Iterative Reconstrained Low-Rank Representation via Weighted Nonconvex Regularizer

To overcome the limitations of existing low-rank representation (LRR) methods, i.e., the error distribution should be known a prior and the leading rank components might be over penalized, this paper proposes a new low-rank representation based model, namely double weighted LRR (DWLRR), using two distinguished properties on the concerned representation matrix. The first characterizes various distributions of the residuals into an adaptively learned weighting matrix for more flexibility of noise resistance. The second employs a parameterized rational penalty as well as a weighting vector s to reveal the importance of different rank components for better approximation to the intrinsic subspace structure. Moreover, we derive a computationally efficient algorithm based on the parallel updating scheme and automatic thresholding operation. Comprehensive experimental results conducted on image clustering demonstrate the robustness and efficiency of DWLRR compared with other state-of-the-art models.

Subspace clustering based on latent low rank representation with Frobenius norm minimization

Low Rank Representation (LRR) based unsupervised clustering methods have achieved great success since these methods could explore low-dimensional subspace structure embedded in original data effectively. The conventional LRR methods generally treat the data as the points in Euclidean space. However, it is no longer suitable for high-dimension data (such as video or imageset). That is because high-dimension data are always considered as non-linear manifold data such as Grassmann manifold. Besides, the typical LRR methods always adopt the traditional single nuclear norm based low rank constraint which can not fully reveal the low rank property of the data representation and often leads to suboptimal solution. In this paper, a new LRR based clustering model is constructed on Grassmann manifold for high-dimension data. In the proposed method, each high-dimension data is formed as a sample on Grassmann manifold with non-linear metric. Meanwhile, a non-convex low rank representation is adopt to reveal the intrinsic property of these high-dimension data and reweighted rank minimization constraint is introduced. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.

Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.

Data clustering is a fundamental topic in machine learning and data mining areas. In recent years, researchers have proposed a series of effective methods based on Low Rank Representation (LRR) which could explore low-dimension subspace structure embedded in original data effectively. The traditional LRR methods are usually designed for vectorial data from linear spaces with Euclidean distance. However, high-dimension data (such as video clip or imageset) are always considered as non-linear manifold data such as Grassmann manifold with non-linear metric. In addition, traditional LRR clustering method always adopt single nuclear norm as low rank constraint which would lead to suboptimal solution and decrease the clustering accuracy. In this paper, we proposed a new low rank method on Grassmann manifold for video or imageset data clustering task. In the proposed method, video or imageset data are formulated as sample data on Grassmann manifold first. And then a double low rank constraint is proposed by combining the nuclear norm and bilinear representation to better construct the representation matrix. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.

Low-rank inter-class sparsity based semi-flexible target least squares regression for feature representation

Recently, low-rank representation (LRR) methods have been widely applied for hyperspectral anomaly detection, due to their potentials in separating the backgrounds and anomalies. However, existing LRR models generally convert 3-D hyperspectral images (HSIs) into 2-D matrices, inevitably leading to the destruction of intrinsic 3-D structure properties in HSIs. To this end, we propose a novel tensor low-rank and sparse representation (TLRSR) method for hyperspectral anomaly detection. A 3-D TLR model is expanded to separate the LR background part represented by a tensorial background dictionary and corresponding coefficients. This representation characterizes the multiple subspace property of the complex LR background. Based on the weighted tensor nuclear norm and the LF,1 sparse norm, a dictionary is designed to make its atoms more relevant to the background. Moreover, a principal component analysis (PCA) method can be assigned as one preprocessing step to exact a subset of HSI bands, retaining enough the HSI object information and reducing computational time of the postprocessing tensorial operations. The proposed model is efficiently solved by the well-designed alternating direction method of multipliers (ADMMs). A comparison with the existing algorithms via experiments establishes the competitiveness of the proposed method with the state-of-the-art competitors in the hyperspectral anomaly detection task.

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. However, conventional LRR methods simply use Euclidean distance to measure the similarity of samples, ignoring the dynamic structure information of data. Meanwhile, recent studies have shown that a probabilistically motivated distance measurement (called effective distance) can model the dynamic structure information of data. In this paper, we propose an effective distance based LRR (EDLRR)method for representation learning. The proposed EDLRR method can not only represent the dynamic structure of data, but also capture the geometric information in the inherent nonlinear data. Our method mainly uses Effective Distance Computation and Effective Distance based Low-Rank Representation. We evaluate our method on datasets in the task of image classification, with results demonstrating the effectiveness of the method.

Multiview subspace clustering is one of the most widely used methods for exploiting the internal structures of multiview data. Most previous studies have performed the task of learning multiview representations by individually constructing an affinity matrix for each view without simultaneously exploiting the intrinsic characteristics of multiview data. In this article, we propose a multiview low-rank representation (MLRR) method to comprehensively discover the correlation of multiview data for multiview subspace clustering. MLRR considers symmetric low-rank representations (LRRs) to be an approximately linear spatial transformation under the new base, that is, the multiview data themselves, to fully exploit the angular information of the principal directions of LRRs, which is adopted to construct an affinity matrix for multiview subspace clustering, under a symmetric condition. MLRR takes full advantage of LRR techniques and a diversity regularization term to exploit the diversity and consistency of multiple views, respectively, and this method simultaneously imposes a symmetry constraint on LRRs. Hence, the angular information of the principal directions of rows is consistent with that of columns in symmetric LRRs. The MLRR model can be efficiently calculated by solving a convex optimization problem. Moreover, we present an intuitive fusion strategy for symmetric LRRs from the perspective of spectral clustering to obtain a compact representation, which can be shared by multiple views and comprehensively represents the intrinsic features of multiview data. Finally, the experimental results based on benchmark datasets demonstrate the effectiveness and robustness of MLRR compared with several state-of-the-art multiview subspace clustering algorithms.

Discriminative feature extraction based on sparse and low-rank representation

Due to the excellent performance in exploring the structure of low-dimensional subspaces, the low-rank representation (LRR) has recently attracted wide attention of the researchers. However, in most current semi-supervised learning problems based on LRR method, the two steps of graph construction and semi-supervised learning are separated. Therefore, the existing label information cannot be well used to guide the construction of the affinity graph. Thus, these methods cannot guarantee the results are the global optimal solutions. In this paper, we propose a graph regularized low-rank representation for semi-supervised learning, termed as GLRSC. Combing the construction of the affinity graph and the semi-supervised learning, and solving the joint optimization, the proposed GLRSC method can get the global optimal solution. The experimental results on some benchmark datasets show that the effectiveness of the proposed GLRSC method.

In this paper, we propose a novel single image super-resolution (SR) method based on low-rank sparse representation with self-similarity learning. Sparse representation is known as a promising method for SR. However, the sparse codes for low resolution (LR) patches gained by conventional method are not faithful to those for the original high resolution (HR) ones. To overcome this defect, we explore the structures of sparse representation for nonlocal similar patches in natural images by low-rank strategy. It assumes that the sparse codes for nonlocal similar patches should be low-rank. By low-rank constraint, similar components of sparse codes are shared and coding noises are removed, which improves coding accuracy and SR performance. Furthermore, we utilize self-similarity learning framework to generate a self-examples dictionary compatible to the low-rank sparse representation based SR. Experimental results demonstrate that our proposed method can recover good SR results both quantitatively and perceptually.

Biomedical cell image contains different types of components. The segmentation of these components is essential for characterizing the overall structure of leucocytes. However, the task is challenging because the data generally possess irregular patterns, varying eccentricity and congestion of inter class substructures. In order to perform the automatic segmentation of leucocytes, many approaches in machine learning have been proposed. Most of the recent methods utilize k-means and fuzzy c-means algorithms. These methods suffer from the under-segmentation and the oversegmentation of data points. We have adopted an efficient Low Rank Representation (LRR) method for the segmentation of cell image patterns. Its overall segmentation performance is very high in comparison to the k-means and fuzzy c-means segmentation methods. It discriminates sub structures by incorporating multiple feature data into the joint representation matrix. The main improvements of our adopted approach, include the global geometric representation of different cell patterns and the control of different sources of noise in the data. Data points of the cell image are evolved with the basic assumption as x = m + n. Where x is the input observation, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex> is the set of data points that lies in the correct subspace and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> represent the noise in the data. The performance of the model was evaluated on the different types of medical images. It has reported the clustering accuracy of 97.98% on the biomedical database. Whereas an accuracy of 93.1 % was reported on ALL-IDB cell dataset.

In this paper, a noise robust tensor based image clustering approach is proposed which can also perform well in the presence of gross errors. Our major contribution is the improved submodule identification technique in noisy environment by incorporating three important improvements: better low rank representation using reweighted nuclear norm, $$l_\frac{1}{2}$$ regularization to accurately capture sparseness and an error term in the model for noise robustness. Reweighted nuclear norm is introduced in the clustering model to capture self-expressiveness property in a better manner. The $$l_\frac{1}{2}$$ norm regularization is applied in place of $$l_1$$ -norm to properly capture the correlation among data members. An error term is introduced into the model to separate noise and data, which brings a noise robust image clustering technique. Combined effect all the three factors results an accurate clustering method even under the presence of severe noise. The performance of the proposed method is tested on different datasets with varying amount of noise. It is found that the proposed method provides better classification accuracy in almost all conditions as compared with existing methods.

Low-rank representation (LRR) has received considerable attention in subspace segmentation due to its effectiveness in exploring low-dimensional subspace structures embedded in data. To preserve the intrinsic geometrical structure of data, a graph regularizer has been introduced into LRR framework for learning the locality and similarity information within data. However, it is often the case that not only the high-dimensional data reside on a non-linear low-dimensional manifold in the ambient space, but also their features lie on a manifold in feature space. In this paper, we propose a dual graph regularized LRR model (DGLRR) by enforcing preservation of geometric information in both the ambient space and the feature space. The proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold. Furthermore, we extend the DGLRR model to include non-negative constraint, leading to a parts-based representation of data. Experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state-of-the-art approaches in image clustering.