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Related Concept Videos

Reducing Line Loss01:18

Reducing Line Loss

446
In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...
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Classification of Signals01:30

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In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...
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Classification of Systems-II01:31

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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
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Classification of Systems-I01:26

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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:
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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Support Vector Machine Classifier With Pinball Loss.

Xiaolin Huang, Lei Shi, Johan A K Suykens

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |September 10, 2015
    PubMed
    Summary

    This study introduces the pinball loss Support Vector Machine (SVM), or pin-SVM, a novel classifier offering improved noise insensitivity and re-sampling stability compared to traditional hinge loss SVMs.

    Area of Science:

    • Machine Learning
    • Statistical Classification
    • Computational Statistics

    Background:

    • Support Vector Machines (SVMs) traditionally use hinge loss, which is sensitive to noisy data and unstable under resampling.
    • Hinge loss is associated with the shortest distance between sets, limiting its robustness.
    • Pinball loss, extensively studied in regression, offers quantile-based distance measures and enhanced stability.

    Purpose of the Study:

    • To introduce and investigate a novel Support Vector Machine (SVM) classifier utilizing the pinball loss function.
    • To evaluate the properties of this pinball loss SVM (pin-SVM), focusing on noise insensitivity, robustness, and misclassification error.
    • To explore the application of an insensitive zone to the pin-SVM for achieving a sparse model.

    Main Methods:

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    • Development of a Support Vector Machine (SVM) classifier incorporating the pinball loss function, termed pin-SVM.
    • Analysis of pin-SVM properties, including its sensitivity to noise, resampling stability, and misclassification error.
    • Integration of an insensitive zone into the pin-SVM framework to promote model sparsity.

    Main Results:

    • The proposed pin-SVM demonstrates significant noise insensitivity and improved re-sampling stability compared to traditional hinge loss SVMs.
    • The pin-SVM maintains the same computational complexity as standard SVMs.
    • Application of an insensitive zone results in a sparser pin-SVM model.

    Conclusions:

    • The pinball loss SVM (pin-SVM) offers a robust and stable alternative to traditional hinge loss SVM classifiers.
    • Pin-SVM provides advantages in handling noisy datasets and ensuring consistent performance across different data samples.
    • The proposed pin-SVM is computationally efficient and can be optimized for sparsity.