Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Machines: Problem Solving II01:30

Machines: Problem Solving II

348
Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. Consider a lifting tong carrying a 100 kg load. It comprises movable sections DAF and CBG linked together with member AB.
348
Machines: Problem Solving I01:22

Machines: Problem Solving I

373
A toggle clamp is a mechanical device commonly used for holding and clamping objects in various applications, such as woodworking, metalworking, and assembly operations. Consider a toggle clamp subjected to a force of 200 N at the handle. The vertical clamping force can be calculated, provided the dimensions of the toggle clamp are known.
The toggle clamp system is a machine structure consisting of movable, pin-connected multi-force members that form a stabilized system to transmit forces. The...
373
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

88
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
88
Associative Learning01:27

Associative Learning

474
Associative learning is a fundamental concept in behavioral psychology, wherein a connection is established between two stimuli or events, leading to a learned response. This process is critical in understanding how behaviors are acquired and modified. Conditioning, the mechanism through which associations are formed, can be divided into two main types: classical conditioning and operant conditioning, each elucidating different aspects of associative learning.
Classical conditioning, also known...
474
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

120
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....
120
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

7.7K
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.
The process of fitting the best-fit...
7.7K

You might also read

Related Articles

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

Sort by
Same author

Computed Quantitative Planar Imaging for Targeted Alpha Therapy: Model-Based Sparse Reconstruction Validated With a Novel <sup>225</sup>Ac Epoxy Phantom.

IEEE transactions on medical imaging·2026
Same author

Hypothesis spaces for deep learning.

Neural networks : the official journal of the International Neural Network Society·2025
Same author

Uniform Convergence of Deep Neural Networks With Lipschitz Continuous Activation Functions and Variable Widths.

IEEE transactions on information theory·2025
Same author

Multi-scale cascaded networks for synthesis of mammogram to decrease intensity distortion and increase model-based perceptual similarity.

Medical physics·2022
Same author

Convergence of deep convolutional neural networks.

Neural networks : the official journal of the International Neural Network Society·2022
Same author

A Fast Convergent Ordered-Subsets Algorithm With Subiteration-Dependent Preconditioners for PET Image Reconstruction.

IEEE transactions on medical imaging·2022
Same journal

Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods.

Applied numerical mathematics : transactions of IMACS·2017
Same journal

Simultaneous optical flow and source estimation: Space-time discretization and preconditioning.

Applied numerical mathematics : transactions of IMACS·2015
Same journal

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

Applied numerical mathematics : transactions of IMACS·2014
Same journal

A study of different modeling choices for simulating platelets within the immersed boundary method.

Applied numerical mathematics : transactions of IMACS·2013
Same journal

Convergence of adaptive BEM for some mixed boundary value problem.

Applied numerical mathematics : transactions of IMACS·2013
Same journal

Estimator reduction and convergence of adaptive BEM.

Applied numerical mathematics : transactions of IMACS·2013
See all related articles

Related Experiment Video

Updated: Aug 4, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
08:27

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines

Published on: January 5, 2024

1.2K

Sparse Machine Learning in Banach Spaces.

Yuesheng Xu1

  • 1Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529, USA.

Applied Numerical Mathematics : Transactions of IMACS
|April 3, 2023
PubMed
Summary
This summary is machine-generated.

This paper introduces sparse machine learning in Banach spaces for graduate students. It explains learning in reproducing kernel Hilbert spaces and sparse learning in reproducing kernel Banach spaces (RKBS) using binary classification examples.

Keywords:
46B4546N1090C30reproducing kernel Banach spacesparse machine learning

More Related Videos

Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model
07:15

Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model

Published on: August 16, 2020

6.9K
Asthma Detection Research Based on Voice Signal Processing and Machine Learning
04:04

Asthma Detection Research Based on Voice Signal Processing and Machine Learning

Published on: July 22, 2025

154

Related Experiment Videos

Last Updated: Aug 4, 2025

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines
08:27

Author Spotlight: Efficient Image Recognition Using Directional Gradient Histogram Technique and Support Vector Machines

Published on: January 5, 2024

1.2K
Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model
07:15

Machine Learning Algorithms for Early Detection of Bone Metastases in an Experimental Rat Model

Published on: August 16, 2020

6.9K
Asthma Detection Research Based on Voice Signal Processing and Machine Learning
04:04

Asthma Detection Research Based on Voice Signal Processing and Machine Learning

Published on: July 22, 2025

154

Area of Science:

  • Mathematics
  • Statistics
  • Engineering
  • Machine Learning

Background:

  • Introduces the fundamental concept of sparse machine learning.
  • Explains learning in reproducing kernel Hilbert spaces and sparse learning in reproducing kernel Banach spaces (RKBS).

Purpose of the Study:

  • To explain sparse machine learning in Banach spaces to graduate students and researchers.
  • To illustrate RKBS concepts using the Banach space .

Main Methods:

  • Uses binary classification as an example.
  • Reviews existing results and presents new theoretical observations on RKBS.

Main Results:

  • Provides an elementary yet rigorous illustration of RKBS concepts.
  • Offers insights into the state-of-the-art in sparse learning.

Conclusions:

  • Discusses open problems critical to RKBS theory.
  • Aims to enhance understanding of sparse machine learning in advanced mathematical spaces.