Subspace Segmentation Research Articles

Multi-kernel subspace stable clustering with exact rank constraints

The identification of cancer subtypes plays a critical role in the early diagnosis of cancer and the delivery of appropriate treatment. Clustering based on comprehensive multi-omic data often yields superior results than clustering using a single data type since each omic type may contain complementary information. However, existing clustering methods cannot fully explore the internal structural information within multi-omic data and can lead to unstable clustering results. This paper proposes a novel multi-omic clustering framework, Multi-Kernel Subspace Stable Clustering with Exact Rank Constraints (MKSSC-ERC), which can effectively explore the correlation and complementary information between different omics types. Specifically, we design a kernel selection criterion that considers both accuracy and diversity and each omic data gets a base kernel. Then, we extract a consistent affinity matrix for these base kernels using subspace segmentation with exact rank constraints, which can refine the extracted shared structures and make them robust to sample noises. In addition, we devise a strategy for selecting the optimal initial cluster centers, which significantly enhances the stability of clustering results. Simulation studies on benchmark multi-omic datasets illustrate substantial gains over existing state-of-the-art methods in survival analysis. MKSSC-ERC is available at https://github.com/xuzihan66/MKSSC-ERC.

Grouping Subspace Segmentation

This work studies the subspace segmentation problem. Given a set of data points which are drawn from a union of multiple subspaces. The goal of subspace segmentation is to cluster the data into the underlying subspaces from which the data are drawn from. The most recent works use spectral clustering based on the affinity matrix obtained by Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Least Squares Regression (LSR). They write each data point as a linear combination of all the data points, and use the representation coefficients to form the affinity matrix. LSR shows that it is more effective due to the grouping effect for data with high correlation. In this work, we propose the Grouping Subspace Segmentation (GSS) method by enhancing the grouping effect of correlated data points. The affinity graph is constructed to encode the local structure of data. Experiments on the real data sets show that the proposed method GSS is more effective than the state-of-the-art methods.

DLP: Duplex Link Prediction Via Subspace Segmentation for Predicting drug-MiRNA Associations.

The arduous and costly journey of drug discovery is increasingly intersecting with computational approaches, which promise to accelerate the analysis of bioassays and biomedical literature. The critical role of microRNAs (miRNAs) in disease progression has been underscored in recent studies, elevating them as potential therapeutic targets. This emphasizes the need for the development of sophisticated computational models that can effectively identify promising drug targets, such as miRNAs. Herein, we present a novel method, termed Duplex Link Prediction (DLP), rooted in subspace segmentation, to pinpoint potential miRNA targets. Our approach initiates with the application of the Network Enhancement (NE) algorithm to refine the similarity metric between miRNAs. Thereafter, we construct two matrices by pre-loading the association matrix from both the drug and miRNA perspectives, employing the K Nearest Neighbors (KNN) technique. The DLSR algorithm is then applied to predict potential associations. The final predicted association scores are ascertained through the weighted mean of the two matrices. Our empirical findings suggest that the DLP algorithm outperforms current methodologies in the realm of identifying potential miRNA drug targets. Case study validations further reinforce the real-world applicability and effectiveness of our proposed method. The code of DLP is freely available at https://github.com/kaizheng-academic/DLP.

Subspace segmentation based co-evolutionary algorithm for balancing convergence and diversity in many-objective optimization

With the increase of the objective dimension of optimization problems, the effect of comparing individuals through Pareto dominance relation drops sharply. While some algorithms enhance Pareto dominance via diversity preservation strategies, performance indicators, and reference vectors, many of them encounter difficulties in balancing the convergence and diversity of populations. Therefore, this paper proposes a subspace segmentation based co-evolutionary algorithm for balancing convergence and diversity in many-objective optimization. First, the decision space is divided into a convergence subspace and a diversity subspace, which are searched in the early and late stages to improve the population convergence and diversity, respectively. Second, a capacity adaptively adjusted archive is used to retain elite individuals with better convergence in the population, which is further used to mate with the population. Moreover, an indicator with penalty factor is proposed to retain the boundary individuals so as to maintain the population diversity. Comparing with 6 advanced many-objective evolutionary algorithms on 63 benchmark cases, the proposed algorithm obtains smallest IGD on 36 benchmark cases, the experimental results show that the proposed algorithm can balance convergence and diversity well and has exhibit competitiveness.

A Personalized Low-Rank Subspace Clustering Method Based on Locality and Similarity Constraints for scRNA-seq Data Analysis.

Single-cell RNA sequencing (scRNA-seq) technology can provide expression profile of single cells, which propels biological research into a new chapter. Clustering individual cells based on their transcriptome is a critical objective of scRNA-seq data analysis. However, the high-dimensional, sparse and noisy nature of scRNA-seq data pose a challenge to single-cell clustering. Therefore, it is urgent to develop a clustering method targeting scRNA-seq data characteristics. Due to its powerful subspace learning capability and robustness to noise, the subspace segmentation method based on low-rank representation (LRR) is broadly used in clustering researches and achieves satisfactory results. In view of this, we propose a personalized low-rank subspace clustering method, namely PLRLS, to learn more accurate subspace structures from both global and local perspectives. Specifically, we first introduce the local structure constraint to capture the local structure information of the data, while helping our method to obtain better inter-cluster separability and intra-cluster compactness. Then, in order to retain the important similarity information that is ignored by the LRR model, we utilize the fractional function to extract similarity information between cells, and introduce this information as the similarity constraint into the LRR framework. The fractional function is an efficient similarity measure designed for scRNA-seq data, which has theoretical and practical implications. In the end, based on the LRR matrix learned from PLRLS, we perform downstream analyses on real scRNA-seq datasets, including spectral clustering, visualization and marker gene identification. Comparative experiments show that the proposed method achieves superior clustering accuracy and robustness.

An enforced block diagonal low-rank representation method for the classification of medical image patterns

Low-rank representation based methods have been used on a variety of medical imaging databases for the segmentation and classification of biomedical images. The subspace segmentation of the data is performed by generating the block diagonal coefficient matrix. Whereas, the data is classified by performing the partitioning of the low-rank representation matrix. There exist several such methods for analysing medical images. The major difference between them lies in the construction of the data dictionary. Most of the time, the input data pattern is used as the dictionary for learning the representation matrix. The direct use of the input data for learning the representation degrades the performance of the model because medical images are subjected to outliers of multiple types, which include environmental lighting, image appearance and varying illumination. These types of errors induce noise in the data. It has been observed that the representation-based model is robust when the training data is clean. If the training data contains corrupted subsamples, the performance of the model drops down. We have addressed the mentioned problem by adopting a class-wise dictionary learning approach. In which the pattern of each class is learnt as the set of tuples in the dictionary. The model has been evaluated on several medical imaging datasets, which includes the Break-his dataset, ALL-IDB, biomedical images, covid CT and chest X-ray. The classification performance of the model is best for the biomedical database (99.16%) followed by the Covid dataset (94%), ALL-IDB database (93.47%) and Break-his dataset (93%).

Recursive Sample Scaling Low-Rank Representation

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

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.

Learning Graph Similarity With Large Spectral Gap

Learning a good graph similarity matrix in data clustering is very crucial. The goal of clustering is to construct a good graph similarity matrix such that the similarity of points between the same classes is largest, and the similarity of points between different classes is smallest. In this paper, a more efficient subspace segmentation approach to learn a similarity matrix with large spectral gap is proposed. In our model, a robust self-representation coefficient matrix is learned by utilizing the Schatten- ${p}$ norm instead of the conventional rank function. Besides, the fast block-diagonal structure of the coefficient representation matrix is enhanced by learning and optimizing the co-association matrix with the soft label of clustering results simultaneously in a unified framework. The affinity graphs constructed in this paper can clearly reveal the intrinsic structures of the data sets. Extensive experiments on the real data sets demonstrate that our proposed method can perform better than the state-of-the-art methods.

RETRACTED: Fast 3D image reconstruction algorithm based on artificial intelligence technology

In order to improve the 3D reconstruction capability of high-resolution fine-grained 3D images, a fast 3D image reconstruction algorithm based on artificial intelligence technology is proposed. The cross-gradient sharpening detection method is used to collect features and extract information from high-resolution fine-grained three-dimensional images, and establish an edge contour feature detection model for high-resolution fine-grained three-dimensional images. Combining the salient feature analysis method and the subspace feature analysis method to cluster and analyze the high-resolution fine-grained three-dimensional image. In the artificial intelligence environment, the saliency of the three-dimensional image is detected and analyzed, and the multi-dimensional segmentation and gray histogram of the high-resolution fine-grained three-dimensional image are reconstructed through the subspace segmentation method. According to the reconstruction results of the gray histogram, fast 3D image reconstruction and image fusion processing are performed. Finally, the accurate detection and recognition of the reconstructed image is realized. The simulation results show that this method has a good effect on 3D image reconstruction, and the time cost of image reconstruction is relatively short. It improves the recognition and feature analysis capabilities of high-resolution fine-grained 3D images, and has good application value in the reconstruction, detection and recognition of high-resolution fine-grained 3D images.

One-Step Robust Low-Rank Subspace Segmentation for Tumor Sample Clustering.

Clustering of tumor samples can help identify cancer types and discover new cancer subtypes, which is essential for effective cancer treatment. Although many traditional clustering methods have been proposed for tumor sample clustering, advanced algorithms with better performance are still needed. Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample. For a gene expression data set, we seek its lowest rank representation matrix and the noise matrix. By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one step. To improve the robustness of the method, capped norm is adopted to remove the extreme data outliers in the noise matrix. Furthermore, we conduct an efficient solution to solve the problem of ORLRS. Experiments on several tumor gene expression data demonstrate the effectiveness of ORLRS.

Multiview Spectral Clustering via Robust Subspace Segmentation.

Multiview clustering refers to partition data according to its multiple views, where information from different perspectives can be jointly used in some certain complementary manner to produce more sensible clusters. It is believed that most of the existing multiview clustering methods technically suffer from possibly corrupted data, resulting in a dramatically decreased clustering performance. To overcome this challenge, we propose a multiview spectral clustering method based on robust subspace segmentation in this article. Our proposed algorithm is composed of three modules, that is: 1) the construction of multiple feature matrices from all views; 2) the formulation of a shared low-rank latent matrix by a low rank and sparse decomposition; and 3) the use of the Markov-chain-based spectral clustering method for producing the final clusters. To solve the optimization problem for a low rank and sparse decomposition, we develop an optimization procedure based on the scheme of the augmented Lagrangian method of multipliers. The experimental results on several benchmark datasets indicate that the proposed method outperforms favorably compared to several state-of-the-art multiview clustering techniques.

A Group Norm Regularized Factorization Model for Subspace Segmentation

Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method for solving subspace segmentation problems, that is, one first obtains an affinity matrix by solving a LRR model and then performs spectral clustering for segmentation. This paper proposes a group norm regularized factorization model (GNRFM) inspired by the LRR model for subspace segmentation and then designs an Accelerated Augmented Lagrangian Method (AALM) algorithm to solve this model. Specifically, we adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving a purpose of low rank, which means no Singular Value Decompositions (SVD) are required and the computational complexity of each step is greatly reduced. We obtain affinity matrices by using different LRR models and then performing cluster testing on different sets of synthetic noisy data and real data, respectively. Compared with traditional models and algorithms, the proposed method is faster and more robust to noise, so the final clustering results are better. Moreover, the numerical results show that our algorithm converges fast and only requires approximately ten iterations.

Efficient Graph Convolutional Self-Representation for Band Selection of Hyperspectral Image

Hyperspectral image (HSI) band selection (BS) is an important task for HSI dimensionality reduction, whose goal is to select an informative band subset containing less redundancy. However, traditional BS methods basically work in the Euclidean domain, and thus, often neglect to consider the structural information of spectral bands. In this article, to make full use of the structural information, a novel BS method termed as efficient graph convolutional self-representation (EGCSR) is proposed by incorporating graph convolution into the self-representation model. Since the proposed method is typically modeled in the non-Euclidean domain, it tends to result in a more robust self-representation coefficient matrix. We provide a closed-form solution to the EGCSR model, which leads to high-computational efficiency. We further propose two strategies to determine the informative band subset from the coefficient matrix. The first is a ranking-based strategy, which ranks every band by calculating the cumulative contribution, and the second is a clustering-based strategy, which treats BS as a band clustering task based on using subspace segmentation. Extensive experimental results on three real HSI datasets show that the proposed EGCSR model is dramatically superior to many existing BS methods, and with high-computational efficiency.

Point Cloud Normal Estimation by Fast Guided Least Squares Representation

Normal estimation is an essential task for scanned point clouds in various CAD/CAM applications. The method (GLSRNE) based on guided least squares representation (GLSR) balances speed with quality well among state-of-the-art methods. First, it segments each neighborhood into multiple sub-neighborhoods. For some neighborhoods, the segmentation is obtained by GLSR which is an efficient subspace segmentation model and widely applied in other applications. The segmentation of the rest neighborhoods is inferred via the subspace structure propagation (SSP) algorithm. Then, each sub-neighborhood is fitted by a plane. The plane achieving the minimum distance with the current point is selected for the final normal estimation. We make improvements for effectiveness and efficiency in the following three aspects. First, to improve the speed of GLSR, we propose a novel iterative algorithm to reduce the computation complexity from $O(n^{3})$ to $O(n^{2})$ with its convergence guaranteed theoretically, where $n$ represents the number of the data points. Moreover, this proposed algorithm will also be useful for other applications. Second, we add a normal constraint for SSP to improve accuracy. Third, when selecting one plane to estimate the final normal, we consider the match between the plane and all neighbors, whereas GLSRNE only considers the match between the plane and the current point. The experiments exhibit that our method is faster than GLSRNE and more effective than GLSRNE and other state-of-the-art methods.

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation.

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Subspace segmentation via self-regularized latent K-means

Low-rank representation (LRR) related algorithms have achieved great successes in subspace segmentation tasks. Among them, matrix factorization based methods usually show better performances than those of other LRR-related algorithms. According to our analyses, we found that the matrix factorization based low-rank algorithms could be regarded as the extensions of classical K-means performed in a latent subspace. From this viewpoint, we proposed a kind of new matrix factorization based algorithm, term self-regularized latent K-means (SRLKM), for subspace segmentation. In SRLKM, we devised a new graph-regularizer by using one of the solution to SRLKM itself. For further clarification about our proposed method, we declared the relationships between SRLKM and some close-related algorithms. Moreover, an optimization algorithm for solving SRLKM problem was provided. Finally, extensive experiments were conducted to show that SRLKM was superior to the related algorithms.

Subspace segmentation-based robust multiple kernel clustering

Multiple kernel clustering (MKC) is an important research topic during the last few decades. It optimally combines a group of pre-specified base kernels to improve clustering performance. Though demonstrating promising performance in various applications, this task is still challenging due to lack of reliable discriminative guidance for the base kernel combination. Moreover, noise from either corrupted data or inappropriately selected base kernel parameters would undermine the intrinsic manifold and makes the problem even harder. In this paper, we integrate subspace segmentation into MKC and propose a robust subspace segmentation-based multiple kernel clustering (SS-MKC) algorithm to address these issues. In our formulation, we unify the constrained kernel polarization and subspace segmentation into a single procedure, where the resultant affinity matrix embedded with robust subspace structural information is utilized to guide the linear combination of base kernels. In addition, we carefully design the noise representation matrix as well as two sparse constraints, i.e., the ℓ1-norm and the probability constraints, to eliminate the adverse effect of noise among base kernels. We then propose a novel Alternative Direction Method of Multiplier (ADMM)-based algorithm to solve the resulting optimization problem. Extensive experiments have been conducted on both synthetic and public benchmark datasets, and the results well demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art MKC methods.

Just‐in‐time learning–multiple subspace support vector data description used for non‐Gaussian dynamic batch process monitoring

AbstractBatch process data are time‐varying dynamic and non‐Gaussian distributed. In addition, for multivariate statistical process monitoring, their variability can be overwhelmed when considering local variability behavior. To address the abovementioned issues, an improved batch process monitoring approach is presented that integrates just‐in‐time learning and multiple subspace support vector data description (JITL‐MSSVDD). A new multiple subspace segmentation method is proposed that classifies a contribution array that is calculated on the mixing matrix of independent component analysis (ICA). Offline, the variable subspace segmentation rule can be obtained from the proposed method. The subspace monitoring models can reduce the risk of the variability being overwhelmed. Online, local modeling samples are collected through JITL, which can reduce the impact of the time‐varying dynamic on modeling accuracy. Then, in accordance with the variable subspace segmentation rule, which is obtained offline, MSSVDD models are constructed to solve non‐Gaussian problems. The advantage of the proposed JITL‐MSSVDD is demonstrated through the standard test model fed‐batch penicillin fermentation process.

Robust Low-rank subspace segmentation with finite mixture noise

Subspace segmentation or clustering remains a challenge of interest in computer vision when handling complex noise existing in high-dimensional data. Most of the current sparse representation or minimum-rank based techniques are constructed on ℓ1-norm or ℓ2-norm losses, which is sensitive to outliers. Finite mixture model, as a class of powerful and flexible tools for modeling complex noise, becomes a must. Among all the choices, exponential family mixture is extremely useful in practice due to its universal approximation ability for any continuous distribution and hence covers a broader scope of characteristics of noise distribution. Equipped with such a modeling idea, this paper focuses on the complex noise contaminated subspace clustering problem by using finite mixture of exponential power (MoEP) distributions. We then harness a penalized likelihood function to perform automatic model selection and hence avoid over-fitting. Moreover, we introduce a novel prior on the singular values of representation matrix, which leads to a novel penalty in our nonconvex and nonsmooth optimization. The parameters of the MoEP model can be estimated with a Maximum A Posteriori (MAP) method. Meanwhile, the subspace is computed with joint weighted ℓp-norm and Schatten-q quasi-norm minimization. Both theoretical and experimental results show the effectiveness of our method.