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Classification at the accuracy limit: facing the problem of data ambiguity.

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Data classification accuracy has a theoretical limit, especially in weakly structured datasets. Powerful classifiers achieve this limit, unaffected by certain data transformations, showing MNIST data is well-structured while EEG sleep data is not.

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Area of Science:

  • Computer Science
  • Machine Learning
  • Data Analysis

Background:

  • Data classification and clustering are fundamental in information processing.
  • Performance degrades in weakly structured datasets with overlapping categories.
  • Theoretical limits for classification accuracy are crucial for understanding performance.

Purpose of the Study:

  • Derive the theoretical limit for classification accuracy in overlapping data categories.
  • Investigate classifier performance at this limit using diverse models.
  • Compare supervised and unsupervised data embeddings on real-world datasets.

Main Methods:

  • Developed a surrogate data generation model with adjustable statistical properties.
  • Evaluated perceptron and Bayesian models against the theoretical accuracy limit.
  • Compared data embeddings from supervised (back-propagation) and unsupervised methods using MNIST and EEG data.

Main Results:

  • All powerful classifiers reached the universal accuracy limit under ideal conditions.
  • The accuracy limit remained unaffected by non-linear, information-reducing data transformations.
  • MNIST data showed significant category separation after both supervised and unsupervised learning; EEG data showed minimal separation.

Conclusions:

  • The theoretical accuracy limit is a key benchmark for classification tasks.
  • MNIST handwritten letters represent 'natural kinds' with inherent structure.
  • EEG sleep recordings are weakly structured, limiting unsupervised clustering's ability to recover human-defined sleep stages.