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Related Concept Videos

State Space Representation01:27

State Space Representation

251
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.
Consider an RLC circuit, a...
251
Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
463
Classification of Systems-I01:26

Classification of Systems-I

236
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
236
State Space to Transfer Function01:21

State Space to Transfer Function

251
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
251
Properties of Fourier series I01:20

Properties of Fourier series I

365
The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM)...
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CoReS: Compatible Representations via Stationarity.

Niccolo Biondi, Federico Pernici, Matteo Bruni

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |April 8, 2023
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    Summary
    This summary is machine-generated.

    This study introduces a new training method for compatible feature representations in visual search. This approach avoids costly re-indexing when updating models with new data, improving efficiency.

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    Area of Science:

    • Computer Science
    • Machine Learning
    • Artificial Intelligence

    Background:

    • Visual search systems require feature extraction from large datasets.
    • Updating representation models necessitates re-indexing, which is computationally expensive and sometimes infeasible.
    • Current methods lack compatibility between old and new features, hindering model upgrades.

    Purpose of the Study:

    • To propose a novel training procedure for learning compatible feature representations.
    • To enable interchangeable use of old and new features over time in visual search.
    • To eliminate the need for re-indexing gallery sets during model updates.

    Main Methods:

    • Introduced CoReS, a training procedure for compatible representations.
    • Utilized fixed classifiers based on polytopes for feature stationarity.
    • Ensured maximal class separation and stationary spatial configuration in the representation space.

    Main Results:

    • The proposed CoReS method demonstrates superior performance over existing state-of-the-art techniques.
    • The procedure is highly effective for multiple training set upgrades, common in real-world applications.
    • Eliminates the need for mapping or pairwise training between old and new models.

    Conclusions:

    • CoReS offers a computationally efficient and practical solution for updating visual search models.
    • The method ensures feature compatibility, enabling seamless integration of new data without re-indexing.
    • This advancement is particularly valuable for large-scale visual search applications with evolving datasets.