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The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...
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An R-Based Landscape Validation of a Competing Risk Model
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Cross-validation of matching correlation analysis by resampling matching weights.

Hidetoshi Shimodaira1

  • 1Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka, Japan.

Neural Networks : the Official Journal of the International Neural Network Society
|January 18, 2016
PubMed
Summary

A new cross-validation method for matching correlation analysis (MCA) accurately estimates matching error by resampling matching weights. This approach is crucial for dimensionality reduction and applicable to cross-domain data.

Keywords:
Associative memoryCanonical correlation analysisCross-validationMultiple domainsResamplingSpectral graph embedding

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Area of Science:

  • Machine Learning
  • Data Science
  • Statistical Analysis

Background:

  • Matching weight quantifies data vector association strength.
  • Dimensionality reduction often involves linear transformations.
  • Existing methods like canonical correlation analysis have limitations.

Purpose of the Study:

  • To introduce a novel cross-validation technique for matching correlation analysis (MCA).
  • To develop a method for estimating matching error with resampled matching weights.
  • To extend MCA for cross-domain data with varying dimensions.

Main Methods:

  • Defined matching error as a weighted sum of squared distances.
  • Utilized spectral graph embedding for optimal linear transformation (MCA).
  • Developed and analyzed a cross-validation scheme by resampling matching weights.

Main Results:

  • Asymptotic theory confirms rescaled cross-validation provides an unbiased estimate of matching error.
  • Demonstrated the inapplicability of data vector resampling for this problem.
  • Introduced cross-domain matching correlation analysis (CDMCA) for multi-domain data.

Conclusions:

  • The proposed cross-validation method is effective for MCA, particularly with sampled matching weights.
  • CDMCA offers a flexible approach for analyzing data from multiple domains.
  • MCA and CDMCA show connections to neural network associative memory models.