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The Manifold Hypothesis and the Curse of Dimensionality in Machine Learning
All machine learning problems that we need to deal with nowadays are exteme highly dimensional. Even basic image problems live in thousands or even millions of dimensions. The curse of dimensionality refers to the various phenomena that arise when analyzing and organ sing data in high dimensional spaces. It only works if we make some very strong assumptions about the regularities and the space of functions which we need to search through.