Deep Subspace Clustering

Uniform Tensor Clustering by Jointly Exploring Sample Affinities of Various Orders

Traditional clustering methods rely on pairwise affinity to divide samples into different subgroups. However, high-dimensional small-sample (HDLSS) data are affected by the concentration effects, rendering traditional pairwise metrics unable to accurately describe relationships between samples, leading to suboptimal clustering results. This article advances the proposition of employing high-order affinities to characterize multiple sample relationships as a strategic means to circumnavigate the concentration effects. We establish a nexus between different order affinities by constructing specialized decomposable high-order affinities, thereby formulating a uniform mathematical framework. Building upon this insight, a novel clustering method named uniform tensor clustering (UTC) is proposed, which learns a consensus low-dimensional embedding for clustering by the synergistic exploitation of multiple-order affinities. Extensive experiments on synthetic and real-world datasets demonstrate two findings: 1) high-order affinities are better suited for characterizing sample relationships in complex data and 2) reasonable use of different order affinities can enhance clustering effectiveness, especially in handling high-dimensional data.

Novel Dual-Constraint-Based Semi-Supervised Deep Clustering Approach

Semi-supervised clustering can be viewed as a clustering paradigm that exploits both labeled and unlabeled data to steer learning accurate data clusters and avoid local minimum solutions. Nonetheless, the attempts to refine existing semi-supervised clustering methods are relatively limited when compared to the advancements witnessed in the current benchmark methods in fully unsupervised clustering. This research introduces a novel semi-supervised method for deep clustering that leverages deep neural networks and fuzzy memberships to better capture the data partitions. In particular, the proposed Dual-Constraint-based Semi-Supervised Deep Clustering (DC-SSDEC) method utilizes two sets of pairwise soft constraints; "should-link" and "shouldNot-link", to guide the clustering process. The intended clustering task is expressed as an optimization of a newly designed objective function. Additionally, DC-SSDEC performance was evaluated through comprehensive experiments using three real-world and benchmark datasets. Moreover, a comparison with related state-of-the-art clustering techniques was conducted to showcase the DC-SSDEC outperformance. In particular, DC-SSDEC significance consists of the proposed dual-constraint formulation and its integration into a novel objective function. This contribution yielded an improvement in the resulting clustering performance compared to relevant state-of-the-art approaches. In addition, the assessment of the proposed model using real-world datasets represents another contribution of this research. In fact, increases of 3.25%, 1.44%, and 1.82% in the clustering accuracy were gained by DC-SSDEC over the best performing single-constraint-based approach, using MNIST, STL-10, and USPS datasets, respectively.

Reweighted Subspace Clustering Guided by Local and Global Structure Preservation

Subspace clustering has attracted significant interest for its capacity to partition high-dimensional data into multiple subspaces. The current approaches to subspace clustering predominantly revolve around two key aspects: 1) the construction of an effective similarity matrix and 2) the pursuit of sparsity within the projection matrix. However, assessing whether the dimensionality of the projected subspace is the true dimensionality of the data is challenging. Therefore, the clustering performance may decrease when dealing with scenarios such as subspace overlap, insufficient projected dimensions, data noise, etc., since the defined dimensionality of the projected lower-dimensional space may deviate significantly from its true value. In this research, we introduce a novel reweighting strategy, which is applied to projected coordinates for the first time and propose a reweighted subspace clustering model guided by the preservation of the both local and global structural characteristics (RWSC). The projected subspaces are reweighted to augment or suppress the importance of different coordinates, so that data with overlapping subspaces can be better distinguished and the redundant coordinates produced by the predefined number of projected dimensions can be further removed. By introducing reweighting strategies, the bias caused by imprecise dimensionalities in subspace clustering can be alleviated. Moreover, global scatter structure preservation and adaptive local structure learning are integrated into the proposed model, which helps RWSC capture more intrinsic structures and its robustness and applicability can then be improved. Through rigorous experiments on both synthetic and real-world datasets, the effectiveness and superiority of RWSC are empirically verified.

GRESS: Grouping Belief-Based Deep Contrastive Subspace Clustering

The self-expressive coefficient plays a crucial role in the self-expressiveness-based subspace clustering method. To enhance the precision of the self-expressive coefficient, we propose a novel deep subspace clustering method, named grouping belief-based deep contrastive subspace clustering (GRESS), which integrates the clustering information and higher-order relationship into the coefficient matrix. Specifically, we develop a deep contrastive subspace clustering module to enhance the learning of both self-expressive coefficients and cluster representations simultaneously. This approach enables the derivation of relatively noiseless self-expressive similarities and cluster-based similarities. To enable interaction between these two types of similarities, we propose a unique grouping belief-based affinity refinement module. This module leverages grouping belief to uncover the higher-order relationships within the similarity matrix, and integrates the well-designed noisy similarity suppression and similarity increment regularization to eliminate redundant connections while complete absent information. Extensive experimental results on four benchmark datasets validate the superiority of our proposed method GRESS over several state-of-the-art methods.

Co-Clustering by Directly Solving Bipartite Spectral Graph Partitioning

Bipartite spectral graph partitioning (BSGP) method as a co-clustering method, has been widely used in document clustering, which simultaneously clusters documents and words by making full use of the duality between documents and words. It consists of two steps: 1) graph construction and 2) singular value decomposition on the bipartite graph to compute a continuous cluster assignment matrix, followed by post-processing to get the discrete solution. However, the generated graph is unstructured and fixed. It heavily relies on the quality of the graph construction. Moreover, the two-stage process may deviate from directly solving the primal problem. In order to tackle these defects, a novel bipartite graph partitioning method is proposed to learn a bipartite graph with exactly c connected components (c is the number of clusters), which can obtain clustering results directly. Furthermore, it is experimentally and theoretically proved that the solution of the proposed model is the discrete solution of the primal BSGP problem for a special situation. Experimental results on synthetic and real-world datasets exhibit the superiority of the proposed method.

Iterative Deep Structural Graph Contrast Clustering for Multiview Raw Data

Multiview clustering has attracted increasing attention to automatically divide instances into various groups without manual annotations. Traditional shadow methods discover the internal structure of data, while deep multiview clustering (DMVC) utilizes neural networks with clustering-friendly data embeddings. Although both of them achieve impressive performance in practical applications, we find that the former heavily relies on the quality of raw features, while the latter ignores the structure information of data. To address the above issue, we propose a novel method termed iterative deep structural graph contrast clustering (IDSGCC) for multiview raw data consisting of topology learning (TL), representation learning (RL), and graph structure contrastive learning to achieve better performance. The TL module aims to obtain a structured global graph with constraint structural information and then guides the RL to preserve the structural information. In the RL module, graph convolutional network (GCN) takes the global structural graph and raw features as inputs to aggregate the samples of the same cluster and keep the samples of different clusters away. Unlike previous methods performing contrastive learning at the representation level of the samples, in the graph contrastive learning module, we conduct contrastive learning at the graph structure level by imposing a regularization term on the similarity matrix. The credible neighbors of the samples are constructed as positive pairs through the credible graph, and other samples are constructed as negative pairs. The three modules promote each other and finally obtain clustering-friendly embedding. Also, we set up an iterative update mechanism to update the topology to obtain a more credible topology. Impressive clustering results are obtained through the iterative mechanism. Comparative experiments on eight multiview datasets show that our model outperforms the state-of-the-art traditional and deep clustering competitors.

Semisupervised Progressive Representation Learning for Deep Multiview Clustering

Multiview clustering has become a research hotspot in recent years due to its excellent capability of heterogeneous data fusion. Although a great deal of related works has appeared one after another, most of them generally overlook the potentials of prior knowledge utilization and progressive sample learning, resulting in unsatisfactory clustering performance in real-world applications. To deal with the aforementioned drawbacks, in this article, we propose a semisupervised progressive representation learning approach for deep multiview clustering (namely, SPDMC). Specifically, to make full use of the discriminative information contained in prior knowledge, we design a flexible and unified regularization, which models the sample pairwise relationship by enforcing the learned view-specific representation of must-link (ML) samples (cannot-link (CL) samples) to be similar (dissimilar) with cosine similarity. Moreover, we introduce the self-paced learning (SPL) paradigm and take good care of two characteristics in terms of both complexity and diversity when progressively learning multiview representations, such that the complementarity across multiple views can be squeezed thoroughly. Through comprehensive experiments on eight widely used image datasets, we prove that the proposed approach can perform better than the state-of-the-art opponents.

Double-Structured Sparsity Guided Flexible Embedding Learning for Unsupervised Feature Selection

In this article, we propose a novel unsupervised feature selection model combined with clustering, named double-structured sparsity guided flexible embedding learning (DSFEL) for unsupervised feature selection. DSFEL includes a module for learning a block-diagonal structural sparse graph that represents the clustering structure and another module for learning a completely row-sparse projection matrix using the l2,0 -norm constraint to select distinctive features. Compared with the commonly used l2,1 -norm regularization term, the l2,0 -norm constraint can avoid the drawbacks of sparsity limitation and parameter tuning. The optimization of the l2,0 -norm constraint problem, which is a nonconvex and nonsmooth problem, is a formidable challenge, and previous optimization algorithms have only been able to provide approximate solutions. In order to address this issue, this article proposes an efficient optimization strategy that yields a closed-form solution. Eventually, through comprehensive experimentation on nine real-world datasets, it is demonstrated that the proposed method outperforms existing state-of-the-art unsupervised feature selection methods.

A parameter free relative density based biclustering method for identifying non-linear feature relations

The existing biclustering algorithms often depend on assumptions like monotonicity or linearity of feature relations for finding biclusters. Though a few algorithms overcome this problem using density-based methods, they tend to miss out many biclusters because they use global criteria for identifying dense regions. The proposed method, PF-RelDenBi, uses local variations in marginal and joint densities for each pair of features to find the subset of observations, forming the basis of the relation between them. It then finds the set of features connected by a common set of observations using a non-linear feature relation index, resulting in a bicluster. This approach allows us to find biclusters based on feature relations, even if the relations are non-linear or non-monotonous. Additionally, the proposed method does not require the user to provide any parameters, allowing its application to datasets from different domains. To study the behaviour of PF-RelDenBi on datasets with different properties, experiments were carried out on sixteen simulated datasets and the performance has been compared with eleven state-of-the-art algorithms. The proposed method is seen to produce better results for most of the simulated datasets. Experiments were conducted with five benchmark datasets and biclusters were detected using PF-RelDenBi. For the first two datasets, the detected biclusters were used to generate additional features that improved classification performance. For the other three datasets, the performance of PF-RelDenBi was compared with the eleven state-of-the-art methods in terms of accuracy, NMI and ARI. The proposed method is seen to detect biclusters with greater accuracy. The proposed technique has also been applied to the COVID-19 dataset to identify some demographic features that are likely to affect the spread of COVID-19.

Typicality-Aware Adaptive Similarity Matrix for Unsupervised Learning

Graph-based clustering approaches, especially the family of spectral clustering, have been widely used in machine learning areas. The alternatives usually engage a similarity matrix that is constructed in advance or learned from a probabilistic perspective. However, unreasonable similarity matrix construction inevitably leads to performance degradation, and the sum-to-one probability constraints may make the approaches sensitive to noisy scenarios. To address these issues, the notion of typicality-aware adaptive similarity matrix learning is presented in this study. The typicality (possibility) rather than the probability of each sample being a neighbor of other samples is measured and adaptively learned. By introducing a robust balance term, the similarity between any pairs of samples is only related to the distance between them, yet it is not affected by other samples. Therefore, the impact caused by the noisy data or outliers can be alleviated, and meanwhile, the neighborhood structures can be well captured according to the joint distance between samples and their spectral embeddings. Moreover, the generated similarity matrix has block diagonal properties that are beneficial to correct clustering. Interestingly, the results optimized by the typicality-aware adaptive similarity matrix learning share the common essence with the Gaussian kernel function, and the latter can be directly derived from the former. Extensive experiments on synthetic and well-known benchmark datasets demonstrate the superiority of the proposed idea when comparing with some state-of-the-art methods.

Fine-Grained Essential Tensor Learning for Robust Multi-View Spectral Clustering

Multi-view subspace clustering (MVSC) has drawn significant attention in recent study. In this paper, we propose a novel approach to MVSC. First, the new method is capable of preserving high-order neighbor information of the data, which provides essential and complicated underlying relationships of the data that is not straightforwardly preserved by the first-order neighbors. Second, we design log-based nonconvex approximations to both tensor rank and tensor sparsity, which are effective and more accurate than the convex approximations. For the associated shrinkage problems, we provide elegant theoretical results for the closed-form solutions, for which the convergence is guaranteed by theoretical analysis. Moreover, the new approximations have some interesting properties of shrinkage effects, which are guaranteed by elegant theoretical results. Extensive experimental results confirm the effectiveness of the proposed method.

Parallelly Adaptive Graph Convolutional Clustering Model

Benefiting from exploiting the data topological structure, graph convolutional network (GCN) has made considerable improvements in processing clustering tasks. The performance of GCN significantly relies on the quality of the pretrained graph, while the graph structures are often corrupted by noise or outliers. To overcome this problem, we replace the pre-trained and fixed graph in GCN by the adaptive graph learned from the data. In this article, we propose a novel end-to-end parallelly adaptive graph convolutional clustering (AGCC) model with two pathway networks. In the first pathway, an adaptive graph convolutional (AGC) module alternatively updates the graph structure and the data representation layer by layer. The updated graph can better reflect the data relationship than the fixed graph. In the second pathway, the auto-encoder (AE) module aims to extract the latent data features. To effectively connect the AGC and AE modules, we creatively propose an attention-mechanism-based fusion (AMF) module to weight and fuse the data representations of the two modules, and transfer them to the AGC module. This simultaneously avoids the over-smoothing problem of GCN. Experimental results on six public datasets show that the effectiveness of the proposed AGCC compared with multiple state-of-the-art deep clustering methods. The code is available at https://github.com/HeXiax/AGCC.

Multiview Subspace Clustering With Multilevel Representations and Adversarial Regularization

Multiview subspace clustering has turned into a promising technique due to its encouraging ability to discover the underlying subspace structure. In recent studies, a lot of subspace clustering methods have been developed to strengthen the clustering performance of multiview data, but these methods rarely consider simultaneously the nonlinear structure and multilevel representation (MLR) information in multiview data as well as the data distribution of latent representation. To address these problems, we develop a new Multiview Subspace Clustering with MLRs and Adversarial Regularization (MvSC-MRAR), where multiple deep auto-encoders are utilized to model nonlinear structure information of multiview data, multiple self-expressive layers are introduced into each deep auto-encoder to extract multilevel latent representations of each view data, and diversity regularizations are designed to preserve complementary information contained in different layers and different views. Furthermore, a universal discriminator based on adversarial training is developed to enforce the output of each encoder to obey a given prior distribution, so that the affinity matrix for spectral clustering (SPC) is more realistic. Comprehensive empirical evaluation with nine real-world multiview datasets indicates that our proposed MvSC-MRAR achieves significant improvements than several state-of-the-art methods in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

Convex Subspace Clustering by Adaptive Block Diagonal Representation

Subspace clustering is a class of extensively studied clustering methods where the spectral-type approaches are its important subclass. Its key first step is to desire learning a representation coefficient matrix with block diagonal structure. To realize this step, many methods were successively proposed by imposing different structure priors on the coefficient matrix. These impositions can be roughly divided into two categories, i.e., indirect and direct. The former introduces the priors such as sparsity and low rankness to indirectly or implicitly learn the block diagonal structure. However, the desired block diagonalty cannot necessarily be guaranteed for noisy data. While the latter directly or explicitly imposes the block diagonal structure prior such as block diagonal representation (BDR) to ensure so-desired block diagonalty even if the data is noisy but at the expense of losing the convexity that the former's objective possesses. For compensating their respective shortcomings, in this article, we follow the direct line to propose adaptive BDR (ABDR) which explicitly pursues block diagonalty without sacrificing the convexity of the indirect one. Specifically, inspired by Convex BiClustering, ABDR coercively fuses both columns and rows of the coefficient matrix via a specially designed convex regularizer, thus naturally enjoying their merits and adaptively obtaining the number of blocks. Finally, experimental results on synthetic and real benchmarks demonstrate the superiority of ABDR to the state-of-the-arts (SOTAs).

Contrastive self-representation learning for data clustering

This paper is concerned with self-representation subspace learning. It is one of the most representative subspace techniques, which has attracted considerable attention for clustering due to its good performance. Among these methods, low-rank representation (LRR) has achieved impressive results for subspace clustering. However, it only considers the similarity between the data itself, while neglecting the differences with other samples. Besides, it cannot well deal with noise and portray cluster-to-cluster relationships well. To solve these problems, we propose a Contrastive Self-representation model for Clustering (CSC). CSC simultaneously takes into account the similarity/dissimilarity between positive/negative pairs when learning the self-representation coefficient matrix of data while the form of the loss function can reduce the effect of noise on the results. Moreover, We use the ℓ1,2-norm regularizer on the coefficient matrix to achieve its sparsity to better characterize the cluster structure. Thus, the learned self-representation coefficient matrix well encodes both the discriminative information and cluster structure. Extensive experiments on seven benchmark databases indicate the superiority of our proposed method.

Robust Discriminant Subspace Clustering With Adaptive Local Structure Embedding

Unsupervised dimension reduction and clustering are frequently used as two separate steps to conduct clustering tasks in subspace. However, the two-step clustering methods may not necessarily reflect the cluster structure in the subspace. In addition, the existing subspace clustering methods do not consider the relationship between the low-dimensional representation and local structure in the input space. To address the above issues, we propose a robust discriminant subspace (RDS) clustering model with adaptive local structure embedding. Specifically, unlike the existing methods which incorporate dimension reduction and clustering via regularizer, thereby introducing extra parameters, RDS first integrates them into a unified matrix factorization (MF) model through theoretical proof. Furthermore, a similarity graph is constructed to learn the local structure. A constraint is imposed on the graph to guarantee that it has the same connected components with low-dimensional representation. In this spirit, the similarity graph serves as a tradeoff that adaptively balances the learning process between the low-dimensional space and the original space. Finally, RDS adopts the l_2,1 -norm to measure the residual error, which enhances the robustness to noise. Using the property of the l_2,1 -norm, RDS can be optimized efficiently without introducing more penalty terms. Experimental results on real-world benchmark datasets show that RDS can provide more interpretable clustering results and also outperform other state-of-the-art alternatives.

Self-Constrained Spectral Clustering

As a leading graph clustering technique, spectral clustering is one of the most widely used clustering methods to capture complex clusters in data. Some additional prior information can help it to further reduce the difference between its clustering results and users' expectations. However, it is hard to get the prior information under unsupervised scene to guide the clustering process. To solve this problem, we propose a self-constrained spectral clustering algorithm. In this algorithm, we extend the objective function of spectral clustering by adding pairwise and label self-constrained terms to it. We provide the theoretical analysis to show the roles of the self-constrained terms and the extensibility of the proposed algorithm. Based on the new objective function, we build an optimization model for self-constrained spectral clustering so that we can simultaneously learn the clustering results and constraints. Furthermore, we propose an iterative method to solve the new optimization problem. Compared to other existing versions of spectral clustering algorithms, the new algorithm can discover a high-quality cluster structure of a data set without prior information. Extensive experiments on benchmark data sets illustrate the effectiveness of the proposed algorithm.

Multiple Kernel Clustering With Compressed Subspace Alignment

Multiple kernel clustering (MKC) has recently achieved remarkable progress in fusing multisource information to boost the clustering performance. However, the O(n²) memory consumption and O(n³) computational complexity prohibit these methods from being applied into median- or large-scale applications, where n denotes the number of samples. To address these issues, we carefully redesign the formulation of subspace segmentation-based MKC, which reduces the memory and computational complexity to O(n) and O(n²) , respectively. The proposed algorithm adopts a novel sampling strategy to enhance the performance and accelerate the speed of MKC. Specifically, we first mathematically model the sampling process and then learn it simultaneously during the procedure of information fusion. By this way, the generated anchor point set can better serve data reconstruction across different views, leading to improved discriminative capability of the reconstruction matrix and boosted clustering performance. Although the integrated sampling process makes the proposed algorithm less efficient than the linear complexity algorithms, the elaborate formulation makes our algorithm straightforward for parallelization. Through the acceleration of GPU and multicore techniques, our algorithm achieves superior performance against the compared state-of-the-art methods on six datasets with comparable time cost to the linear complexity algorithms.

scDSSC: Deep Sparse Subspace Clustering for scRNA-seq Data

Single cell RNA sequencing (scRNA-seq) enables researchers to characterize transcriptomic profiles at the single-cell resolution with increasingly high throughput. Clustering is a crucial step in single cell analysis. Clustering analysis of transcriptome profiled by scRNA-seq can reveal the heterogeneity and diversity of cells. However, single cell study still remains great challenges due to its high noise and dimension. Subspace clustering aims at discovering the intrinsic structure of data in unsupervised fashion. In this paper, we propose a deep sparse subspace clustering method scDSSC combining noise reduction and dimensionality reduction for scRNA-seq data, which simultaneously learns feature representation and clustering via explicit modelling of scRNA-seq data generation. Experiments on a variety of scRNA-seq datasets from thousands to tens of thousands of cells have shown that scDSSC can significantly improve clustering performance and facilitate the interpretability of clustering and downstream analysis. Compared to some popular scRNA-deq analysis methods, scDSSC outperformed state-of-the-art methods under various clustering performance metrics.

Multiview Subspace Clustering via Co-Training Robust Data Representation

Taking the assumption that data samples are able to be reconstructed with the dictionary formed by themselves, recent multiview subspace clustering (MSC) algorithms aim to find a consensus reconstruction matrix via exploring complementary information across multiple views. Most of them directly operate on the original data observations without preprocessing, while others operate on the corresponding kernel matrices. However, they both ignore that the collected features may be designed arbitrarily and hard guaranteed to be independent and nonoverlapping. As a result, original data observations and kernel matrices would contain a large number of redundant details. To address this issue, we propose an MSC algorithm that groups samples and removes data redundancy concurrently. In specific, eigendecomposition is employed to obtain the robust data representation of low redundancy for later clustering. By utilizing the two processes into a unified model, clustering results will guide eigendecomposition to generate more discriminative data representation, which, as feedback, helps obtain better clustering results. In addition, an alternate and convergent algorithm is designed to solve the optimization problem. Extensive experiments are conducted on eight benchmarks, and the proposed algorithm outperforms comparative ones in recent literature by a large margin, verifying its superiority. At the same time, its effectiveness, computational efficiency, and robustness to noise are validated experimentally.

Agglomerative Neural Networks for Multiview Clustering

Conventional multiview clustering methods seek a view consensus through minimizing the pairwise discrepancy between the consensus and subviews. However, pairwise comparison cannot portray the interview relationship precisely if some of the subviews can be further agglomerated. To address the above challenge, we propose the agglomerative analysis to approximate the optimal consensus view, thereby describing the subview relationship within a view structure. We present an agglomerative neural network (ANN) based on constrained Laplacian rank to cluster multiview data directly without a dedicated postprocessing step (e.g., using K -means). We further extend ANN with a learnable data space to handle data of complex scenarios. Our evaluations against several state-of-the-art multiview clustering approaches on four popular data sets show the promising view-consensus analysis ability of ANN. We further demonstrate ANN's capability in analyzing complex view structures, extensibility through our case study and robustness and effectiveness of data-driven modifications.

Dual-Graph Global and Local Concept Factorization for Data Clustering

Considering a wide range of applications of nonnegative matrix factorization (NMF), many NMF and their variants have been developed. Since previous NMF methods cannot fully describe complex inner global and local manifold structures of the data space and extract complex structural information, we propose a novel NMF method called dual-graph global and local concept factorization (DGLCF). To properly describe the inner manifold structure, DGLCF introduces the global and local structures of the data manifold and the geometric structure of the feature manifold into CF. The global manifold structure makes the model more discriminative, while the two local regularization terms simultaneously preserve the inherent geometry of data and features. Finally, we analyze convergence and the iterative update rules of DGLCF. We illustrate clustering performance by comparing it with latest algorithms on four real-world datasets.

Significant DBSCAN+: Statistically Robust Density-based Clustering

Cluster detection is important and widely used in a variety of applications, including public health, public safety, transportation, and so on. Given a collection of data points, we aim to detect density-connected spatial clusters with varying geometric shapes and densities, under the constraint that the clusters are statistically significant. The problem is challenging, because many societal applications and domain science studies have low tolerance for spurious results, and clusters may have arbitrary shapes and varying densities. As a classical topic in data mining and learning, a myriad of techniques have been developed to detect clusters with both varying shapes and densities (e.g., density-based, hierarchical, spectral, or deep clustering methods). However, the vast majority of these techniques do not consider statistical rigor and are susceptible to detecting spurious clusters formed as a result of natural randomness. On the other hand, scan statistic approaches explicitly control the rate of spurious results, but they typically assume a single “hotspot” of over-density and many rely on further assumptions such as a tessellated input space. To unite the strengths of both lines of work, we propose a statistically robust formulation of a multi-scale DBSCAN, namely Significant DBSCAN+, to identify significant clusters that are density connected. As we will show, incorporation of statistical rigor is a powerful mechanism that allows the new Significant DBSCAN+ to outperform state-of-the-art clustering techniques in various scenarios. We also propose computational enhancements to speed-up the proposed approach. Experiment results show that Significant DBSCAN+ can simultaneously improve the success rate of true cluster detection (e.g., 10–20% increases in absolute F1 scores) and substantially reduce the rate of spurious results (e.g., from thousands/hundreds of spurious detections to none or just a few across 100 datasets), and the acceleration methods can improve the efficiency for both clustered and non-clustered data.

Deep Subspace Mutual Learning For Cancer Subtypes Prediction

MOTIVATION

Precise prediction of cancer subtypes is of significant importance in cancer diagnosis and treatment. Disease etiology is complicated existing at different omics levels, hence integrative analysis provides a very effective way to improve our understanding of cancer.

RESULTS

We propose a novel computational framework, named Deep Subspace Mutual Learning (DSML). DSML has the capability to simultaneously learn the subspace structures in each available omics data and in overall multi-omics data by adopting deep neural networks, which thereby facilitates the subtypes prediction via clustering on multi-level, single level, and partial level omics data. Extensive experiments are performed in five different cancers on three levels of omics data from The Cancer Genome Atlas. The experimental analysis demonstrates that DSML delivers comparable or even better results than many state-of-the-art integrative methods.

AVAILABILITY

An implementation and documentation of the DSML is publicly available at https://github.com/polytechnicXTT/Deep-Subspace-Mutual-Learning.git.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Pseudo-Supervised Deep Subspace Clustering

Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However, self-reconstruction loss of an AE ignores rich useful relation information and might lead to indiscriminative representation, which inevitably degrades the clustering performance. It is also challenging to learn high-level similarity without feeding semantic labels. Another unsolved problem facing DSC is the huge memory cost due to n×n similarity matrix, which is incurred by the self-expression layer between an encoder and decoder. To tackle these problems, we use pairwise similarity to weigh the reconstruction loss to capture local structure information, while a similarity is learned by the self-expression layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain knowledge acquired during network training, are further employed to supervise similarity learning. Joint learning and iterative training facilitate to obtain an overall optimal solution. Extensive experiments on benchmark datasets demonstrate the superiority of our approach. By combining with the k -nearest neighbors algorithm, we further show that our method can address the large-scale and out-of-sample problems. The source code of our method is available: https://github.com/sckangz/SelfsupervisedSC.

Adaptive Weighted Graph Fusion Incomplete Multi-View Subspace Clustering

With the enormous amount of multi-source data produced by various sensors and feature extraction approaches, multi-view clustering (MVC) has attracted developing research attention and is widely exploited in data analysis. Most of the existing multi-view clustering methods hold on the assumption that all of the views are complete. However, in many real scenarios, multi-view data are often incomplete for many reasons, e.g., hardware failure or incomplete data collection. In this paper, we propose an adaptive weighted graph fusion incomplete multi-view subspace clustering (AWGF-IMSC) method to solve the incomplete multi-view clustering problem. Firstly, to eliminate the noise existing in the original space, we transform complete original data into latent representations which contribute to better graph construction for each view. Then, we incorporate feature extraction and incomplete graph fusion into a unified framework, whereas two processes can negotiate with each other, serving for graph learning tasks. A sparse regularization is imposed on the complete graph to make it more robust to the view-inconsistency. Besides, the importance of different views is automatically learned, further guiding the construction of the complete graph. An effective iterative algorithm is proposed to solve the resulting optimization problem with convergence. Compared with the existing state-of-the-art methods, the experiment results on several real-world datasets demonstrate the effectiveness and advancement of our proposed method.

Distributed Compressed Hyperspectral Sensing Imaging Based on Spectral Unmixing

The huge volume of hyperspectral imagery demands enormous computational resources, storage memory, and bandwidth between the sensor and the ground stations. Compressed sensing theory has great potential to reduce the enormous cost of hyperspectral imagery by only collecting a few compressed measurements on the onboard imaging system. Inspired by distributed source coding, in this paper, a distributed compressed sensing framework of hyperspectral imagery is proposed. Similar to distributed compressed video sensing, spatial-spectral hyperspectral imagery is separated into key-band and compressed-sensing-band with different sampling rates during collecting data of proposed framework. However, unlike distributed compressed video sensing using side information for reconstruction, the widely used spectral unmixing method is employed for the recovery of hyperspectral imagery. First, endmembers are extracted from the compressed-sensing-band. Then, the endmembers of the key-band are predicted by interpolation method and abundance estimation is achieved by exploiting sparse penalty. Finally, the original hyperspectral imagery is recovered by linear mixing model. Extensive experimental results on multiple real hyperspectral datasets demonstrate that the proposed method can effectively recover the original data. The reconstruction peak signal-to-noise ratio of the proposed framework surpasses other state-of-the-art methods.