  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.
