Dimensionality reduction techniques for data exploration

Data exploration, or the search for features in data that may indicate deeper relationships among variables, relies heavily on visual methods because of the power of the human eye to detect structures. However, for large data sets with many variables and dimensions, the number of dimensions of the data can be reduced by applying dimensionality reduction techniques. This paper reviews current linear and nonlinear dimensionality reduction techniques. The nonlinear dimensionality reduction techniques which deal with finding a lower dimensional embedding of a nonlinear manifold can be classified under manifold learning algorithms. For basic types of nonlinear manifolds, experiments were performed on some of the current dimensionality reduction techniques. The nonlinear dimensionality reduction techniques generally do not perform well in the presence of noise, as seen from the results. When faced with a larger amount of noise, one of the algorithms was not able to converge to a solution. Thus, in order to apply nonlinear dimensionality reduction techniques effectively, the neighborhood, the density, and noise levels need to be taken into account.