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Short text clustering is a significant yet challenging task, where short texts generated from the Internet are extremely sparse, noisy, and ambiguous. The sparse nature makes traditional clustering methods, e.g.,k-means family and topic modeling, much less effective. Fortunately, recent arts of document distance, e.g., word mover's distance, and document representation, e.g., BERT, can accurately measure the similarities of short texts, especially their nearest neighbors. Inspired by those arts and observations, we induce short text clusters by directly factorizing the informative affinity matrix of nearest neighbors into the product of the cluster assignment matrix, following the intuition that neighboring short texts tend to be assigned to the same cluster. However, due to the noisy nature of short texts, many of them can be regarded as outliers or near outliers, resulting in many noisy neighboring similarities within the affinity matrix. To further alleviate this problem, we enhance the affinity matrix factorization by (1) incorporating a sparse noisy matrix to directly capture noisy neighboring similarities and (2) regularizing the cluster assignment matrix by ℓ 2 , 1 norm to eliminate hard-to-clustering short texts (called pseudo-outliers), so as to indirectly neglect noisy neighboring similarities corresponding to them. After this factorization for pre-clustering, we train a classifier over the resulting clusters and adopt it to assign each pseudo-outlier to one cluster finally. We call this novel clustering method as anomaly-aware symmetric non-negative matrix factorization ( A 2 snmf). Experimental results on benchmark short text datasets demonstrate that A 2 snmf performs very competitively with the existing baseline methods. The code is available at the website https://github.com/wizardbo/A3SNMF_functions. [ABSTRACT FROM AUTHOR]

Graph-based semi-supervised learning’s inherent ability to exploit the underlying structure of data distribution for supplementing label propagation has gained momentum over recent years. However, its effectiveness highly relies on the graph's structure quality and deteriorates when dealing with high dimensional, noisy, unevenly distributed data thus, necessitating adaptivity with sparsity in graph construction. To achieve this, an Exponentially Regularized Optimal Sparse Graph (EROSG) is introduced that inculcates these characteristics by exploring local connectivity ensuring efficient label propagation with reduced complexity. Accordingly, EROSG constructs the affinity matrix using a novel distance metric to widen the sample-wise interclass deviation and strengthen the local connectivity. The resulting affinity matrix is then optimized by Lagrangian multipliers with non-negative and SoftMax constraints to yield the adaptive sparse graph facilitating label propagation. Extensive analysis of EROSG on diverse datasets demonstrates consistent and superior accuracy of over 93% with a minimum availability of 5–10% of labeled data which is lacking in its competitors. Also, EROSG’s parameter-free nature lessens realization complexity emphasizing the need of the hour. [ABSTRACT FROM AUTHOR]

The design and analysis of gas detection chips directly affect their detection efficiency and applicability. Detection devices are currently restricted by detection principles, facing drawbacks like intricate structural design, limited applicability, and low detection efficiency. We have designed a complete set of design and analysis scheme for a peptide gas detection chip. First, we selected specific and high-affinity peptide combinations from existing peptide-gas affinity datasets. Then, the peptide chip's arrangement was grouped according to the variations in peptides' affinity towards different gases. Peptides were arranged based on their affinity levels within each group, striking a balance between discrimination and flexibility in the design of the chip. Finally, we evaluated the analysis methods by generating simulated data based on a reference affinity matrix constructed from actual data. Due to the preprocessing role of chip design on affinity data, all methods can effectively accomplish gas classification. In gas concentration prediction tasks, our method reduced mean square error to 0.41, significantly outperforming other methods. This gas detection scheme shortens the development cycle of chip design and analysis methods, fully utilizing the specificity of peptides, enhancing gas analysis effectiveness, and demonstrating the agile development of gas detection chips.

The integration of multi-omics data has emerged as a promising approach for gaining comprehensive insights into complex diseases such as cancer. This paper proposes a novel approach to identify cancer subtypes through the integration of multi-omics data for clustering. The proposed method, named LIDAF utilises affinity matrices based on linear relationships between and within different omics datasets (Linear Inter and Intra Dataset Affinity Fusion (LIDAF)). Canonical Correlation Analysis is in this paper employed to create distance matrices based on Euclidean distances between canonical variates. The distance matrices are converted to affinity matrices and those are fused in a three-step process. The proposed LIDAF addresses the limitations of the existing method resulting in improvement of clustering performance as measured by the Adjusted Rand Index and the Normalized Mutual Information score. Moreover, our proposed LIDAF approach demonstrates a notable enhancement in 50% of the -log10 rank p-values obtained from Cox survival analysis, surpassing the performance of the best-reported method. This improvement in -log10 rank p-values stands out as a major finding, underscoring the significance of the proposed method in identifying distinct cancer subtypes.

Graph matching is a fundamental NP-problem in computer graphics and computer vision. In this work, we present an approximate graph matching method. Given two graphs to be matched, the proposed method first constructs an association graph to convert the problem of graph matching into a problem of selecting nodes on the constructed graph. The nodes of the association graph represent candidate correspondences between the two original graphs. An affinity matrix is then computed based on the local, intermediate and global information of the original graphs' nodes, each element of which is used to measure the mutual consistency of a correspondence pair within the association graph. Updating the affinity of each correspondence pair with the affinities of relevant correspondences, our method then utilizes the reweighted random walks strategy to simulate random walks on the association graph and to iteratively obtain a quasi-stationary distribution. Finally, our method applies the Hungarian algorithm to discretize the distribution. Experimental results on four common datasets verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The economic downturn in recent years has had a significant negative impact on corporates performance. In the last two years, as in the last years of 2010s, many companies have been influenced by the economic conditions and some have gone bankrupt. This has led to an increase in companies' financial risk. One of the significant branches of financial risk is the emph{company's credit risk}. Lenders and investors attach great importance to determining a company's credit risk when granting a credit facility. Credit risk means the possibility of default on repayment of facilities received by a company. There are various models for assessing credit risk using statistical models or machine learning. In this paper, we will investigate the machine learning task of the binary classification of firms into bankrupt and healthy based on the emph{spectral graph theory}. We first construct an emph{adjacency graph} from a list of firms with their corresponding emph{feature vectors}. Next, we first embed this graph into a one-dimensional Euclidean space and then into a two dimensional Euclidean space to obtain two lower-dimensional representations of the original data points. Finally, we apply the emph{support vector machine} and the emph{multi-layer perceptron} neural network techniques to proceed binary emph{node classification}. The results of the proposed method on the given dataset (selected firms of Tehran stock exchange market) show a comparative advantage over PCA method of emph{dimension reduction}. Finally, we conclude the paper with some discussions on further research directions.

Multi-view clustering (MVC) can integrate the complementary information between different views to remarkably improve clustering performance. However, the existing methods suffer from the following drawbacks: (1) multi-view data are often lying on high-dimensional space and inevitably corrupted by noise and even outliers, which poses challenges for fully exploiting the intrinsic structure of views; (2) the non-convex objective functions prone to becoming stuck into bad local minima; and (3) the high-order structure information has been largely ignored, resulting in suboptimal solution. To alleviate these problems, this paper proposes a novel method, namely Self-paced Latent Embedding Space Learning (SLESL). Specifically, the views are projected into a latent embedding space to dimensional-reduce and clean the data, from simplicity to complexity in a self-paced manner. Meanwhile, multiple candidate graphs are learned in the latent space by using embedded self-expressiveness learning. After that, these graphs are stacked into a tensor to exploit the high-order structure information of views, such that a refined consensus affinity graph can be obtained for spectral clustering. The experimental results demonstrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

Recently, the popularity of multi-view clustering (MVC) has increased, and many MVC methods have been developed. However, the affinity matrix that is learned by the MVC method is only block diagonal if noise and outliers are not included in the data.; however, data always contain noise and outliers. As a result, the affinity matrix is unreliable for subspace clustering because it is neither clean nor robust enough, which affects clustering performance. To compensate for these shortcomings, in this paper, we propose a novel clean and robust affinity matrix (CRAA) learning method for MVC. Specifically, firstly, the global structure of data is obtained by constructing the representation space shared by all views. Next, by borrowing the idea of robust principal component analysis (RPCA), the affinity matrix is divided into two parts, i.e., a cleaner and more robust affinity matrix and a noisy matrix. Then, the two-step procedure is integrated into a unified optimization framework and a cleaner and robust affinity matrix is learned. Finally, based on the augmented Lagrangian multiplier (ALM) method, an efficient optimization procedure for obtaining the CRAA is also developed. In fact, the main idea for obtaining a cleaner and more robust affinity matrix can also be generalized to other MVC methods. The experimental results on eight benchmark datasets show that the clustering performance of the CRAA is better than that of some of the state-of-the-art clustering methods in terms of NMI, ACC, F-score, Recall and ARI metrics. [ABSTRACT FROM AUTHOR]

Spectral Clustering (SC) is an important method in areas such as data mining, image processing, computer science and so on. It attracts more and more attention owing to its effectiveness in unsupervised learning. However, SC has poor performance in the high-dimensional data. Traditional SC methods conduct the spectral embedding of the affinity matrix among data at the first beginning, and then obtain clustering results by the K -means clustering. The also have drawbacks int two processing steps: the clustering results are sensitive to the affinity matrix which may be inaccurate and the post-processing K -means may also be limited by its initialization problem. In the paper, a new approach which joints spectral embedding and clustering with structured graph optimization (called JSEGO) is proposed. In the new model, the low-dimensional representation of data can first be obtained by the spectral embedding method, which can handle with the high-dimensional data better. Then, the optimization similarity matrix would be obtained with such the embedded data. Furthermore, the learning structure graph gives feedback to the similarity matrix to generate better spectral embedded data. As a result, better similarity matrix and clustering result can be obtained by the iterations simultaneously, which are often conducted in two separate steps in the spectral clustering. As a result, the drawbacks introduced by the two processing introduces can be solved. At last, we use an alternative optimization method in the new model and conduct the theoretical analysis by comparing this proposed method with K -means clustering. Experiments based on synthetic data and actual benchmark data prove the advantage of this new approach. [ABSTRACT FROM AUTHOR]

The object of multi-view subspace clustering is to uncover the latent low-dimensional structure by segmenting a collection of high-dimensional multi-source data into their corresponding subspaces. Existing methods imposed various constraints on the affinity matrix and/or the cluster labels to promote segmentation accuracy, and demonstrated effectiveness in some applications. However, the previous constraints are inefficient to ensure the ideal discriminative capability of the corresponding method. In this paper, we propose to learn view-specific affinity matrices and a common cluster indicator matrix jointly in a unified minimization problem, in which the affinity matrices and the cluster indicator matrix can guide each other to facilitate the final segmentation. To enforce the ideal discrimination, we use a block diagonal inducing regularity to constrain the affinity matrices as well as the cluster indicator matrix. Such coupled regularities are double insurances to promote clustering accuracy. We call it Coupled Block Diagonal Regularized Multi-view Subspace Clustering (CBDMSC). Based on the alternative minimization method, an algorithm is proposed to solve the new model. We evaluate our method by several metrics and compare it with several state-of-the-art related methods on some commonly used datasets. The results demonstrate that our method outperforms the state-of-the-art methods in the vast majority of metrics. [ABSTRACT FROM AUTHOR]

• Semi-supervised hashing-based affinity matrix computation method is proposed for DSC. • Unsupervised extension of the HAM-DSC is proposed for unsupervised clustering cases. • HAM-DSC yields the better experimental clustering performance with lowest time cost. Dominant set clustering has been widely used to solve a variety of problems such as image segmentation, video analysis, and image retrieval. However, the key problem of it is the need of a given affinity matrix to provide similarity for every pair of data points. The affinity matrix is either user-given or computed using a pairwise computation, which is impractical for big data situations. Therefore, this work proposes a semi-supervised hashing-based affinity matrix computation method (HAM) for dominant set clustering (HAM-DSC) for cases of semi-supervised clustering where labels are available to a portion of data. The HAM computes affinity matrix efficiently based on Hamming distance between learned hash codes, which preserve semantic similarities effectively. To deal with unsupervised clustering problems, an unsupervised extension of the HAM-DSC is also given in this work. Experimental results on 7 real-world datasets show that the HAM-DSC yields an overall better performance together with lower time costs compared to dominant set clustering using other affinity matrix computation methods. [ABSTRACT FROM AUTHOR]

Iris recognition in less constrained environments is challenging as the images taken therein contain severe noisy factors. How to represent iris texture for accurate and robust recognition in such environments is still an open issue. Towards addressing this problem, this paper proposes a novel convolutional network (ConvNet) for effective iris texture representation. The key of the proposed ConvNet is an interaction block which computes an affinity matrix among all pairwise high-level features for learning second-order relationships. The interaction block can model relationships of neighboring and long-range features, and is architecture-agnostic, suitable for different deep network architectures. To further improve the robustness of iris representation, we encode the affinity matrix based on ordinal measure. In addition, we develop a mask network corresponding to the feature learning network, which can exclude the noisy factors during iris matching. We perform thorough ablation studies to evaluate the effectiveness of the proposed networks. Experiments have shown that the proposed networks outperform state-of-the-art (SOTA) methods, achieving a false reject rate (FRR) of 5.49%, 10.41% and 5.80% at 10− 6 false accept rate (FAR) on ND-IRIS-0405, CASIA-IrisV4-Thousand and CASIA-IrisV4-Lamp respectively. And the improvements in equal error rates (EERs) are 0.41%, 0.72% and 0.40%, respectively, as compared with the SOTA methods. [ABSTRACT FROM AUTHOR]

In the era of big data, there are an increasing number of multisource information data, and multi-view clustering (MVC) algorithms have developed rapidly. However, the affinity matrix learned by most MVC methods is not clean and precise enough and cannot describe the latent structure of multi-view data accurately, which results in poor clustering performance. In this paper, we propose a novel Double Structure Scaled Simplex Representation (DSSSR) method for MVC. Initially, we concatenate the multi-view data into a joint representation. Then, we use the scaled simplex representation (SSR) method on the concatenated data to obtain the affinity matrix. However, the affinity matrix is not clean and precise. Therefore, we use the SSR method again on the obtained affinity matrix to obtain a more accurate and clean affinity matrix. Furthermore, the two-step SSR is integrated into a unified optimization framework, a clean and accurate affinity matrix can be obtained, and the sum of each column vector of the affinity matrix is constrained to be nonnegative and equal to s (0 < s < 1), which can be adjusted to obtain the best clustering performance. Finally, an efficient optimization algorithm based on the augmented Lagrangian method (ALM) for solving the objective function is also designed. The experimental results on some datasets show that this algorithm has better clustering performance than some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this article, we integrate the spatial-spectral information of hyperspectral image (HSI) samples into nonnegative matrix factorization (NMF) for affinity matrix learning to address the issue of HSI clustering. This technique consists of three main components: 1) oversegmentation for computing the spectral-spatial affinity matrix; 2) NMF with the guidance of the obtained affinity matrix; and 3) density-based spectral clustering on the final affinity matrix. First, the HSI is oversegmented into superpixels via the entropy rate superpixel algorithm. The spectral-spatial affinity matrix is defined based on the class-consistency assumption of all the HSI samples in each superpixel and the similar HSI samples between adjacent superpixels. Second, to integrate the spectral-spatial information into NMF, the obtained affinity matrix is used to guide the iterative process of NMF. The spectral-spatial affinity matrix is then weighted by the affinity matrix in the obtained low-dimensional subspace to form the final affinity matrix. Third, density-based spectral clustering is applied to the final affinity matrix to obtain clustering maps. Experimental results on three public benchmark HSIs demonstrate that the proposed method is superior to the considered state-of-the-art baseline methods on both the computational cost and clustering accuracy.

Each type of cancer usually has several subtypes with distinct clinical implications, and therefore the discovery of cancer subtypes is an important and urgent task in disease diagnosis and therapy. Using single-omics data to predict cancer subtypes is difficult because genomes are dysregulated and complicated by multiple molecular mechanisms, and therefore linking cancer genomes to cancer phenotypes is not an easy task. Using multi-omics data to effectively predict cancer subtypes is an area of much interest; however, integrating multi-omics data is challenging. Here, we propose a novel method of multi-omics data integration for clustering to identify cancer subtypes (MDICC) that integrates new affinity matrix and network fusion methods. Our experimental results show the effectiveness and generalization of the proposed MDICC model in identifying cancer subtypes, and its performance was better than those of currently available state-of-the-art clustering methods. Furthermore, the survival analysis demonstrates that MDICC delivered comparable or even better results than many typical integrative methods. [ABSTRACT FROM AUTHOR]

This paper proposes a new method that detects the repeated keyword/phrase patterns from speech utterances by performing pattern discovery at the phoneme level. Prior to this method, we have developed a pattern discovery method using frame-level features. Even though the method's performance is decent, it allows a considerable number of false positives. This paper aims to extract the desired keywords by examining the match between the speech utterances at the phoneme level instead of frame level to reduce the false positives and improve the accuracy. In this work, initially, we segment the speech utterances into phoneme-like regions using an affinity matrix. Then, the matched phoneme regions present in a pair of speech utterances are identified. A new 3-neighbor depth-first search traversal technique is proposed to discover the sequence of phoneme matches. Finally, the distance scores in the sequence of phoneme matches are validated to identify the desired keyword patterns. The performance of the proposed method is evaluated on the Hindi and Bengali news databases and compared with the state-of-the-art techniques. Based on the detected keyword patterns, the speech utterances are divided into groups using a standard clustering algorithm. The derived clusters represent the broader domain-specific groups which are useful for efficient speech retrieval task. [ABSTRACT FROM AUTHOR]

The most basic and significant issue in complex network analysis is community detection, which is a branch of machine learning. Most current community detection approaches, only consider a network's topology structures, which lose the potential to use node attribute information. In attributed networks, both topological structure and node attributed are important features for community detection. In recent years, the spectral clustering algorithm has received much interest as one of the best performing algorithms in the subcategory of dimensionality reduction. This algorithm applies the eigenvalues of the affinity matrix to map data to low-dimensional space. In the present paper, a new version of the spectral cluster, named Attributed Spectral Clustering (ASC), is applied for attributed graphs that the identified communities have structural cohesiveness and attribute homogeneity. Since the performance of spectral clustering heavily depends on the goodness of the affinity matrix, the ASC algorithm will use the Topological and Attribute Random Walk Affinity Matrix (TARWAM) as a new affinity matrix to calculate the similarity between nodes. TARWAM utilizes the biased random walk to integrate network topology and attribute information. It can improve the similarity degree among the pairs of nodes in the same density region of the attributed network, without the need for parameter tuning. The proposed approach has been compared to other primary and new attributed graph clustering algorithms based on synthetic and real datasets. The experimental results show that the proposed approach is more effective and accurate compared to other state-of-the-art attributed graph clustering techniques. [ABSTRACT FROM AUTHOR]

Researchers have thought about clustering approaches that incorporate traditional clustering methods and deep learning techniques. These approaches normally boost the performance of clustering. Getting knowledge from large data-sets is quite an interesting task. In this case, we use some dimensionality reduction and clustering techniques. Spectral clustering is gaining popularity recently because of its performance. Lately, numerous techniques have been introduced to boost spectral clustering performance. One of the most significant part of these techniques is to construct a similarity graph. We introduced weighted k-nearest neighbors technique for the construction of similarity graph. Using this new metric for the construction of affinity matrix, we achieved good results as we tested it both on real and artificial data-sets.

The essential problem of multi-view spectral clustering is to learn a good common representation by effectively utilizing multi-view information. A popular strategy for improving the quality of the common representation is utilizing global and local information jointly. Most existing methods capture local manifold information by graph regularization. However, once local graphs are constructed, they do not change during the whole optimization process. This may lead to a degenerated common representation in the case of existing unreliable graphs. To address this problem, rather than directly using fixed local representations, we propose a dynamic strategy to construct a common local representation. Then, we impose a fusion term to maximize the common structure of the local and global representations so that they can boost each other in a mutually reinforcing manner. With this fusion term, we integrate local and global representation learning in a unified framework and design an alternative iteration based optimization procedure to solve it. Extensive experiments conducted on a number of benchmark datasets support the superiority of our algorithm over several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

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.

Nowadays, multi-view clustering has attracted more and more attention, which provides a way to partition multi-view data into their corresponding clusters. Previous studies assume that each data instance appears in all views. However, in real-world applications, it is common that each view may contain some missing data instances, resulting in incomplete multi-view data. To address the incomplete multi-view clustering problem, we will propose an auto-weighted incomplete multi-view clustering method in this paper, which learns a common representation of the instances and an affinity matrix of the learned representation simultaneously in a unified framework. Learning the affinity matrix of the representation guides to learn a more discriminative and compact consensus representation for clustering. Moreover, by considering the impact of the significance of different views, an adaptive weighting strategy is designed to measure the importance of each view. An efficient iterative algorithm is proposed to optimize the objective function. Experimental results on various real-world datasets show that the proposed method can improve the clustering performance in comparison with the state-of-the-art methods in most cases.

Abstract Background Identifying different types of cancer based on gene expression data has become hotspot in bioinformatics research. Clustering cancer gene expression data from multiple cancers to their own class is a significance solution. However, the characteristics of high-dimensional and small samples of gene expression data and the noise of the data make data mining and research difficult. Although there are many effective and feasible methods to deal with this problem, the possibility remains that these methods are flawed. Results In this paper, we propose the graph regularized low-rank representation under symmetric and sparse constraints (sgLRR) method in which we introduce graph regularization based on manifold learning and symmetric sparse constraints into the traditional low-rank representation (LRR). For the sgLRR method, by means of symmetric constraint and sparse constraint, the effect of raw data noise on low-rank representation is alleviated. Further, sgLRR method preserves the important intrinsic local geometrical structures of the raw data by introducing graph regularization. We apply this method to cluster multi-cancer samples based on gene expression data, which improves the clustering quality. First, the gene expression data are decomposed by sgLRR method. And, a lowest rank representation matrix is obtained, which is symmetric and sparse. Then, an affinity matrix is constructed to perform the multi-cancer sample clustering by using a spectral clustering algorithm, i.e., normalized cuts (Ncuts). Finally, the multi-cancer samples clustering is completed. Conclusions A series of comparative experiments demonstrate that the sgLRR method based on low rank representation has a great advantage and remarkable performance in the clustering of multi-cancer samples.

Hyperspectral image super-resolution by fusing high-resolution multispectral image (HR-MSI) and low-resolution hyperspectral image (LR-HSI) aims at reconstructing high resolution spatial-spectral information of the scene. Existing methods mostly based on spectral unmixing and sparse representation are often developed from a low-level vision task perspective, they cannot sufficiently make use of the spatial and spectral priors available from higher-level analysis. To this issue, this paper proposes a novel HSI super-resolution method that fully considers the spatial/spectral subspace low-rank relationships between available HR-MSI/LR-HSI and latent HSI. Specifically, it relies on a new subspace clustering method named “structured sparse low-rank representation” (SSLRR), to represent the data samples as linear combinations of the bases in a given dictionary, where the sparse structure is induced by low-rank factorization for the affinity matrix. Then we exploit the proposed SSLRR model to learn the SSLRR along spatial/spectral domain from the MSI/HSI inputs. By using the learned spatial and spectral low-rank structures, we formulate the proposed HSI super-resolution model as a variational optimization problem, which can be readily solved by the ADMM algorithm. Compared with state-of-the-art hyperspectral super-resolution methods, the proposed method shows better performance on three benchmark datasets in terms of both visual and quantitative evaluation. [ABSTRACT FROM AUTHOR]

In this article, we integrate the spatial-spectral information of hyperspectral image (HSI) samples into nonnegative matrix factorization (NMF) for affinity matrix learning to address the issue of HSI clustering. This technique consists of three main components: 1) oversegmentation for computing the spectral-spatial affinity matrix; 2) NMF with the guidance of the obtained affinity matrix; and 3) density-based spectral clustering on the final affinity matrix. First, the HSI is oversegmented into superpixels via the entropy rate superpixel algorithm. The spectral-spatial affinity matrix is defined based on the class-consistency assumption of all the HSI samples in each superpixel and the similar HSI samples between adjacent superpixels. Second, to integrate the spectral-spatial information into NMF, the obtained affinity matrix is used to guide the iterative process of NMF. The spectral-spatial affinity matrix is then weighted by the affinity matrix in the obtained low-dimensional subspace to form the final affinity matrix. Third, density-based spectral clustering is applied to the final affinity matrix to obtain clustering maps. Experimental results on three public benchmark HSIs demonstrate that the proposed method is superior to the considered state-of-the-art baseline methods on both the computational cost and clustering accuracy. [ABSTRACT FROM AUTHOR]

Multi-view clustering refers to the task of partitioning numerous unlabeled multimedia data into several distinct clusters using multiple features. In this paper, we propose a novel nonlinear method called joint learning multi-view clustering (JLMVC) to jointly learn kernel representation tensor and affinity matrix. The proposed JLMVC has three advantages: (1) unlike existing low-rank representation-based multi-view clustering methods that learn the representation tensor and affinity matrix in two separate steps, JLMVC jointly learns them both; (2) using the “kernel trick,” JLMVC can handle nonlinear data structures for various real applications; and (3) different from most existing methods that treat representations of all views equally, JLMVC automatically learns a reasonable weight for each view. Based on the alternating direction method of multipliers, an effective algorithm is designed to solve the proposed model. Extensive experiments on eight multimedia datasets demonstrate the superiority of the proposed JLMVC over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The key step of spectral clustering is learning the affinity matrix to measure the similarity among data points. This paper proposes a new spectral clustering method, which uses mutual k nearest neighbor to obtain the affinity matrix by removing the influence of noise. Then, the characteristics of high-dimensional data are self-represented to ensure local important information of data by using affinity matrix in standardized processing. Furthermore, we also use the normalization method to further improve the performance of clustering. Experimental analysis on eight benchmark data sets showed that our proposed method outperformed the state-of-the-art clustering methods in terms of clustering performance such as cluster accuracy and normalized mutual information. [ABSTRACT FROM AUTHOR]

Graph matching is an essential NP-problem in computer vision and pattern recognition. In this paper, we propose an approximate graph matching method. This method formulates the problem of computing the correspondences between two graphs as a problem of selecting nodes on an association graph. The nodes of the association graph represent candidate correspondences between the two original graphs. Our method first constructs an affinity matrix based on both the global and local information of the original graphs' nodes. Each element of this matrix is used to measure the mutual consistency of a pair of nodes within the association graph. Our method then applies the reweighted random walks technique that preserves the one-to-one matching constraint to simulate random walks on the association graph and to iteratively compute a quasi-stationary distribution. To discretize this distribution, our method finally applies the Hungarian algorithm and obtains an approximate matching between the original two graphs. Experimental results demonstrate the effectiveness of our method for graph matching and the ability of our method for being robust to outlier and deformation noise. [ABSTRACT FROM AUTHOR]

Multi-view subspace clustering aims to learn an appropriate affinity matrix to investigate the relationship between data. However, the learned affinity matrix always has limited representation ability and unclear intrinsic structure. To address the problem, we propose a novel two-step learning strategy to enhance the quality of the affinity matrix. First, we design a generalized framework to calculate the affinity matrix for each view. Unlike most subspace clustering methods that focus on constructing the coefficient matrices, the proposed framework combines the subspace-based and graph-based models to simultaneously learn the coefficient and similarity matrices under a consistency constraint. Thus, the data structure information and multiple views correlation can be captured and propagated between these matrices, which is conducive to generating an informative affinity matrix. Further, we present a post-processing technology called unified good neighbors learning to make the obtained affinity matrix have good sparsity and connectivity. Specifically, we find the good neighbors of each sample by all the views and reassign their coefficients in the final affinity matrix to reflect the essential correlation between samples. Finally, we develop an efficient optimization algorithm and provide the theoretical analyses for the proposed problem. Extensive experiments conducted on six popular multi-view datasets demonstrate the effectiveness of our method. The source code is available at https://github.com/taozhang1223/TAML. • Two-step affinity matrix learning is proposed for multi-view clustering. • The subspace and graph models are combined to capture the data structure. • The unified good neighbors learning is used to reflect the sample correlation. • The efficient algorithms and theoretical analyses are provided for our model. [ABSTRACT FROM AUTHOR]

In click-based deep interactive segmentation, click encoding and fusion with multi-scale features are vital for manipulating segmentation performance. Existing click encoding methods only incorporate position priors but lack semantics, leading to unstable interaction efficiency. Meanwhile, in order to fuse multi-scale features, current methods extract these features at the abstract semantic level but neglect the constraints imposed by detailed information on semantic features. This oversight makes the network prone to over-segmentation. To address these challenges, we propose a cross-self attention guided by semantic click embedding for interactive segmentation. First, we build semantic click embeddings from the semantic features by embedding positive clicks into continuous connected semantic regions while preserving the role of correction for negative clicks. This enriches the semantic priors for appropriate clicks. Next, we utilize the self-attention mechanism to leverage both detailed and semantic features of the network, constructing a cross-attention mechanism that suppresses the over-segmentation phenomenon. Finally, the semantic click embedding is utilized to weight the affinity matrix of the attention mechanism, ensuring that long-distance dependencies are only relevant to the target of interest. Comprehensive experiments prove that our approach improves interaction efficiency and achieves state-of-the-art performance on public datasets. [ABSTRACT FROM AUTHOR]

Most existing clustering methods employ the original multi-view data as input to learn the similarity matrix which characterizes the underlying cluster structure shared by multiple views. This reduces the flexibility of multi-view clustering methods due to the fact that multi-view data usually contains noise or the variation between multi-view data points, which should belong to the same cluster, is larger than the variation between data points belonging to different clusters. To address these problems, we propose a novel multi-view clustering model, namely adaptive latent similarity learning (ALSL) for multi-view clustering. ALSL employs the adaptively learned graph, which characterizes the relationship between clusters, as the new input to learn the latent data representation and integrates the latent similarity representation learning, manifold learning and spectral clustering into a unified framework. With the complementarity of multiple views, the latent similarity representation characterizes the underlying cluster structure shared by multiple views. Our model is intuitive and can be optimized efficiently by using the Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) algorithm. Extensive experiments on benchmark datasets have demonstrated the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Background: Identifying different types of cancer based on gene expression data has become hotspot in bioinformatics research. Clustering cancer gene expression data from multiple cancers to their own class is a significance solution. However, the characteristics of high-dimensional and small samples of gene expression data and the noise of the data make data mining and research difficult. Although there are many effective and feasible methods to deal with this problem, the possibility remains that these methods are flawed. Results: In this paper, we propose the graph regularized low-rank representation under symmetric and sparse constraints (sgLRR) method in which we introduce graph regularization based on manifold learning and symmetric sparse constraints into the traditional low-rank representation (LRR). For the sgLRR method, by means of symmetric constraint and sparse constraint, the effect of raw data noise on low-rank representation is alleviated. Further, sgLRR method preserves the important intrinsic local geometrical structures of the raw data by introducing graph regularization. We apply this method to cluster multi-cancer samples based on gene expression data, which improves the clustering quality. First, the gene expression data are decomposed by sgLRR method. And, a lowest rank representation matrix is obtained, which is symmetric and sparse. Then, an affinity matrix is constructed to perform the multi-cancer sample clustering by using a spectral clustering algorithm, i.e., normalized cuts (Ncuts). Finally, the multi-cancer samples clustering is completed. Conclusions: A series of comparative experiments demonstrate that the sgLRR method based on low rank representation has a great advantage and remarkable performance in the clustering of multi-cancer samples. [ABSTRACT FROM AUTHOR]

Change detection (CD) in heterogeneous multitemporal satellite images is an emerging and challenging topic in remote sensing. In particular, one of the main challenges is to tackle the problem in an unsupervised manner. In this paper, we propose an unsupervised framework for bitemporal heterogeneous CD based on the comparison of affinity matrices and image regression. First, our method quantifies the similarity of affinity matrices computed from colocated image patches in the two images. This is done to automatically identify pixels that are likely to be unchanged. With the identified pixels as pseudotraining data, we learn a transformation to map the first image to the domain of the other image and vice versa. Four regression methods are selected to carry out the transformation: Gaussian process regression, support vector regression, random forest regression (RFR), and a recently proposed kernel regression method called homogeneous pixel transformation. To evaluate the potentials and limitations of our framework and also the benefits and disadvantages of each regression method, we perform experiments on two real data sets. The results indicate that the comparison of the affinity matrices can already be considered a CD method by itself. However, image regression is shown to improve the results obtained by the previous step alone and produces accurate CD maps despite of the heterogeneity of the multitemporal input data. Notably, the RFR approach excels by achieving similar accuracy as the other methods, but with a significantly lower computational cost and with fast and robust tuning of hyperparameters. [ABSTRACT FROM AUTHOR]

Previous multi-view spectral clustering methods are a two-step strategy, which first learns a fixed common representation (or common affinity matrix) of all the views from original data and then conducts k-means clustering on the resulting common affinity matrix. The two-step strategy is not able to output reasonable clustering performance since the goal of the first step (i.e., the common affinity matrix learning) is not designed for achieving the optimal clustering result. Moreover, the two-step strategy learns the common affinity matrix from original data, which often contain noise and redundancy to influence the quality of the common affinity matrix. To address these issues, in this paper, we design a novel One-step Multi-view Spectral Clustering (OMSC) method to output the common affinity matrix as the final clustering result. In the proposed method, the goal of the common affinity matrix learning is designed to achieving optimal clustering result and the common affinity matrix is learned from low-dimensional data where the noise and redundancy of original high-dimensional data have been removed. We further propose an iterative optimization method to fast solve the proposed objective function. Experimental results on both synthetic datasets and public datasets validated the effectiveness of our proposed method, comparing to the state-of-the-art methods for multi-view clustering. [ABSTRACT FROM AUTHOR]

Traditional graph clustering methods consist of two sequential steps, i.e., constructing an affinity matrix from the original data and then performing spectral clustering on the resulting affinity matrix. This two-step strategy achieves optimal solution for each step separately, but cannot guarantee that it will obtain the globally optimal clustering results. Moreover, the affinity matrix directly learned from the original data will seriously affect the clustering performance, since high-dimensional data are usually noisy and may contain redundancy. To address the above issues, this paper proposes a Low-rank Sparse Subspace (LSS) clustering method via dynamically learning the affinity matrix from low-dimensional space of the original data. Specifically, we learn a transformation matrix to project the original data to their low-dimensional space, by conducting feature selection and subspace learning in the sample self-representation framework. Then, we utilize the rank constraint and the affinity matrix directly obtained from the original data to construct a dynamic and intrinsic affinity matrix. Moreover, each of these three matrices is updated iteratively while fixing the other two. In this way, the affinity matrix learned from the low-dimensional space is the final clustering results. Extensive experiments are conducted on both synthetic and real datasets to show that our proposed LSS method outperforms the state-of-the-art clustering methods. [ABSTRACT FROM AUTHOR]

The image segmentation technique is a vital component of vision-based fruit harvesting robots because the accuracy of this technique greatly affects the recognition and identification by robots. However, the uncertainty and ambiguity of natural scenes in orchards make image segmentation a challenging task. Here, we developed a new algorithm to detect and remove the shadows generated under intense illumination and direct sunlight conditions. Group pixels and edge probability maps were fused in our algorithm to generate superpixel blocks with precise boundaries. We applied an affinity matrix to obtain an ultrametric contour map to detect shadows and then used a relighting method to remove the detected shadows. Additionally, the shadow detection and removal and image segmentation procedures were evaluated. Our shadow detection results showed that the root mean square error decreased from 7.9% to 6.4% when an edge probability map was applied. Using the new shadow removal algorithm, the precision, balanced accuracy, specificity, and modified segmentation accuracy were improved by 10, 11, 4.5, and 10.1%, respectively. The average segmentation processing time was 0.59 s, which meets the requirements of real-time applications (

Abstract Cancer samples clustering based on biomolecular data has been becoming an important tool for cancer classification. The recognition of cancer types is of great importance for cancer treatment. In this paper, in order to improve the accuracy of cancer recognition, we propose to use Laplacian regularized Low-Rank Representation (LLRR) to cluster the cancer samples based on genomic data. In LLRR method, the high-dimensional genomic data are approximately treated as samples extracted from a combination of several low-rank subspaces. The purpose of LLRR method is to seek the lowest-rank representation matrix based on a dictionary. Because a Laplacian regularization based on manifold is introduced into LLRR, compared to the Low-Rank Representation (LRR) method, besides capturing the global geometric structure, LLRR can capture the intrinsic local structure of high-dimensional observation data well. And what is more, in LLRR, the original data themselves are selected as a dictionary, so the lowest-rank representation is actually a similar expression between the samples. Therefore, corresponding to the low-rank representation matrix, the samples with high similarity are considered to come from the same subspace and are grouped into a class. The experiment results on real genomic data illustrate that LLRR method, compared with LRR and MLLRR, is more robust to noise and has a better ability to learn the inherent subspace structure of data, and achieves remarkable performance in the clustering of cancer samples. [ABSTRACT FROM AUTHOR]

In recent years, graph based subspace clustering has attracted considerable attentions in computer vision, as its capability of clustering data efficiently. However, the graph weights built by using representation coefficients are not the exact ones as the traditional definition. That is, the two steps are conducted in independent manner such that an overall optimal result cannot be guaranteed. To this end, in this paper, a novel subspace clustering via learning an adaptive graph affinity matrix is proposed, where the soft label and the representation coefficients of data are learned in an unified framework. First, the proposed method learns a robust representation for the data through least square regression, which reveals the subspace structure within data and captures various noises inside. Second, the segmentation is sought by conducting spectral clustering simultaneously. Most importantly, during the optimization process, the segmentation is utilized to iteratively enhance the block-diagonal structure of the learned representation to further assist the clustering process. Experimental results on several famous databases demonstrate that the proposed method performs better against the state-of-the-art approaches, in clustering. [ABSTRACT FROM AUTHOR]

In this letter, we propose a novel low-rank-represen-tation (LRR) based manifold-regularization approach for zero-shot learning (ZSL). Most existing regularization-based ZSL approaches perform the alignment between visual feature space and semantic space based on the affinity matrix constructed from the test instances. The affinity matrix plays a significant role in exploiting the manifold structures of visual feature space, hence we propose to use the LRR to guide the affinity-matrix construction by exploring the subspace structures of data. Considering the locality and similarity information among data, we incorporate a Laplacian regularization term to the LRR framework to ensure that the learned affinity matrix can capture the local geometric structures in data. We also explicitly impose the nonnegative sparse constraint on the affinity matrix to facilitate the learning of local manifold structures. Moreover, we use an effective manifold-regularization methodology to learn discriminative semantic representations of test instances, leading to significant improvements in classification performance over the unseen classes. Extensive experiments on three benchmark datasets demonstrate that the proposed approach outperforms the state of the arts. [ABSTRACT FROM AUTHOR]

Saliency detection is an essential pre-processing step for intensifying image objects in many computer vision fields. Other than most bottom-up methods, in this paper, we propose a novel saliency model based on high-level image edges and low-level feature contrast. Edges are inherent features for an image, and it can locate the object via a salient selection. With this theory, an accurate object contour is generated after two salient discriminations for edge-contiguous superpixel couples. After position is confirmed, foreground and background of the image can be divided by the contour. With an ingrowth model, we then obtain a foreground (or background) seeds referencing spatial adjacent relation. According to the seed set, a homologous saliency map is computed via a seed-based saliency approach, which is proposed on the basis of affinity matrix. Compared with some pre-existing algorithms, low-level information is utilized purposefully by salient edges in the presented method, which makes the extracted fore regions more precise. [ABSTRACT FROM AUTHOR]

Subspace clustering (SC) methods have attracted widespread attention from interested researchers, and a variety of SC methods have been proposed recently. In general, SC methods obtain an affinity matrix, on which spectral clustering is used. Obviously, affinity matrices obtained by different algorithms are not the same, and their clustering effects are also different. A question then arises of whether the affinity matrices obtained by different algorithms can be merged to improve the clustering performance. The answer may be yes I n this paper, we design a new SC method, i.e., robust subspace clustering via multi-affinity matrices fusion (RSC/MAMF). Specifically, several classical SC algorithms, i.e., sparse subspace clustering (SSC), low-rank representation (LRR) and least squares regression (LSR), are first chosen to derive their own affinity matrices. To make full use of the information of different affinity matrices, and to mine the subspace structure thoroughly, we further fuse the derived affinity matrices, i.e., splice them into a 3-order tensor, and impose a weighted tensor nuclear norm (WTNN) to it, which not only mines and fuses the information of the different affinity matrices but also removes their noise. Additionally, to further explore the consistency of the different affinity matrices, spectral embedding is also unified into the final objective function. We propose an optimization algorithm to address the optimization problem of RSC/MAMF, which utilizes the Augmented Lagrange Multiplier (ALM) method. Experiments show that the multi-affinity matrices fusion idea is feasible, and RSC/MAMF outperforms the state-of-the-art SC methods. [ABSTRACT FROM AUTHOR]

This paper proposes a new subspace clustering method based on sparse sample self-representation (SSR). The proposed method considers SSR to solve the problem that affinity matrix does not strictly follow the structure of subspace, and also utilizes sparse constraint to ensure the robustness to noise and outliers in subspace clustering. Specifically, we propose to first construct a self-representation matrix for all samples and combine an l -norm regularizer with an l -norm regularizer to guarantee that each sample can be represented as a sparse linear combination of its related samples. Then, we conduct the resulting matrix to build an affinity matrix. Finally, we apply spectral clustering on the affinity matrix to conduct clustering. In order to validate the effectiveness of the proposed method, we conducted experiments on UCI datasets, and the experimental results showed that our proposed method reduced the minimal clustering error, outperforming the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Traditional subspace clustering methods [such as sparse subspace clustering (SSC), least squares representation (LSR) and smooth representation clustering] either considered the grouping effect or the sparsity to group original data into clusters. This paper demonstrates the necessary of both the grouping effect and the sparsity for conducting subspace clustering, by proposing a new Self-Representation and Subspace Clustering based on Grouping Effect ( SRGE) method. Specifically, first of all, a row sparse $$\ell_{2,1}$$ -norm regularizer is utilized to represent each sample by other samples. Then, the grouping effect of the data is designed to ensure that the coefficient of close samples is similar, aiming at generating a diagonal block self-representation coefficient matrix. Finally, an affinity matrix is obtained for conducting spectral clustering. The proposed method can be regarded as a trade-off between SSC and LSR. The experimental results of segmentation on real datasets showed that the proposed method significantly outperformed the state-of-the-art methods in terms of all kinds of evaluation metrics. [ABSTRACT FROM AUTHOR]

Discovery of new protease inhibitors may result in potential therapeutic agents or useful biotechnological tools. Obtainment of these molecules from natural sources requires simple, economic, and highly efficient purification protocols. The aim of this work was the obtainment of affinity matrices by the covalent immobilization of dipeptidyl peptidase IV (DPP-IV) and papain onto cellulose membranes, previously activated with formyl (FCM) or glyoxyl groups (GCM). GCM showed the highest activation grade (10.2 µmol aldehyde/cm2). We implemented our strategy for the rational design of immobilized derivatives (RDID) to optimize the immobilization. pH 9.0 was the optimum for the immobilization through the terminal α-NH2, configuration predicted as catalytically competent. However, our data suggest that protein immobilization may occur via clusters of few reactive groups. DPP-IV−GCM showed the highest maximal immobilized protein load (2.1 µg/cm2), immobilization percentage (91%), and probability of multipoint covalent attachment. The four enzyme-support systems were able to bind at least 80% of the reversible competitive inhibitors bacitracin/cystatin, compared with the available active sites in the immobilized derivatives. Our results show the potentialities of the synthesized matrices for affinity purification of protease inhibitors and confirm the robustness of the RDID strategy to optimize protein immobilization processes with further practical applications. [ABSTRACT FROM AUTHOR]

P-wave time picking is of great significance in microseismic data processing. However, traditional time picking methods do not consider the difference of low-dimensional manifold features between signal and noise which can be extracted more effectively in low signal to noise ratio scenarios. In this letter, we develop a new method named spectral multimanifold clustering for picking P-wave arrivals. It can extract the low-dimensional manifold features from a suitable affinity matrix. In this approach, the manifold features of data are concentrated by residual statics estimation and a suitable affinity matrix is constructed using structural similarity and local similarity. Then, by using unnormalized spectral clustering, the low-dimensional manifold features extracted from the affinity matrix can be classified into noise cluster and signal cluster. Finally, the initial time of the signal cluster is considered to be the first arrival time in microseismic data. We design a series of experiments using both synthetic and field microseismic data. Our proposed method demonstrates higher accuracy, better stability, and noise immunity than either the short and long time average method or the akaike information criterion method. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new framework for hierarchical image segmentation based on iterative contraction and merging. In the proposed framework, we treat the hierarchical image segmentation problem as a sequel of optimization problems, with each optimization process being realized by a contraction-and-merging process to identify and merge the most similar data pairs at the current resolution. At the beginning, we perform pixel-based contraction and merging to quickly combine image pixels into initial region-elements with visually indistinguishable intra-region color difference. After that, we iteratively perform region-based contraction and merging to group adjacent regions into larger ones to progressively form a segmentation dendrogram for hierarchical segmentation. Comparing with the state-of-the-art techniques, the proposed algorithm can not only produce high-quality segmentation results in a more efficient way, but also keep a lot of boundary details in the segmentation results. [ABSTRACT FROM PUBLISHER]

In this paper, we address the spectral clustering problem by effectively constructing an affinity matrix with a large EigenGap . Although the faultless Block-Diagonal structure is highly in demand for accurate spectral clustering, the relaxed Block-Diagonal affinity matrix with a large EigenGap is more effective and easier to obtain. A global EigenGap scheme is proposed by utilizing the Fractional Eigenvalues Sum (FEVS) penalty of maximizing top eigenvalues and minimizing the residual. The closed-form solution of the FEVS term and the proximity term is also presented. We then propose a Global-Local Affinity Matrix model that integrates the global EigenGap with local pairwise distance measure for graph construction. Furthermore, we also combine the state-of-the-art subspace recovery methods such as LRR and RSIM with our proposed model to learn an effective affinity matrix for high dimensional data. To the best of our knowledge, this is the first research that attempts to pursue such a relaxed Block-Diagonal structure with a large EigenGap . Extensive experiments on face clustering and motion segmentation clearly demonstrate the significant advantages of the novel methods. [ABSTRACT FROM AUTHOR]

In sparse subspace clustreing (SSC), non‐zero coefficients in the sparse representations are transformed to positive values to construct the affinity matrix. However, negative coefficients are not supposed to cause positive correlation in nature, so that the clustering performance may be undermined. In this Letter, non‐negative SSC by orthogonal matching pursuit (nSSCOMP) with a negative re‐purpose module is introduced for a reasonable clustering graph to improve the clustering performance, also an assemble negatives of negatives algorithm is proposed to strengthen the effectiveness of affinity matrix. The analysis indicates that the authors' approach can make the coefficient matrix contains only non‐negative values and bring additional positive correlations. Their approach is the first to process negative values after sparse representations are already calculated, without specify non‐negativity constraints beforehand. Experimental results demonstrate with the nSSCOMP not only the clustering accuracy and subspace‐preserving property can be improved, but also time complexity be kept. [ABSTRACT FROM AUTHOR]