# How to apply the diffusion maps when the matrix is PSD but not positivity preserving?

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?