With the burgeoning applications of 3D model in various fields, the 3D shaperetrieval technology is confronted with increasing challenges. The ability toaccurately and efficiently recognize non-rigid shapes plays an essential rolefor innovative design and shape manipulation. In this thesis, a strong andfast shape Fisher Vector model for non-rigid 3D shape retrieval is introduced. Firstly, the heat kernel signatures (HKS) and scale-invariant heatkernel signatures (SI-HKS) are used to convert a 3D shape model into aset of local descriptors under an identical coordinate system. Subsequently,Fisher Vector method characterizes such set of local descriptors via computing their deviations from a universal generative Gaussian Mixture Model. As a 'latent' supervised learning manner, Fisher Vector can not only achievesignificantly high retrieval accuracy benefiting from the hybrid advantagesof generative and discriminative models, but also take far less cost for calculating the vectorial representations and for subsequently classifier training.In the final shape classification process, instead of the traditional metriclearning method, a linear SVM is adopted to classify the vectorial representations for effectively shape retrieval. Through theoretical analysis, we showthe proposed shape VI Fisher Vector model is superior to the state-of-the-artmethods for non-rigid 3D shape retrieval. Besides, in experimental verification, our proposed model can achieve the best performance among the compared approaches in terms of accuracy and efficiency on both SHREC'10and SHREC'14 benchmarks. Besides, extreme learning machine (ELM) currently has been well recognized as an effective learning algorithm with extremely fast learning speed and high generalization performance. However, to deal with the regression applications involving big data, the stability and accuracy of ELM shall be further enhanced. In this thesis, a new hybrid machine learning method called robust AdaBoost.RT based ensemble ELM (RAE-ELM) for regression problems is proposed, which combined ELM with the novel robust AdaBoost.RT algorithm to achieve better approximation accuracy than using only single ELM network. The robust threshold for each weak learner will be adaptive according to the weak learner’s performance on the corresponding problem dataset. Therefore, RAE-ELM could output the final hypotheses in optimally weighted ensemble of weak learners. On the other hand, ELM is a quick learner with high regression performance, which makes it a good candidate of ‘weak’ learners. We prove that the empirical error of the RAE-ELM is within a significantly superior bound. The experimental verification has shown that the proposed RAE-ELM outperforms other state-of-the-art algorithms on many real-world regression problems. What is more, AdaBoost algorithm is a popular ensemble method that combines several weak learners to improve the generalization performance. In this thesis, we develop a generic AdaBoost framework for any weak learner on regression problems that utilizes a robust threshold as the regression criterion, where the robust threshold for each weak learner will be adaptive according to individual weak learner’s performance on the corresponding problem dataset. It overcomes the limitations existed in the available AdaBoost.RT algorithm and its variants where the threshold value is manually specified, which may only be ideal for a very limited set of cases. Moreover, we first rigorously provide a comprehensive theoretical analysis of robust AdaBoost.RT algorithm so as to fill the gaps on the theoretical foundation of the AdaBoost.RT. At the beginning, we prove that the more general bound on the empirical error of the novel robust AdaBoost.RT algorithm with fraction of training examples is within a limited soft margin, which demonstrates that the proposed algorithm can avoid over-fitting. Subsequently, we further analyze bounds on the generalization error of the novel VII algorithm directly under the probably approximately correct (PAC) learnable. The performance of the proposed robust AdaBoost.RT learning algorithm is superior to other nine learning algorithms via experimental study using benchmark applications.