Sparse Subspace Clustering Algorithm Research Articles

Joint learning framework of superpixel generation and fuzzy sparse subspace clustering for color image segmentation

Sparse subspace clustering (SSC) is an important image segmentation method that constructs a self-representation coefficient matrix to represent the relationships between pixels, and then uses spectral clustering to achieve clustering. Compared with other unsupervised segmentation algorithms, SSC has good segmentation performance. However, SSC has a high computational complexity when processing large-sized image. To improve computational efficiency, many researchers have proposed superpixel-based SSC algorithms, which process superpixels instead of pixels and improve efficiency through preprocessing. Due to the sensitivity of superpixel generation to noise, superpixel-based SSC algorithms still have poor robustness. Additionally, preprocessing increases the complexity of the algorithm. To address these issues, this paper proposes a robust superpixel-based fuzzy sparse subspace clustering algorithm. This algorithm combines fuzzy sparse subspace clustering with superpixel generation, and it constructs a unified optimization learning framework through fuzzy C-multiple-means clustering to improve segmentation performance and reduce complexity. Additionally, this paper introduces additional features of superpixel in sparse subspace clustering to further enhance the segmentation performance of the algorithm. Experiment results indicate that the proposed algorithm not only outperforms existing state-of-the-art robust segmentation algorithms independent of superpixels, but also is superior to the latest superpixel-based segmentation algorithms.

Adaptive fuzzy weighted C-mean image segmentation algorithm combining a new distance metric and prior entropy

The fuzzy C-mean clustering algorithm (FCM) is effective in image segmentation. However, its sensitivity to initialization settings and the limitation of the Euclidean distance metric in measuring similarity lead to unsatisfactory image segmentation. To overcome these shortcomings, we propose an adaptive fuzzy weighted C-mean image segmentation algorithm that combines a new distance metric and prior entropy. This algorithm significantly contributes in three aspects. First, we employ an improved sparse subspace clustering (SSC) algorithm based on the superpixel image for initialization settings. This step aims to obtain the initial number of clusters and the membership matrix, ensuring the algorithm’s convergence to the optimal solution. Second, to better capture differences between image regions, we introduce a novel distance metric that combines Euclidean and non-Euclidean distances. Simultaneously, the fuzzy weight is introduced to mitigate redundant feature interference, making the clustering result more reasonable. Finally, leveraging prior entropy – a maximum entropy under conditional constraints – we refine the algorithm’s adaptability to unknown features, thereby improving clustering accuracy. Comparative experiments with several state-of-the-art algorithms validate the effectiveness and robustness of our proposed algorithm.

Deciphering the Immune Complexity in Esophageal Adenocarcinoma and Pre-Cancerous Lesions With Sequential Multiplex Immunohistochemistry and Sparse Subspace Clustering Approach.

Esophageal adenocarcinoma (EAC) develops from a chronic inflammatory environment across four stages: intestinal metaplasia, known as Barrett’s esophagus, low- and high-grade dysplasia, and adenocarcinoma. Although the genomic characteristics of this progression have been well defined via large-scale DNA sequencing, the dynamics of various immune cell subsets and their spatial interactions in their tumor microenvironment remain unclear. Here, we applied a sequential multiplex immunohistochemistry (mIHC) platform with computational image analysis pipelines that allow for the detection of 10 biomarkers in one formalin-fixed paraffin-embedded (FFPE) tissue section. Using this platform and quantitative image analytics, we studied changes in the immune landscape during disease progression based on 40 normal and diseased areas from endoscopic mucosal resection specimens of chemotherapy treatment- naïve patients, including normal esophagus, metaplasia, low- and high-grade dysplasia, and adenocarcinoma. The results revealed a steady increase of FOXP3+ T regulatory cells and a CD163+ myelomonocytic cell subset. In parallel to the manual gating strategy applied for cell phenotyping, we also adopted a sparse subspace clustering (SSC) algorithm allowing the automated cell phenotyping of mIHC-based single-cell data. The algorithm successfully identified comparable cell types, along with significantly enriched FOXP3 T regulatory cells and CD163+ myelomonocytic cells as found in manual gating. In addition, SCC identified a new CSF1R+CD1C+ myeloid lineage, which not only was previously unknown in this disease but also increases with advancing disease stages. This study revealed immune dynamics in EAC progression and highlighted the potential application of a new multiplex imaging platform, combined with computational image analysis on routine clinical FFPE sections, to investigate complex immune populations in tumor ecosystems.

Inductive Latent Space Sparse and Low-rank Subspace Clustering Algorithm

Sparse subspace clustering (SSC) and low-rank representation (LRR) are the most popular algorithms for subspace clustering. However, SSC and LRR are transductive methods and cannot deal with the new data not involved in the training data. When a new data comes, SSC and LRR need to calculate over all the data again, which is a time-consuming thing. On the other hand, for high-dimensional data, dimensionality reduction is firstly performed before running SSC and LRR algorithms which isolate the dimensionality reduction and the following subspace clustering. To overcome these shortcomings, in this paper, two sparse and low-rank subspace clustering algorithms based on simultaneously dimensionality reduction and subspace clustering which can deal with out-of-sample data were proposed. The proposed algorithms divide the whole data set into in-sample data and out-of-sample data. The in-sample data are used to learn the projection matrix and the sparse or low-rank representation matrix in the low-dimensional space. The membership of in-sample data is obtained by spectral clustering. In the low dimensional embedding space, the membership of out of sample data is obtained by collaborative representation classification (CRC). Experimental results on a variety of data sets verify that our proposed algorithms can handle new data in an efficient way.

A simple and effective spectral-spatial method for mapping large-scale coastal wetlands using China ZY1-02D satellite hyperspectral images

This paper proposes a simple and effective spatial-spectral (SESS) method for mapping large-scale coastal wetlands using China ZY1-02D satellite hyperspectral data. First, the improved sparse subspace clustering algorithm is implemented to select presentative bands, and then the multi-scale low-rank decomposition algorithm is employed to extract multi-scale spatial features. After that, the extracted spatial and selected spectral features are stacked and fused using presented Landmark-neighborhood preserving embedding algorithm. Finally, the low-dimensional fused features are classified with two popular classifiers (i.e., random forest and support vector machine) to map coastal wetlands. Experiments results show that the SESS obtains the highest classification accuracy of 96.92% and 94.84% on Yellow River Delta and Yancheng coastal wetlands of China, respectively, exhibiting good capability in accurately identifying complicated ground objects. This paper is the first attempt to investigate the potentials of China ZY1-02D satellite hyperspectral data, and the SESS can also be applied into other hyperspectral data.

Research on self-adaptive clustering algorithms for large data sparse networks based on information entropy

With the advent of the era of artificial intelligence and information technology, a large number of data and information pour into all walks of life. These data packages include many online and offline data such as text files, audio and video. However, so many data are unnecessary in real life. The application of data clustering algorithm based on artificial intelligence technology can solve such problems very well. However, the traditional clustering algorithm relies too much on manual operation when choosing clustering centers, which greatly reduces the efficiency of the whole algorithm. At the same time, the traditional clustering algorithm based on sparse network has too many coefficients in its coefficient matrix design, so it can not aggregate the relevant data well. This paper will measure the correlation of related data based on information entropy, and innovatively improve the existing sparse data network model. A model training algorithm based on multi-strategy pattern optimization is proposed to realize the automatic selection of clustering centers and reduce the training time of the algorithm. In terms of data clustering correlation, this paper proposes an optimized adaptive clustering algorithm based on the joint model of sparse subspace clustering algorithm model and the norm of adaptive subspace segmentation. In the experimental part, this paper compares the proposed algorithm with the traditional density peak clustering algorithm. The experimental results show that the proposed algorithm has obvious advantages in text data collection and classification, image data collection and filtering.

Multibody Nonrigid Structure from Motion Segmentation Based on Sparse Subspace Clustering

Sparse subspace clustering (SSC) is one of the latest methods of dividing data points into subspace joints, which has a strong theoretical guarantee. However, affine matrix learning is not very effective for segmenting multibody nonrigid structure from motion. To improve the segmentation performance and efficiency of the SSC algorithm in segmenting multiple nonrigid motions, we propose an algorithm that deploys the hierarchical clustering to discover the inner connection of data and represents the entire sequence using some of trajectories (in this paper, we refer to these trajectories as the set of anchor trajectories). Only the corresponding positions of the anchor trajectories have nonzero weights. Furthermore, in order to improve the affinity coefficient and strong connection between trajectories in the same subspace, we optimise the weight matrix by integrating the multilayer graphs and good neighbors. The experiments prove that our methods are effective.

RP-LGMC: Rating prediction based on local and global information with matrix clustering

Recommendation system has attracted large amount of attention in the field of E-commerce research. Traditional MF (Matrix Factorization) methods take a global view on the user-item rating matrix to derive latent user vectors and latent item vectors for rating prediction. However, there is an inherent structure in the user-item rating matrix and a local correspondence between user clusters and item clusters as the users induce the items and the items imply the users in a recommendation system. Motivated by this observation, this paper proposes a novel rating prediction approach called RP-LGMC (Rating Prediction based on Local and Global information with Matrix Clustering) based on matrix factorization by making use of the local correspondence between user clusters and item clusters. The RP-LGMC approach consists of three components. The first component is to partition the user-item rating matrix into small blocks by the sparse subspace clustering (SCC) algorithm with co-clustering its rows (users) and columns (items) simultaneously. The second component is local distillation to extract those dense and stable blocks by thresholding block density and standard deviation. The third component is to predict the ratings with residual approximation on the local blocks and SVD++ on the global blocks of the original user-item matrixR. The RP-LGMC approach can not only reduce the data sparsity but also increase the computation scalability. Experiments on the MovieLens-25 M dataset demonstrate that the proposed RP-LGMC approach performs better than most state-of-the-art methods in terms of recommendation accuracy and has lower computation complexity than the SVD++ algorithm.

P.141 Topological data analysis for genetic-driven stratification of patients with major depressive disorder

The clustering of hyperspectral images is a challenging task because of the high dimensionality of the data. Sparse subspace clustering (SSC) algorithm is one of the popularly used clustering algorithm for high dimensionality data. However, SSC has not fully used the spectral and spatial information during similarity matrix construction based on single sparse representation coefficient for hyperspectral Imagery (HSI) clustering. In this paper, two novel similarity matrix construction methods named as Cosine-Euclidean similarity matrix (abbreviated as CE) and Cosine-Euclidean dynamic weighting similarity matrix (abbreviated as CEDW) are proposed for HSI clustering. They can combine the high spectral information and rich spatial information. Firstly, CE utilizes the cosine similarity of spectral information based on overall sparse representation vectors and classical Euclidean distance of spatial information to construct a novel similarity matrix. Secondly, inheriting CE merits, dynamic weighting adjustment method is introduced to CEDW for some external influence factors to the HSI information. Several experiments on HSI demonstrated that the proposed algorithms are effective for HSI clustering.

Multimodal MRI Brain Tumor Image Segmentation Using Sparse Subspace Clustering Algorithm.

Brain tumors are one of the most deadly diseases with a high mortality rate. The shape and size of the tumor are random during the growth process. Brain tumor segmentation is a brain tumor assisted diagnosis technology that separates different brain tumor structures such as edema and active and tumor necrosis tissues from normal brain tissue. Magnetic resonance imaging (MRI) technology has the advantages of no radiation impact on the human body, good imaging effect on structural tissues, and an ability to realize tomographic imaging of any orientation. Therefore, doctors often use MRI brain tumor images to analyze and process brain tumors. In these images, the tumor structure is only characterized by grayscale changes, and the developed images obtained by different equipment and different conditions may also be different. This makes it difficult for traditional image segmentation methods to deal well with the segmentation of brain tumor images. Considering that the traditional single-mode MRI brain tumor images contain incomplete brain tumor information, it is difficult to segment the single-mode brain tumor images to meet clinical needs. In this paper, a sparse subspace clustering (SSC) algorithm is introduced to process the diagnosis of multimodal MRI brain tumor images. In the absence of added noise, the proposed algorithm has better advantages than traditional methods. Compared with the top 15 in the Brats 2015 competition, the accuracy is not much different, being basically stable between 10 and 15. In order to verify the noise resistance of the proposed algorithm, this paper adds 5%, 10%, 15%, and 20% Gaussian noise to the test image. Experimental results show that the proposed algorithm has better noise immunity than a comparable algorithm.

Probability model of sensitive similarity measures in information retrieval

In today’s Internet age, a lot of data is stored and used, which is very important. In people’s daily life, if these data are sorted, information retrieval technology will be used, and in information retrieval, some information retrieval inaccuracies often appear. Information retrieval model is an important framework and method for fast, complete, and accurate user information retrieval. With the rapid development of information technology, great changes have taken place in people’s production and life. Various information network technologies are widely used in people’s lives. The resulting flow of information shows explosive growth, information retrieval. User requirements are getting higher and higher. How to complete personalized information retrieval in a large amount of mixed information, so that retrieval technology can help us obtain effective retrieval results, has become a realistic problem worth exploring. In this article, the application of probability model based on sensitive similarity measure in information retrieval model is analyzed, and a similarity measure algorithm based on spectral clustering is proposed. By improving the similarity measure, the sensitivity problem of scale parameters is overcome and the retrieval precision is improved. In order to better reflect the superiority of the proposed algorithm, this article compares with ng-jordan-weiss (NJW) and deep sparse subspace clustering (DSSC) algorithms. The experimental results show that the proposed algorithm is superior to NJW and DSSC algorithms for different data sets in different evaluation indicators (Rand and F-measure).

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

Subspace clustering has been widely applied to detect meaningful clusters in high-dimensional data spaces. And the sparse subspace clustering (SSC) obtains superior clustering performance by solving a relaxed $\ell _{0}$ -minimization problem with $\ell _{1}$ -norm. Although the use of $\ell _{1}$ -norm instead of the $\ell _{0}$ one can make the object function convex, it causes large errors on large coefficients in some cases. In this paper, we study the sparse subspace clustering algorithm based on a nonconvex modeling formulation. Specifically, we introduce a nonconvex pseudo-norm that makes a better approximation to the $\ell _{0}$ -minimization than the traditional $\ell _{1}$ -minimization framework and consequently finds a better affinity matrix. However, this formulation makes the optimization task challenging due to that the traditional alternating direction method of multipliers (ADMM) encounters troubles in solving the nonconvex subproblems. In view of this, the reweighted techniques are employed in making these subproblems convex and easily solvable. We provide several guarantees to derive the convergence results, which proves that the nonconvex algorithm is globally convergent to a critical point. Experiments on two real-world problems of motion segmentation and face clustering show that our method outperforms state-of-the-art techniques.

Research on Community Detection of Online Social Network Members Based on the Sparse Subspace Clustering Approach

The text data of the social network platforms take the form of short texts, and the massive text data have high-dimensional and sparse characteristics, which does not make the traditional clustering algorithm perform well. In this paper, a new community detection method based on the sparse subspace clustering (SSC) algorithm is proposed to deal with the problem of sparsity and the high-dimensional characteristic of short texts in online social networks. The main ideal is as follows. First, the structured data including users’ attributions and user behavior and unstructured data such as user reviews are used to construct the vector space for the network. And the similarity of the feature words is calculated by the location relation of the feature words in the synonym word forest. Then, the dimensions of data are deduced based on the principal component analysis in order to improve the clustering accuracy. Further, a new community detection method of social network members based on the SSC is proposed. Finally, experiments on several data sets are performed and compared with the K-means clustering algorithm. Experimental results show that proper dimension reduction for high dimensional data can improve the clustering accuracy and efficiency of the SSC approach. The proposed method can achieve suitable community partition effect on online social network data sets.

Hyperspectral image clustering via sparse dictionary‐based anchored regression

Clustering for hyperspectral images (HSIs) is a very challenging task because HSIs usually have large spectral variability, high dimensionality, and complex structures. The main issue of this study is to develop an improved sparse subspace clustering (SSC) method for HSIs. As an extension of spectral clustering, SSC algorithm has achieved great success; however, the direct self-representation dictionary which is created by raw samples has poor representation power and also the widely used dictionary learning (DL) such as K-Singular Value Decomposition (K-SVD) faces with the problems of high computational complexity. In this study, the authors propose a novel HSI clustering method based on sparse DL and anchored regression. The proposed method follows three stages: (i) sparse DL; (ii) anchored subspace construction and regression; and (iii) representation-based spectral clustering. Specifically, we adopt a fast sparse DL method under a double sparsity constrained optimising model to capture the intrinsic HSIs. To establish a compact subspace for collaborative representation, we present an anchored subspace construction method by using atoms clustering and grouping methods. Owing to the anchored subspace, we can fast compute the representation coefficients with a predefined projection matrix. Experimental results demonstrate that the proposed method achieves the best performance for the HSIs clustering.

A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the dimensionality of data points to be clustered is compressed due to the constraints of measurement, computation, or privacy. In this paper, we study the theoretical properties of a popular subspace clustering algorithm named sparse subspace clustering (SSC) and establish formal success conditions of SSC on dimensionality-reduced data. Our analysis applies to the most general fully deterministic model, where both underlying subspaces and data points within each subspace are deterministically positioned, and also a wide range of dimensionality reduction techniques (e.g., Gaussian random projection, uniform subsampling, and sketching) that fall into a subspace embedding framework. Finally, we apply our analysis to a differentially private SSC algorithm and established both privacy and utility guarantees of the proposed method.

An ordered sparse subspace clustering algorithm based on p‐Norm

AbstractImages in video may include both Gaussian noise and geometric rotation. Thus, it is challenging to represent an image sequence in its intrinsically low‐dimensional space in a noise‐robust and rotation‐robust manner. In this paper, we propose a novel‐ordered sparse subspace clustering algorithm based on a p‐norm to achieve an effective clustering of sequential data under heavy noise conditions. We also use the wavelet‐histogram of oriented gradient (HOG) transform in the kernel view to extract both the global features (with the wavelet process) and the local features (with the HOG process) from the image. In addition, we assign different weights to different features to obtain a sparse coefficient matrix that helps to emphasize the global and local correlations in each sample. Similarly, the clustering algorithm based on the p‐norm for sequential images emphasizes the within‐class correlations amongst samples. Therefore, in this paper, we select additional denoising main components under a Laplacian constraint to achieve a better block‐diagonal structure and highlight the independence of different clusters. Extensive experiments performed on various public datasets (including the ordered face dataset, handwritten recognition dataset, video scene segmentation dataset, and object recognition dataset) demonstrate that the proposed method is more resilient to noise and rotation than other representative sparse subspace clustering methods.

Time series clustering based on sparse subspace clustering algorithm and its application to daily box-office data analysis

Movie box-office research is an important work for the rapid development of the film industry, and it is also a challenging task. Our study focuses on finding the regular box-office revenue patterns. Clustering algorithm is unsupervised machine learning algorithm which classifies the data in the absence of early knowledge of the classes. Unlike static data, the time series data vary with time. The work focused on time series clustering analysis is relatively less than those focused on static data. In this paper, the sparse subspace clustering (SSC) algorithm is introduced to analyze the time series data. The SSC algorithm has a better performance both on the artificial data set and the daily box-office data than recently developed well-known clustering algorithm such as K-means and spectral clustering algorithm. On the artificial data set, SSC is more suitable for time series, whether from the angle of clustering error or visualization. On the actual data, movies are divided into five clusters by SSC algorithm, and each cluster represents a distinct type of distribution pattern. And these patterns can be used in movie recommendation, film evaluation and can guide theater exhibitors and distributors. In addition, this is the first time to apply SSC to deal with time series clustering problem and get a pleasant effect.

Noisy Subspace Clustering via Matching Pursuits

Sparsity-based subspace clustering algorithms have attracted significant attention thanks to their excellent performance in practical applications. A prominent example is the sparse subspace clustering (SSC) algorithm by Elhamifar and Vidal, which performs spectral clustering based on an adjacency matrix obtained by sparsely representing each data point in terms of all the other data points via the Lasso. When the number of data points is large or the dimension of the ambient space is high, the computational complexity of SSC quickly becomes prohibitive. Dyer et al. observed that SSC-OMP obtained by replacing the Lasso by the greedy orthogonal matching pursuit (OMP) algorithm results in significantly lower computational complexity, while often yielding comparable performance. The central goal of this paper is an analytical performance characterization of SSC-OMP for noisy data. Moreover, we introduce and analyze the SSC-MP algorithm, which employs matching pursuit (MP) in lieu of OMP. Both SSC-OMP and SSC-MP are proven to succeed even when the subspaces intersect and when the data points are contaminated by severe noise. The clustering conditions we obtain for SSC-OMP and SSC-MP are similar to those for SSC and for the thresholding-based subspace clustering (TSC) algorithm due to Heckel and B\"olcskei. Analytical results in combination with numerical results indicate that both SSC-OMP and SSC-MP with a data-dependent stopping criterion automatically detect the dimensions of the subspaces underlying the data. Moreover, experiments on synthetic and on real data show that SSC-MP compares very favorably to SSC, SSC-OMP, TSC, and the nearest subspace neighbor algorithm, both in terms of clustering performance and running time. In addition, we find that, in contrast to SSC-OMP, the performance of SSC-MP is very robust with respect to the choice of parameters in the stopping criteria.

Structural Reweight Sparse Subspace Clustering

Subspace clustering aims to segment a group of data points into a union of subspaces. Reweight sparse subspace clustering is one of the state-of-the-art algorithms which proposed an iterative weighted subspace clustering. The reweight matrix helps to improve the performance of the affinity matrix construction process but it easily falls into a local minimization. In this paper, we propose a structural reweight sparse subspace clustering algorithm which introduces the structural information into reweight subspace clustering. The structural information achieved in spectral clustering process is useful for the subsequent iterative optimization process which helps to obtain a better local minimization. The experimental results on the Extended Yale B, Hopkins 155, and COIL 20 datasets demonstrate that our algorithm achieves a better performance on subspace clustering problem.

Entropy-based active sparse subspace clustering

Sparse Subspace Clustering (SSC) is widely used in data mining and machine learning. Some studies have been developed to add pairwise constraints as side information to improve the clustering results. However, most of these algorithms are “passive” in the sense that the side information is provided beforehand. In this paper, we propose a novel extension for SSC with active learning framework, in which we aim to select the most informative pairwise constraints to guide the SSC for accurate clustering results. Specifically, in the first step, an entropy-based query strategy is proposed to select the most uncertain pairwise constraints. Next, constrained sparse subspace clustering algorithms are followed to integrate the selected pairwise constraints and obtain the final clustering results. Two steps are effectively performed in an iterative manner until satisfactory results are achieved. Experimental results on two face datasets clustering well demonstrate the effectiveness of the proposed method.