  This paper presents a novel L1-norm semi-supervised learning algorithm for
robust image analysis by giving new L1-norm formulation of Laplacian
regularization which is the key step of graph-based semi-supervised learning.
Since our L1-norm Laplacian regularization is defined directly over the
eigenvectors of the normalized Laplacian matrix, we successfully formulate
semi-supervised learning as an L1-norm linear reconstruction problem which can
be effectively solved with sparse coding. By working with only a small subset
of eigenvectors, we further develop a fast sparse coding algorithm for our
L1-norm semi-supervised learning. Due to the sparsity induced by sparse coding,
the proposed algorithm can deal with the noise in the data to some extent and
thus has important applications to robust image analysis, such as noise-robust
image classification and noise reduction for visual and textual bag-of-words
(BOW) models. In particular, this paper is the first attempt to obtain robust
image representation by sparse co-refinement of visual and textual BOW models.
The experimental results have shown the promising performance of the proposed
algorithm.
