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

Distance Problem

Distance Problem

When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...

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.

Distance Measurements by Taping

Distance Measurements by Taping

Tapes are essential in surveying for accurate, durable, and short-distance measurements. Made from lightweight, nylon-coated steel, they offer flexibility and strength for rugged outdoor use. The nylon coating protects against rust and wear, extending the tape's life. Standard lengths, around 30 meters, are marked in meters and millimeters for precision.Surveyors select tapes based on site conditions and accuracy needs. Lightweight, nylon-coated tapes are commonly used for ease of handling and...

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...

Lagrange Multipliers: Two Constraints

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.

Routh-Hurwitz Criterion II

Routh-Hurwitz Criterion II

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 column of the Routh...

You might also read

Related Articles

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

Sort by

Same author

EGCN++: A New Fusion Strategy for Ensemble Learning in Skeleton-Based Rehabilitation Exercise Assessment.

IEEE transactions on pattern analysis and machine intelligence·2024

Same author

MMNet: A Model-Based Multimodal Network for Human Action Recognition in RGB-D Videos.

IEEE transactions on pattern analysis and machine intelligence·2022

Same author

Determining dependency and redundancy for identifying gene-gene interaction associated with complex disease.

Journal of bioinformatics and computational biology·2020

Same author

Predicting microRNA-disease associations from lncRNA-microRNA interactions via Multiview Multitask Learning.

Briefings in bioinformatics·2020

Same author

Learning Representations to Predict Intermolecular Interactions on Large-Scale Heterogeneous Molecular Association Network.

iScience·2020

Same author

Learning Representation of Molecules in Association Network for Predicting Intermolecular Associations.

IEEE/ACM transactions on computational biology and bioinformatics·2020

Same journal

Universal perceptron and DNA-like learning algorithm for binary neural networks: LSBF and PBF implementations.

IEEE transactions on neural networks·2013

Same journal

Guest editorial: special section on white box nonlinear prediction models.

IEEE transactions on neural networks·2011

Same journal

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

IEEE transactions on neural networks·2011

Same journal

Guest editorial: special section on data-based control, modeling, and optimization.

IEEE transactions on neural networks·2011

Same journal

Neural network-based multiple robot simultaneous localization and mapping.

IEEE transactions on neural networks·2011

Same journal

Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems.

IEEE transactions on neural networks·2011

See all related articles

Search research articles

Related Experiment Videos

Tensor distance based multilinear locality-preserved maximum information embedding.

Yang Liu¹, Yan Liu, Keith C C Chan

¹Department of Computing, the Hong Kong Polytechnic University, Kowloon, Hong Kong, China. csygliu@comp.polyu.edu.hk

IEEE Transactions on Neural Networks

|September 30, 2010

Summary

This summary is machine-generated.

This study introduces a unified framework for tensor-based dimensionality reduction using a new tensor distance metric and a multilinear locality-preserved maximum information embedding algorithm for improved data analysis.

Related Experiment Videos

Area of Science:

Machine Learning
Data Science
Multivariate Statistics

Background:

Traditional dimensionality reduction methods often rely on Euclidean distance, which has limitations.
Preserving the inherent structure of high-order data is crucial for effective analysis.

Purpose of the Study:

To develop a unified framework for tensor-based dimensionality reduction.
To introduce a novel tensor distance metric and a multilinear locality-preserved maximum information embedding algorithm.

Main Methods:

A new tensor distance (TD) metric is proposed, considering relationships among coordinates.
A multilinear locality-preserved maximum information embedding (MLPMIE) algorithm works directly on high-order tensor data.
The TD-MLPMIE integrates TD into tensor embedding to preserve local geometry and global discrimination.

Main Results:

The proposed TD-MLPMIE framework achieves stable performance improvements.
The method demonstrates effectiveness across various standard datasets.
The new TD metric overcomes limitations of traditional Euclidean distance.

Conclusions:

The unified framework provides an effective approach for tensor-based dimensionality reduction.
The TD-MLPMIE algorithm offers enhanced data representation by preserving tensor structure.
This work advances the field of dimensionality reduction for complex, high-order data.