Principal Component Analysis (PCA) is an effective tool for dimensionality reduction, transforming high dimensional data into a representation that has fewer dimensions (although these dimensions are not from the original set of dimensions). This new set of dimensions captures the variation within the high dimensional dataset. How do you find this space? Well, PCA is equivalent to determining the breakdown M = L + E, where L is a matrix that has a small number of linearly independent vectors (our dimensions) and E is a matrix of errors (corruption in the data). The matrix of errors, E, has been minimized. One assumption in this optimization problem, though, is that our corruption, E, is characterized by Gaussian noise .