Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services that a user may like. On the other hand, classification technique deals with the categorization of a data object into one of the several predefined classes. In the multi-label classification problem, unlike the traditional multi-class classification setting, each instance can be simultaneously associated with a subset of labels. The focus of thesis is on the development of novel techniques for collaborative filtering and multi-label classification. We propose a novel method of constructing a hierarchical bi-level maximum margin matrix factorization to handle matrix completion of ordinal rating matrix. Taking the cue from the alternative formulation of support vector machines, a novel loss function is derived by considering proximity as an alternative criterion instead of margin maximization criterion for matrix factorization framework. We extended the concept of matrix factorization for yet another important problem of machine learning namely multi-label classification which deals with the classification of data with multiple labels. We propose a novel piecewise-linear embedding method with a low-rank constraint on parametrization to capture nonlinear intrinsic relationships that exist in the original feature and label space. We also study the embedding of labels together with the group information with an objective to build an efficient multi-label classifier. We assume the existence of a low-dimensional space onto which the feature vectors and label vectors can be embedded. We ensure that labels belonging to the same group share the same sparsity pattern in their low-rank representations.