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

Laws of Logarithms I01:30

Laws of Logarithms I

98
Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions...
98
Introduction to Logarithmic Functions01:14

Introduction to Logarithmic Functions

84
Logarithmic functions are the inverses of exponential functions and are used to solve for exponents. The general form is y = logₐ(x), where a > 0 and a ≠ 1. This function returns the power to which the base a must be raised to obtain x. The logarithmic function is only defined for x > 0, and its range includes all real numbers.Graphically, logarithmic and exponential functions are reflections of each other across the line y = x. The graph of y = logₐ(x) passes through...
84
Applications of Logarithms01:28

Applications of Logarithms

83
Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
83
Types of Functions III01:28

Types of Functions III

79
Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...
79
Laws of Logarithms II01:28

Laws of Logarithms II

95
Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
95
Lossless Lines01:23

Lossless Lines

294
In electrical engineering, a lossless transmission line is characterized by a purely imaginary propagation constant and a resistive characteristic impedance. The ABCD parameters, which describe the relationship between the input and output voltages and currents, indicate an equivalent π circuit with an imaginary series impedance and a shunt admittance. This results in a transmission line that, when the product of the phase constant (beta) and the length of the line is less than pi, exhibits...
294

You might also read

Related Articles

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

Sort by
Same author

Reducing cost in DNA-based data storage by sequence analysis-aided soft information decoding of variable-length reads.

Bioinformatics (Oxford, England)·2023
Same author

FCLQC: fast and concurrent lossless quality scores compressor.

BMC bioinformatics·2021
Same author

Cooperative sequence clustering and decoding for DNA storage system with fountain codes.

Bioinformatics (Oxford, England)·2021
Same author

Information Geometric Approach on Most Informative Boolean Function Conjecture.

Entropy (Basel, Switzerland)·2020
Same author

Universality of Logarithmic Loss in Successive Refinement.

Entropy (Basel, Switzerland)·2020
Same author

CROMqs: An infinitesimal successive refinement lossy compressor for the quality scores.

Journal of bioinformatics and computational biology·2020

Related Experiment Video

Updated: Nov 27, 2025

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System
10:27

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

Published on: June 12, 2019

9.0K

Universality of Logarithmic Loss in Fixed-Length Lossy Compression.

Albert No1

  • 1Department of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

Logarithmic loss is a universal distortion measure for fixed-length lossy compression. This finding simplifies compression problems and introduces a new clustering algorithm for categorical data.

Keywords:
categorical data clusteringfixed-length lossy compressionlogarithmic lossrate-distortion

More Related Videos

Author Spotlight: Advancing Understanding of Age-Related Lens Stiffness Changes
05:19

Author Spotlight: Advancing Understanding of Age-Related Lens Stiffness Changes

Published on: April 5, 2024

2.6K
Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

7.8K

Related Experiment Videos

Last Updated: Nov 27, 2025

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System
10:27

A Uniaxial Compression Experiment with CO2-Bearing Coal Using a Visualized and Constant-Volume Gas-Solid Coupling Test System

Published on: June 12, 2019

9.0K
Author Spotlight: Advancing Understanding of Age-Related Lens Stiffness Changes
05:19

Author Spotlight: Advancing Understanding of Age-Related Lens Stiffness Changes

Published on: April 5, 2024

2.6K
Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

7.8K

Area of Science:

  • Information Theory
  • Computer Science
  • Data Science

Background:

  • Lossy compression aims to reduce data size while minimizing distortion.
  • Existing distortion criteria can complicate the design of compression schemes.
  • Logarithmic loss offers a potential simplification for compression problems.

Purpose of the Study:

  • Establish logarithmic loss as a universal distortion criterion in fixed-length lossy compression.
  • Demonstrate the equivalence between arbitrary distortion criteria and logarithmic loss.
  • Introduce a novel clustering algorithm for categorical data.

Main Methods:

  • Theoretical analysis of fixed-length lossy compression.
  • Establishing a strong equivalence between different distortion criteria.
  • Leveraging algebraic structures for clustering applications.

Main Results:

  • Universality of logarithmic loss as a distortion criterion is proven.
  • Any fixed-length lossy compression problem is equivalent to one with logarithmic loss.
  • An algebraic structure in the reconstruction alphabet is identified.

Conclusions:

  • Logarithmic loss provides a unified framework for lossy compression.
  • The established equivalence simplifies the search for optimal compression schemes.
  • A new clustering algorithm for categorical data is proposed based on this framework.