  Despite the fact that nonlinear subspace learning techniques (e.g. manifold
learning) have successfully applied to data representation, there is still room
for improvement in explainability (explicit mapping), generalization
(out-of-samples), and cost-effectiveness (linearization). To this end, a novel
linearized subspace learning technique is developed in a joint and progressive
way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning
str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label
classification. The J-Play learns high-level and semantically meaningful
feature representation from high-dimensional data by 1) jointly performing
multiple subspace learning and classification to find a latent subspace where
samples are expected to be better classified; 2) progressively learning
multi-coupled projections to linearly approach the optimal mapping bridging the
original space with the most discriminative subspace; 3) locally embedding
manifold structure in each learnable latent subspace. Extensive experiments are
performed to demonstrate the superiority and effectiveness of the proposed
method in comparison with previous state-of-the-art methods.
