Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Classification of Systems-I

Classification of Systems-I

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:

Linear Circuits

Linear Circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...

Linearization and Approximation

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...

Introduction to Learning

Introduction to Learning

Learning is the process of acquiring knowledge or skills through practice or experience, leading to long-lasting behavioral changes. This acquisition occurs through interaction with the environment and requires practice or experience. For instance, mastering a skill such as surfing requires considerable practice and experience, highlighting the essential role of repeated interactions with the environment in learning.
In contrast to learned behaviors, unlearned behaviors such as crying, sexual...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

Linear time-invariant Systems

Linear time-invariant Systems

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 calculated...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Cross-validation with active pattern selection for neural-network classifiers.

IEEE transactions on neural networks·2008

Same author

Optimal linear compression under unreliable representation and robust PCA neural models.

IEEE transactions on neural networks·2008

Same author

Local PCA algorithms.

IEEE transactions on neural networks·2008

Same author

No association of clock gene T3111C polymorphism and affective disorders.

European neuropsychopharmacology : the journal of the European College of Neuropsychopharmacology·2004

Same author

Study of family history in seasonal affective disorder.

Neuropsychobiology·2001

Same author

No evidence for in vivo regulation of midbrain serotonin transporter availability by serotonin transporter promoter gene polymorphism.

Biological psychiatry·2001

Search research articles

Related Experiment Videos

Learning in linear neural networks: a survey.

P F Baldi¹, K Hornik

¹Div. of Biol., California Inst. of Technol., Pasadena, CA.

IEEE Transactions on Neural Networks

|January 1, 1995

Summary

This summary is machine-generated.

This study analyzes linear neural networks, exploring learning, generalization, and self-organization. It connects these concepts to principal component analysis (PCA) and highlights open research questions in artificial intelligence.

Related Experiment Videos

Area of Science:

Artificial Intelligence
Machine Learning
Computational Neuroscience

Background:

Linear networks offer a simplified model for understanding complex neural network behaviors.
Analytical solutions for learning, generalization, and self-organization are often achievable in linear models.
Connections to classical statistical methods like Principal Component Analysis (PCA) provide valuable insights.

Purpose of the Study:

To survey known results on linear networks concerning learning, generalization, and self-organization.
To explore the error landscape of backpropagation learning in linear networks.
To unify the understanding of various unsupervised learning algorithms and their properties.

Main Methods:

Analytical treatment of learning dynamics in linear networks.
Analysis of generalization error evolution over time.
Investigation of unsupervised learning algorithms and their statistical underpinnings.
Examination of the impact of noise on backpropagation.

Main Results:

Characterization of the error function landscape for backpropagation.
Understanding the temporal dynamics of generalization in linear models.
A unified perspective on unsupervised learning algorithms, linking them to PCA.
Analysis of noise effects on network performance.

Conclusions:

Linear networks serve as crucial testbeds for fundamental AI questions.
The study provides a comprehensive overview and new results on linear network properties.
Open questions are identified, guiding future research in neural network theory.