Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art training techniques, while taking much less time to train a model. Experiments show that the speedup of training ELM is up to the 5 orders of magnitude comparing to standard Error Back-propagation algorithm. ELM is a recently discovered technique that has proved its efficiency in classic regression and classification tasks, including multi-class cases. In this thesis, extensions of ELMs for non-typical for Artificial Neural Networks (ANNs) problems are presented. The first extension, described in the third chapter, allows to use ELMs to get probabilistic outputs for multi-class classification problems. The standard way of solving this type of problems is based "majority vote" of classifier's raw outputs. This approach can rise issues if the penalty for misclassification is different for different classes. In this case, having probability outputs would be more useful. In the scope of this extension, two methods are proposed. Additionally, an alternative way of interpreting probabilistic outputs is proposed. ELM method prove useful for non-linear dimensionality reduction and visualization, based on repetitive re-training and re-evaluation of model. The fourth chapter introduces adaptations of ELM-based visualization for classification and regression tasks. A set of experiments has been conducted to prove that these adaptations provide better visualization results that can then be used for perform classification or regression on previously unseen samples. Shape registration of 3D models with non-isometric distortion is an open problem in 3D Computer Graphics and Computational Geometry. The fifth chapter discusses a novel approach for solving this problem by introducing a similarity metric for spectral descriptors. Practically, this approach has been implemented in two methods. The first one utilizes Siamese Neural Network to embed original spectral descriptors into a lower dimensional metric space, for which the Euclidean distance provides a good measure of similarity. The second method uses Extreme Learning Machines to learn similarity metric directly for original spectral descriptors. Over a set of experiments, the consistency of the proposed approach for solving deformable registration problem has been proven. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]