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

Piecewise-Defined Functions01:28

Piecewise-Defined Functions

Piecewise defined functions are mathematical models where different expressions define a function over distinct intervals of the domain. These functions are useful for representing systems with varying behaviors depending on input values.For example, the function:  uses a linear rule for inputs less than or equal to –1 and a quadratic rule for values greater than –1. Although it has two formulas, it still defines a single function.Another common type is the absolute value function, given...
Linearization and Approximation01:26

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...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Classification of Systems-I01:26

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:
Classification of Systems-II01:31

Classification of Systems-II

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,
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

You might also read

Related Articles

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

Sort by
Same author

Recursive algorithms for implementing digital image filters.

IEEE transactions on pattern analysis and machine intelligence·2012
Same author

A gestalt-guided heuristic boundary follower for x-ray images of lung nodules.

IEEE transactions on pattern analysis and machine intelligence·2011
Same author

A visual neural classifier.

IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society·2008
Same author

Computer-aided, case-based diagnosis of mammographic regions of interest containing microcalcifications.

Academic radiology·2000
Same author

Biplane X-ray angiograms, intravascular ultrasound, and 3D visualization of coronary vessels.

International journal of cardiac imaging·2000
Same author

Reconstructing the 3-D medial axes of coronary arteries in single-view cineangiograms.

IEEE transactions on medical imaging·1994
Same journal

TraGraph-GS: Trajectory Graph-based Gaussian Splatting for Arbitrary Large-Scale Scene Rendering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

SWIFT: A Small-World Interaction Framework for Flow-Aware Trajectory Prediction in Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

HardFlow: Hard-Constrained Sampling for Flow-Matching Models Via Trajectory Optimization.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Industrial Brain: Self-Evolving Neuro-Symbolic Autonomy with Causal Resilience for Cyber-Physical Systems.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Adaptive Hardness-Driven Dictionary Distillation for Incomplete Streaming View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Mixture of Global and Local Experts with Diffusion Transformer for Controllable Face Generation.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Videos

Locally trained piecewise linear classifiers.

J Sklansky1, L Michelotti

  • 1SENIOR MEMBER, IEEE, Departments of Electrical Engineering, Information and Computer Science and Radiological Sciences, University of California, Irvine, CA 92717.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a novel computer algorithm for data classification, achieving near-optimal error rates with minimal memory. The technique efficiently designs classifiers by approximating decision surfaces using linear segments, enhancing data processing.

Related Experiment Videos

Area of Science:

  • Computer Science
  • Machine Learning
  • Pattern Recognition

Background:

  • Classifying multi-dimensional data is crucial for many applications.
  • Existing methods may require significant memory or computational resources.
  • Achieving Bayes-minimum error rates is a key goal in classification algorithm design.

Purpose of the Study:

  • To present a versatile technique for designing efficient computer algorithms (classifiers) for two-class data separation.
  • To develop classifiers that achieve near Bayes-minimum error rates with reduced memory requirements.
  • To enable flexible classifier design across diverse class densities.

Main Methods:

  • Designing computer algorithms for separating multi-dimensional data (feature vectors) into two classes.
  • Generating a piecewise-linear approximation of the Bayes-optimum decision surface from close-opposed data cluster pairs.
  • Employing a window training procedure on linear segments for flexibility and efficient data base construction.
  • Utilizing adjacency and incidence matrices for interactive classifier simplification and switching theory for decision logic minimization.

Main Results:

  • The developed classifiers achieve performance close to Bayes-minimum error rates.
  • The technique requires relatively small amounts of memory.
  • The design procedure allows for flexibility across a wide range of class densities.
  • Efficient data bases are constructible due to localized training data consumption.

Conclusions:

  • The described versatile technique offers an efficient method for designing high-performance classifiers.
  • The approach balances accuracy with memory efficiency, making it suitable for various applications.
  • Interactive simplification tools and switching theory contribute to optimized decision logic.