Complex-Valued Neural Networks: Learning Algorithms and Applications
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Complex-Valued Neural Networks: Learning Algorithms and Applications
DE PB NW
ISBN: 9783659582417 bzw. 3659582417, in Deutsch, LAP Lambert Academic Publishing, Taschenbuch, neu.
Lieferung aus: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, BuchWeltWeit Inh. Ludwig Meier e.K. [57449362], Bergisch Gladbach, Germany.
Neuware - Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. 140 pp. Englisch.
Von Händler/Antiquariat, BuchWeltWeit Inh. Ludwig Meier e.K. [57449362], Bergisch Gladbach, Germany.
Neuware - Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. 140 pp. Englisch.
2
Complex-Valued Neural Networks: Learning Algorithms and Applications
DE PB NW
ISBN: 9783659582417 bzw. 3659582417, in Deutsch, LAP Lambert Academic Publishing, Taschenbuch, neu.
Lieferung aus: Deutschland, Versandkostenfrei.
Complex-Valued Neural Networks: Learning Algorithms and Applications: Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. Englisch, Taschenbuch.
Complex-Valued Neural Networks: Learning Algorithms and Applications: Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. Englisch, Taschenbuch.
3
Complex-Valued Neural Networks: Learning Algorithms and Applications (2018)
DE PB NW
ISBN: 9783659582417 bzw. 3659582417, in Deutsch, 140 Seiten, LAP Lambert Academic Publishing, Taschenbuch, neu.
Lieferung aus: Deutschland, Versandkosten nach: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, Syndikat Buchdienst, [4235284].
Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. 2018, Taschenbuch / Paperback, Neuware, H: 220mm, B: 150mm, 140, Internationaler Versand, Selbstabholung und Barzahlung, PayPal, offene Rechnung, Banküberweisung.
Von Händler/Antiquariat, Syndikat Buchdienst, [4235284].
Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. 2018, Taschenbuch / Paperback, Neuware, H: 220mm, B: 150mm, 140, Internationaler Versand, Selbstabholung und Barzahlung, PayPal, offene Rechnung, Banküberweisung.
4
Symbolbild
Complex-Valued Neural Networks: Learning Algorithms and Applications
DE PB NW
ISBN: 9783659582417 bzw. 3659582417, in Deutsch, Taschenbuch, neu.
Lieferung aus: Deutschland, Versandkostenfrei.
Von Händler/Antiquariat, European-Media-Service Mannheim [1048135], Mannheim, Germany.
Publisher/Verlag: LAP Lambert Academic Publishing | Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. | Format: Paperback | Language/Sprache: english | 140 pp.
Von Händler/Antiquariat, European-Media-Service Mannheim [1048135], Mannheim, Germany.
Publisher/Verlag: LAP Lambert Academic Publishing | Complex-valued data arise in various applications, such as radar and array signal processing, magnetic resonance imaging, communication systems, and processing data in the frequency domain. To deal with such data properly, neural networks are extended to the complex domain, referred to as complex-valued neural networks (CVNNs), allowing the network parameters to be complex numbers and the computations to follow the complex algebraic rules. Unlike the real-valued case, the nonlinear functions in the CVNNs do not have standard complex derivatives as the Cauchy-Riemann equations do not hold for them. Consequently, the traditional approach for deriving learning algorithms reformulates the problem in the real domain which is often tedious. In this work, we first develop a systematic and simpler approach using Wirtinger calculus to derive the learning algorithms in the CVNNs. It is shown that adopting three steps: (i) computing a pair of derivatives in the conjugate coordinate system, (ii) using coordinate transformation between real and conjugate coordinates, and (iii) organizing derivative computations through functional dependency graph greatly simplify the derivations. | Format: Paperback | Language/Sprache: english | 140 pp.
6
Symbolbild
Complex-Valued Neural Networks: Learning Algorithms and Applications (2018)
EN PB NW
ISBN: 9783659582417 bzw. 3659582417, in Englisch, 140 Seiten, LAP Lambert Academic Publishing, Taschenbuch, neu.
Lieferung aus: Deutschland, Versandfertig in 4 - 5 Werktagen, Versandkostenfrei. Tatsächliche Versandkosten können abweichen.
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Von Händler/Antiquariat, averdo24.
Die Beschreibung dieses Angebotes ist von geringer Qualität oder in einer Fremdsprache. Trotzdem anzeigen
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