2 research outputs found
Low Rank Regularization: A Review
Low rank regularization, in essence, involves introducing a low rank or
approximately low rank assumption for matrix we aim to learn, which has
achieved great success in many fields including machine learning, data mining
and computer version. Over the last decade, much progress has been made in
theories and practical applications. Nevertheless, the intersection between
them is very slight. In order to construct a bridge between practical
applications and theoretical research, in this paper we provide a comprehensive
survey for low rank regularization. We first review several traditional machine
learning models using low rank regularization, and then show their (or their
variants) applications in solving practical issues, such as non-rigid structure
from motion and image denoising. Subsequently, we summarize the regularizers
and optimization methods that achieve great success in traditional machine
learning tasks but are rarely seen in solving practical issues. Finally, we
provide a discussion and comparison for some representative regularizers
including convex and non-convex relaxations. Extensive experimental results
demonstrate that non-convex regularizers can provide a large advantage over the
nuclear norm, the regularizer widely used in solving practical issues.Comment: 16 pages,4 figures,4 table
Discriminative Local Sparse Representation by Robust Adaptive Dictionary Pair Learning
In this paper, we propose a structured Robust Adaptive Dic-tionary Pair
Learning (RA-DPL) framework for the discrim-inative sparse representation
learning. To achieve powerful representation ability of the available samples,
the setting of RA-DPL seamlessly integrates the robust projective dictionary
pair learning, locality-adaptive sparse representations and discriminative
coding coefficients learning into a unified learning framework. Specifically,
RA-DPL improves existing projective dictionary pair learning in four
perspectives. First, it applies a sparse l2,1-norm based metric to encode the
recon-struction error to deliver the robust projective dictionary pairs, and
the l2,1-norm has the potential to minimize the error. Sec-ond, it imposes the
robust l2,1-norm clearly on the analysis dictionary to ensure the sparse
property of the coding coeffi-cients rather than using the costly l0/l1-norm.
As such, the robustness of the data representation and the efficiency of the
learning process are jointly considered to guarantee the effi-cacy of our
RA-DPL. Third, RA-DPL conceives a structured reconstruction weight learning
paradigm to preserve the local structures of the coding coefficients within
each class clearly in an adaptive manner, which encourages to produce the
locality preserving representations. Fourth, it also considers improving the
discriminating ability of coding coefficients and dictionary by incorporating a
discriminating function, which can ensure high intra-class compactness and
inter-class separation in the code space. Extensive experiments show that our
RA-DPL can obtain superior performance over other state-of-the-arts.Comment: Accepted by IEEE TNNL