ChemCam is a remote laser-induced breakdown spectroscopy (LIBS) instrument that will arrive on Mars in 2012, on-board the Mars Science Laboratory Rover. The LIBS technique is crucial to accurately identify samples and quantify elemental abundances at various distances from the rover. In this study, we compare different linear and nonlinear multivariate techniques to visualize and discriminate clusters in two dimensions (2D) from the data obtained with ChemCam. We have used principal components analysis (PCA) and independent components analysis (ICA) for the linear tools and compared them with the nonlinear Sammon's map projection technique. We demonstrate that the Sammon's map gives the best 2D representation of the data set, with optimization values from 2.8% to 4.3% (0% is a perfect representation), together with an entropy value of 0.81 for the purity of the clustering analysis. The linear 2D projections result in three (ICA) and five times (PCA) more stress, and their clustering purity is more than twice higher with entropy values about 1.8. We show that the Sammon's map algorithm is faster and gives a slightly better representation of the data set if the initial conditions are taken from the ICA projection rather than the PCA projection. We conclude that the nonlinear Sammon's map projection is the best technique for combining data visualization and clustering assessment of the ChemCam LIBS data in 2D. PCA and ICA projections on more dimensions would improve on these numbers at the cost of the intuitive interpretation of the 2D projection by a human operator.