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

Hyperbolas01:30

Hyperbolas

172
A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
172
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

177
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
177
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

445
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
445
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

952
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
952
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

731
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
731
Parabolas01:30

Parabolas

113
A parabola is a fundamental curve in the family of conic sections arising from the intersection of a plane with a double-napped cone when the plane is parallel to the cone’s slant height. This geometric condition yields a unique open curve defined by its equidistance from a fixed point, the focus, and a fixed line, the directrix.A parabola is mathematically defined as the locus of all points in a plane that are equidistant from the focus and the directrix. In Cartesian coordinates, the...
113

You might also read

Related Articles

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

Sort by
Same author

Promera: a unified model for biomolecular structure prediction, filtering, and design.

bioRxiv : the preprint server for biology·2026
Same author

Memorization in large language models in medicine prevalence characteristics and implications.

Nature communications·2026
Same author

Privacy-enhancing sequential learning under heterogeneous selection bias in multi-site electronic health records data.

Journal of the American Medical Informatics Association : JAMIA·2026
Same author

Thousandfold Expansion Microscopy.

bioRxiv : the preprint server for biology·2026
Same author

SwitchCraft: A Programmatic Framework for Designing State-Switching Proteins.

ArXiv·2026
Same author

Multi-resolution modeling of a discrete stochastic process identifies causes of cancer.

... International Conference on Learning Representations·2026
Same journal

Towards the Efficient Inference by Incorporating Automated Computational Phenotypes under Covariate Shift.

Proceedings of machine learning research·2026
Same journal

Endo-SemiS: Towards Robust Semi-Supervised Image Segmentation for Endoscopic Video.

Proceedings of machine learning research·2026
Same journal

Perspective: Machine Learning for Health Should Consider Social Drivers of Health.

Proceedings of machine learning research·2026
Same journal

Classifying Phonotrauma Severity from Vocal Fold Images with Soft Ordinal Regression.

Proceedings of machine learning research·2026
Same journal

Does Domain-Specific Retrieval Augmented Generation Help LLMs Answer Consumer Health Questions?

Proceedings of machine learning research·2026
Same journal

Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential.

Proceedings of machine learning research·2026
See all related articles

Related Experiment Video

Updated: Dec 11, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.4K

Large-Margin Classification in Hyperbolic Space.

Hyunghoon Cho1, Benjamin DeMeo2, Jian Peng3

  • 1Massachusetts Institute of Technology.

Proceedings of Machine Learning Research
|August 25, 2020
PubMed
Summary
This summary is machine-generated.

We introduce hyperbolic Support Vector Machines (SVM) for accurate data classification in hyperbolic space. This method respects hyperbolic geometry, improving analysis of complex networks and word embeddings.

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.7K
Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
08:59

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

7.4K

Related Experiment Videos

Last Updated: Dec 11, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.4K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.7K
Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
08:59

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

7.4K

Area of Science:

  • Machine Learning
  • Data Science
  • Computational Geometry

Background:

  • Hierarchical data relationships are often better represented in hyperbolic space than Euclidean space.
  • Existing classification methods may not preserve the geometric properties of hyperbolic data.
  • Accurate analysis requires tools tailored to hyperbolic geometry.

Purpose of the Study:

  • To develop a hyperbolic Support Vector Machine (SVM) classifier.
  • To enable accurate classification of data points within hyperbolic space.
  • To provide a framework for analyzing data with inherent hyperbolic geometry.

Main Methods:

  • Formulated hyperbolic Support Vector Machines (SVM) as a hyperbolic counterpart to Euclidean SVM.
  • Generalized Euclidean kernel SVM to hyperbolic space, enabling nonlinear decision boundaries.
  • Provided a geometric interpretation for indefinite kernels in hyperbolic space.

Main Results:

  • Hyperbolic SVM demonstrated improved classification accuracy in simulations.
  • The method showed enhanced performance on real-world complex network data.
  • Effective classification was achieved on hyperbolic word embedding datasets.

Conclusions:

  • Hyperbolic SVM offers a robust method for data classification in hyperbolic spaces.
  • The approach respects the underlying geometry, avoiding distortions from Euclidean methods.
  • Enables end-to-end analysis of hierarchically structured data without inappropriate tools.