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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
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Conscious and Non-conscious Representations of Emotional Faces in Asperger's Syndrome
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Representation Learning by Rotating Your Faces.

Luan Tran, Xi Yin, Xiaoming Liu

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    |September 6, 2018
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    Summary
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    This study introduces Disentangled Representation learning-Generative Adversarial Network (DR-GAN) for improved face recognition. DR-GAN jointly learns representations and frontalizes faces, outperforming existing methods in pose-invariant face recognition.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Large pose discrepancies in face images pose a significant challenge for automatic face recognition systems.
    • Current methods often tackle pose invariance by either frontalizing faces or learning separate pose-invariant representations.

    Purpose of the Study:

    • To propose a novel approach that jointly learns face representations and performs face frontalization for enhanced pose-invariant recognition.
    • To develop a method that leverages the synergy between representation learning and pose normalization.

    Main Methods:

    • Introduced a Disentangled Representation learning-Generative Adversarial Network (DR-GAN) with an encoder-decoder generator structure.
    • Employed explicit disentanglement of identity representation from pose variations using a pose code and discriminator-based pose estimation.
    • Designed DR-GAN to accept single or multiple input images for unified identity representation generation and synthetic image creation.

    Main Results:

    • The DR-GAN model demonstrated a capability for both generative (face synthesis) and discriminative (recognition) tasks.
    • Achieved superior performance in learning robust identity representations and synthesizing realistic face images with arbitrary poses.
    • Outperformed state-of-the-art methods in quantitative and qualitative evaluations on diverse face databases.

    Conclusions:

    • Jointly learning representations and frontalizing faces is more effective than sequential approaches.
    • DR-GAN offers a powerful framework for pose-invariant face recognition and face image manipulation.
    • The proposed method advances the state of the art in handling large pose variations in face recognition.