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In order to apply the diffusion maps in a matrix $C\in\mathbb R^{n\times n}$ , that matrix must obey some restrictions,

  • C is symmetric: $C_{ij} = C_{ji}$,
  • C is positivity preserving (PP): $\forall i, j$, $C_{ij}\ge0$,
  • C is positive semi-definite (PSD)

However, I'm stuck on a problem with a PSD correlation matrix with negative entries. So I want to know how can I transform a generic PSD matrix into a PSD / PP matrix?

If that transformation is not so trivial, how can I make an embedding of a set of points into an Euclidean space using only the correlation matrix as input?

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