCA EXIN Error Function -- 6.7 Conclusion -- References -- Index. 330 $a"Written by three leaders in the field of neural based algorithms, Neural Based Orthogonal Data Fitting proposes several neural networks, all endowed with a complete theory which not only explains their behavior, but also compares them with the existing neural and traditional algorithms. The algorithms are studied from different points of view, including: as a differential geometry problem, as a dynamic problem, as a stochastic problem, and as a numerical problem. All algorithms have also been analyzed on real time problems (large dimensional data matrices) and have shown accurate solutions. Where most books on the subject are dedicated to PCA (principal component analysis) and consider MCA (minor component analysis) as simply a consequence, this is the fist book to start from the MCA problem and arrive at important conclusions about the PCA problem."--$cProvided by publisher. 410 0$aAdaptive and learning systems for signal processing, communication, and control ;$v38 606 $aNeural networks (Computer science) 606 $aNumerical analysis 606 $aOrthogonalization methods 615 0$aNeural networks (Computer science) 615 0$aNumerical analysis. 615 0$aOrthogonalization methods. 676 $a006.3/2 676 $a621.399 700 $aCirrincione$b Giansalvo$f1959-$0845624 701 $aCirrincione$b Maurizio$f1961-$0845625 801 0$bCaBNVSL 801 1$bCaBNVSL 801 2$bCaBNVSL 906 $aBOOK 912 $a9910139216203321 996 $aNeural-based orthogonal data fitting$91887794 997 $aUNINA