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Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

Multi-input and Multi-variable systems

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...

Multiple Bar Graph

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can include as many parameters as possible. However, each parameter must have the same unit of measurement.
Each bar or column in the multiple bar graph represents a data value. These graphs are used primarily in interrelating two or more sets of data. The categories of different kinds of data are listed along the horizontal or x-axis, whereas...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

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Related Experiment Video

Updated: Nov 27, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Multi-Graph Multi-Label Learning Based on Entropy.

Zixuan Zhu¹, Yuhai Zhao¹

¹College of Computer Science and Engineering, Northeastern University, Shenyang 110819, China.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study introduces Multi-Graph Multi-Label Learning, representing objects with multiple graphs and labels for improved accuracy. The novel algorithm enhances feature selection and classification efficiency for complex data.

Keywords:

entropy extreme learning machine informative subgraphs multi-graph multi-label

More Related Videos

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Related Experiment Videos

Last Updated: Nov 27, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Area of Science:

Machine Learning
Computer Vision
Data Mining

Background:

Multi-Graph Learning extends Multi-Instance Learning, showing recent success.
The novel problem of Multi-Graph Multi-Label Learning, where objects are bags of graphs with multiple labels, remains unaddressed.
This problem is relevant to image classification and medicinal analysis.

Purpose of the Study:

To propose an innovative algorithm for Multi-Graph Multi-Label Learning.
To improve classification accuracy by using multiple graphs instead of instances.
To address semantic ambiguity using multiple labels and informative subgraph mining.

Main Methods:

Representing objects as bags of multiple graphs for enhanced precision.
Utilizing multiple labels to resolve semantic ambiguity.
Employing entropy-based subgraph mining for informative feature selection.
Degenerating the problem into Multi-Instance Multi-Label Learning and solving with MIML-ELM.

Main Results:

The proposed algorithm demonstrates superior performance compared to existing methods.
Effectiveness and efficiency gains were observed in performance studies.
The approach successfully handles graph-structured data with multiple labels.

Conclusions:

The developed algorithm effectively addresses the novel Multi-Graph Multi-Label Learning problem.
The method offers improved accuracy and efficiency in relevant applications.
This work opens new avenues for research in multi-modal and multi-label learning.