Multidimensional Scaling (MDS) projects data to a higher-dimensional space in order to increasing the distance between data points.

In self-organizing maps the objective is to minimize an energy (error) function.

In locally linear embedding (LLE), each data point is described as a linear combination of its neighbors.

The objective of scaling and projection methods is to project data into a lower-dimensional space, e.g. to allow better model selection.

Generative Topographic Mapping (GTM) is a non-linear latent variable model which maps latent variables to observations.

The objective in t-SNE is minimization of the KL divergence between the similarities of the (high-dimensional) inputs and the (low-dimensional) mapped outputs.

Projection pursuit performs projections such that the extracted signal is as Gaussian as possible.

Isomap uses a geodesic distance matrix, whose largest eigenvectors are the coordinates of the projected space.