LEADER 05469nam 2200757Ia 450 001 9911020448503321 005 20200520144314.0 010 $a9786613100795 010 $a9781118097748 010 $a1118097742 010 $a9781283100793 010 $a1283100797 010 $a9780470638286 010 $a0470638281 010 $a9780470638279 010 $a0470638273 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(OCoLC)739118460 035 $a(PPN)264394453 035 $a(Perlego)1010366 035 $a(EXLCZ)992560000000058231 100 $a20100804d2010 uy 0 101 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 $aHoboken, NJ $cJohn Wiley & Sons$dc2010 215 $a1 online resource (278 p.) 225 1 $aAdaptive and learning systems for signal processing, communication, and control 300 $aDescription based upon print version of record. 311 08$a9780471322702 311 08$a0471322709 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, communications, and control. 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 $a006.3/2 700 $aCirrincione$b Giansalvo$f1959-$01636045 701 $aCirrincione$b Maurizio$f1961-$01636046 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020448503321 996 $aNeural-based orthogonal data fitting$93977135 997 $aUNINA