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In this paper, we propose novel algorithms for low dimensionality nonnegative embedding of vectorial and/or relational data, as well as nonnegative projections for dimensionality reduction. We start by introducing a novel algorithm for Metric Multidimensional Scaling (MMS). We propose algorithms for Nonnegative Locally Linear Embedding (NLLE) and Nonnegative Laplacian Eigenmaps (NLE). By reformulating the problem of MMS, NLLE and NLE for finding projections we propose algorithms for Nonnegative Principal Component Analysis (NPCA), for Nonnegative Orthogonal Neighbourhood Preserving Projections (NONPP) and Nonnegative Orthogonal Locality Preserving Projections (NOLPP). We demonstrate some first preliminary results of the proposed methods in data visualization.