  A significant challenge to make learning techniques more suitable for general
purpose use is to move beyond i) complete supervision, ii) low dimensional
data, iii) a single task and single view per instance. Solving these challenges
allows working with "Big Data" problems that are typically high dimensional
with multiple (but possibly incomplete) labelings and views. While other work
has addressed each of these problems separately, in this paper we show how to
address them together, namely semi-supervised dimension reduction for
multi-task and multi-view learning (SSDR-MML), which performs optimization for
dimension reduction and label inference in semi-supervised setting. The
proposed framework is designed to handle both multi-task and multi-view
learning settings, and can be easily adapted to many useful applications.
Information obtained from all tasks and views is combined via reconstruction
errors in a linear fashion that can be efficiently solved using an alternating
optimization scheme. Our formulation has a number of advantages. We explicitly
model the information combining mechanism as a data structure (a
weight/nearest-neighbor matrix) which allows investigating fundamental
questions in multi-task and multi-view learning. We address one such question
by presenting a general measure to quantify the success of simultaneous
learning of multiple tasks or from multiple views. We show that our SSDR-MML
approach can outperform many state-of-the-art baseline methods and demonstrate
the effectiveness of connecting dimension reduction and learning.
