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A Well-posed problem should have the following properties:

  • a solution exists
  • the solution is unique
  • the solution's behavior changes continuously with the initial conditions.

A problem which is not well-posed is called ill-posed.

In some research papers, like this, pattern recognition is defined as an ill-posed problem.

Why do they define pattern recognition as an ill-posed problem?

Alexis
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mrazizi
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    Welcome to CV, mraziz! I encourage you to edit your question (the link to do so is at lower left) in order to briefly quote or recap the linked article. In general CrossValidated frowns on providing links directing the community to go elsewhere in order to understand a question or an answer. – Alexis Oct 29 '19 at 21:31

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Quoting Wikipedia

Inverse problems are often ill-posed. For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data.

In pattern recognition (aka machine learning), the solutions would also depend on the choice of algorithm, hyperparameters, or even random seeds used for training.

Moreover, with pattern recognition it is not even guaranteed that the solution exists, e.g. if you are conducting cluster analysis, or classification given some data, there is no guarantee that this data is suitable for such analysis. Surely, the algorithms will try their best with finding some pattern given any data, but that doesn't mean that there was any real pattern.

Tim
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