Regularized models and algorithms for machine learning

Multi-lable learning (ML), multi-instance multi-label learning (MIML), large network learning and random under-sampling system are four active research topics in machine learning which have been studied intensively recently. So far, there are still a lot of open problems to be figured out in these topics which attract worldwide attention of researchers. This thesis mainly focuses on several novel methods designed for these research tasks respectively. Then main difference between ML learning and traditional classification task is that in ML learning, one object can be characterized by several different labels (or classes). One important observation is that the labels received by similar objects in ML data are usually highly correlated with each other. In order to exploring this correlation of labels between objects which might be a key issue in ML learning, we consider to require the resulting label indicator to be low rank. In the proposed model, nuclear norm which is a famous convex relaxation of intractable matrix rank is introduced to label indicator in order to exploiting the underlying correlation in label domain. Motivated by the idea of spectral clustering, we also incorporate information from feature domain by constructing a graph among objects based on their features. Then with partial label information available, we integrate them together into a convex low rank based model designed for ML learning. The proposed model can be solved efficiently by using alternating direction method of multiplier (ADMM). We test the performance on several benchmark ML data sets and make comparisons with the state-of-art algorithms. The classification results demonstrate the efficiency and effectiveness of the proposed low rank based methods. One step further, we consider MIML learning problem which is usually more complicated than ML learning: besides the possibility of having multiple labels, each object can be described by multiple instances simultaneously which may significantly increase the size of data. To handle the MIML learning problem we first propose and develop a novel sparsity-based MIML learning algorithm. Our idea is to formulate and construct a transductive objective function for label indicator to be learned by using the method of random walk with restart that exploits the relationships among instances and labels of objects, and computes the affinities among the objects. Then sparsity can be introduced in the labels indicator of the objective function such that relevant and irrelevant objects with respect to a given class can be distinguished. The resulting sparsity-based MIML model can be given as a constrained convex optimization problem, and it can be solved very efficiently by using the augmented Lagrangian method (ALM). Experimental results on benchmark data have shown that the proposed sparse-MIML algorithm is computationally efficient, and effective in label prediction for MIML data. We demonstrate that the performance of the proposed method is better than the other testing MIML learning algorithms. Moreover, one big concern of an MIML learning algorithm is computational efficiency, especially when figuring out classification problem for large data sets. Most of the existing methods for solving MIML problems in literature may take a long computational time and have a huge storage cost for large MIML data sets. In this thesis, our main aim is to propose and develop an efficient Markov Chain based learning algorithm for MIML problems. Our idea is to perform labels classification among objects