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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...
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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.
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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Merging of Numerical Intervals in Entropy-Based Discretization.

Jerzy W Grzymala-Busse1,2, Teresa Mroczek2

  • 1Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS 66045, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

Merging intervals in data discretization significantly impacts error rates, with no single best approach universally outperforming others. Experimentation across datasets is recommended to determine optimal merging strategies for improved data mining accuracy.

Keywords:
data miningdiscretizationentropynumerical attributes

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Area of Science:

  • Data Mining and Machine Learning
  • Information Science

Background:

  • Discretization converts numerical data into discrete intervals.
  • Multiple-scanning is a competitive discretization methodology.
  • Interval merging is a postprocessing step in multiple-scanning.

Purpose of the Study:

  • To evaluate the impact of interval merging on error rates in multiple-scanning discretization.
  • To compare three merging strategies: no merging, merging by smallest entropy, and merging by biggest entropy.

Main Methods:

  • Conducted experiments on 17 numerical datasets using multiple-scanning discretization.
  • Applied tenfold cross-validation within the C4.5 system to measure error rates.
  • Performed Friedman rank sum test and compared averages and standard deviations over 30 repetitions.

Main Results:

  • Initial tests showed statistically insignificant differences between merging approaches.
  • Repeated experiments revealed statistically significant differences (1% significance level) between no merging and merging by smallest entropy.
  • Significant differences were also observed when comparing no merging with merging by biggest entropy.

Conclusions:

  • The choice between no merging and interval merging significantly affects error rates, varying by dataset.
  • No universally superior merging strategy exists.
  • The optimal approach requires empirical testing of all three strategies for each specific dataset.