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A new learning system called a statistical self-organizing learning system (SSOLS), combining functional-link neural networks, statistical hypothesis testing, and self-organization of a number of enhancement nodes, is introduced for remote sensing applications. Its structure consists of two stages, a mapping stage and a learning stage. The input training vectors are initially mapped to the enhancement vectors in the mapping stage by multiplying with a random matrix, followed by pointwise nonlinear transformations. Starting with only one enhancement node, the enhancement layer incrementally adds an extra node in each iteration. The optimum dimension of the enhancement layer is determined by using an efficient leave-one-out cross-validation method. In this way, the number of enhancement nodes is also learned automatically. A t-test algorithm can also be applied to the mapping stage to mitigate the effect of overfitting and to further reduce the number of enhancement nodes required, resulting in a more compact network. In the learning stage, both the input vectors and the enhancement vectors are fed into a least squares learning module to obtain the estimated output vectors. This is made possible by choosing the output layer linear. In addition, several SSOLSs can be trained independently in parallel to form a consensual SSOLS, whose final output is a linear combination of the outputs of each SSOLS module. The SSOLS is simple, fast to compute, and suitable for remote sensing applications, especially with hyperspectral image data of high dimensionality.