Laplacian Regularized Low-Rank Representation and Its Applications

Abstract

Low-rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest-rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low-dimensional manifolds embedded in a high-dimensional ambient space. However, the LRR method does not take into account the non-linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR). By taking advantage of the graph regularizer, our proposed method not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information in data. The extensive experimental results on image clustering, semi-supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.

Determining a Flexible Low-Rank Graph Using Subspace Clustering

“…The issues including the estimation of low-rank networks have attracted extensive consideration late years [14][4] [16]. The low-rank regularize in LRR has a profound connection with the current hypothetical advances on hearty primary segment examination (RPCA) [5][6], which prompts new and intense demonstrating alternatives for some applications.…”

“…As of late, enlivened by the advances of SSC and LRR, numerous chart based subspace grouping calculations have been developed [13] [19][4] [14]. For instance, to protect the complex structure of information, Cai et.…”

“…al. fused Laplacain diagram requirements into the standard LRR model to safeguard the geometric data from single side [14] and twoside [4] viewpoint. When all is said in done, this kind of subspace bunching can be assembled into ghostly grouping based strategies, which have been exhibited to perform extremely well for some applications in PC vision [19].…”

“…The other is that it might prompt a traded off bunching execution. In spite of the fact that the diagram regularized inadequate [13] or low-rank [14][4] subspace bunching technique can accomplish great outcomes, Wij must be precomputed which may not mirror the genuine closeness between information focuses. That is, two focuses, lying in various subspaces (e.g., close to the crossing point of two subspaces), could be extremely near each other, and the other way around.…”

Consistent multi-layer subtask tracker via hyper-graph regularization

“…Both the pairwise graph and the hyper-graph regularizer are introduced into the tracking model to learn the global and local structure information. L = D W − Z W is the graph Laplacian matrix [45][46][47] , D W is a diagonal degree matrix whose entries are given D W i, j = j Z W i, j . Z is the weight matrix, which describes the similarity measure between every pair of subtask representations.…”