  Multiview learning problem refers to the problem of learning a classifier
from multiple view data. In this data set, each data points is presented by
multiple different views. In this paper, we propose a novel method for this
problem. This method is based on two assumptions. The first assumption is that
each data point has an intact feature vector, and each view is obtained by a
linear transformation from the intact vector. The second assumption is that the
intact vectors are discriminative, and in the intact space, we have a linear
classifier to separate the positive class from the negative class. We define an
intact vector for each data point, and a view-conditional transformation matrix
for each view, and propose to reconstruct the multiple view feature vectors by
the product of the corresponding intact vectors and transformation matrices.
Moreover, we also propose a linear classifier in the intact space, and learn it
jointly with the intact vectors. The learning problem is modeled by a
minimization problem, and the objective function is composed of a Cauchy error
estimator-based view-conditional reconstruction term over all data points and
views, and a classification error term measured by hinge loss over all the
intact vectors of all the data points. Some regularization terms are also
imposed to different variables in the objective function. The minimization
problem is solve by an iterative algorithm using alternate optimization
strategy and gradient descent algorithm. The proposed algorithm shows it
advantage in the compression to other multiview learning algorithms on
benchmark data sets.
