Spectral grouping using the Nyström method

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Graph Neural Networks for Graph Drawing

Graph drawing techniques have been developed in the last few years with the purpose of producing esthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of gradient descent and related optimization algorithms. In this article, we propose a novel framework for the development of Graph Neural Drawers (GNDs), machines that rely on neural computation for constructing efficient and complex maps. GND is Graph Neural Networks (GNNs) whose learning process can be driven by any provided loss function, such as the ones commonly employed in Graph Drawing. Moreover, we prove that this mechanism can be guided by loss functions computed by means of feedforward neural networks, on the basis of supervision hints that express beauty properties, like the minimization of crossing edges. In this context, we show that GNNs can nicely be enriched by positional features to deal also with unlabeled vertexes. We provide a proof-of-concept by constructing a loss function for the edge crossing and provide quantitative and qualitative comparisons among different GNN models working under the proposed framework.

Identifying Regenerated Saplings by Stratifying Forest Overstory Using Airborne LiDAR Data

Identifying the spatiotemporal distributions and phenotypic characteristics of understory saplings is beneficial in exploring the internal mechanisms of plant regeneration and providing technical assistances for continues cover forest management. However, it is challenging to detect the understory saplings using 2-dimensional (2D) spectral information produced by conventional optical remotely sensed data. This study proposed an automatic method to detect the regenerated understory saplings based on the 3D structural information from aerial laser scanning (ALS) data. By delineating individual tree crown using the improved spectral clustering algorithm, we successfully removed the overstory canopy and associated trunk points. Then, individual understory saplings were segmented using an adaptive-mean-shift-based clustering algorithm. This method was tested in an experimental forest farm of North China. Our results showed that the detection rates of understory saplings ranged from 94.41% to 152.78%, and the matching rates increased from 62.59% to 95.65% as canopy closure went down. The ALS-based sapling heights well captured the variations of field measurements [R2 = 0.71, N = 3,241, root mean square error (RMSE) = 0.26 m, P < 0.01] and terrestrial laser scanning (TLS)-based measurements (R2 = 0.78, N =443, RMSE = 0.23 m, P < 0.01). The ALS-based sapling crown width was comparable with TLS-based measurements (R2 = 0.64, N = 443, RMSE = 0.24 m). This study provides a solution for the quantification of understory saplings, which can be used to improve forest ecosystem resilence through regulating the dynamics of forest gaps to better utilize light resources.

A fast, scalable and versatile tool for analysis of single-cell omics data

Single-cell omics technologies have revolutionized the study of gene regulation in complex tissues. A major computational challenge in analyzing these datasets is to project the large-scale and high-dimensional data into low-dimensional space while retaining the relative relationships between cells. This low dimension embedding is necessary to decompose cellular heterogeneity and reconstruct cell-type-specific gene regulatory programs. Traditional dimensionality reduction techniques, however, face challenges in computational efficiency and in comprehensively addressing cellular diversity across varied molecular modalities. Here we introduce a nonlinear dimensionality reduction algorithm, embodied in the Python package SnapATAC2, which not only achieves a more precise capture of single-cell omics data heterogeneities but also ensures efficient runtime and memory usage, scaling linearly with the number of cells. Our algorithm demonstrates exceptional performance, scalability and versatility across diverse single-cell omics datasets, including single-cell assay for transposase-accessible chromatin using sequencing, single-cell RNA sequencing, single-cell Hi-C and single-cell multi-omics datasets, underscoring its utility in advancing single-cell analysis.

Rapid fluctuations in functional connectivity of cortical networks encode spontaneous behavior

Experimental work across species has demonstrated that spontaneously generated behaviors are robustly coupled to variations in neural activity within the cerebral cortex. Functional magnetic resonance imaging data suggest that temporal correlations in cortical networks vary across distinct behavioral states, providing for the dynamic reorganization of patterned activity. However, these data generally lack the temporal resolution to establish links between cortical signals and the continuously varying fluctuations in spontaneous behavior observed in awake animals. Here, we used wide-field mesoscopic calcium imaging to monitor cortical dynamics in awake mice and developed an approach to quantify rapidly time-varying functional connectivity. We show that spontaneous behaviors are represented by fast changes in both the magnitude and correlational structure of cortical network activity. Combining mesoscopic imaging with simultaneous cellular-resolution two-photon microscopy demonstrated that correlations among neighboring neurons and between local and large-scale networks also encode behavior. Finally, the dynamic functional connectivity of mesoscale signals revealed subnetworks not predicted by traditional anatomical atlas-based parcellation of the cortex. These results provide new insights into how behavioral information is represented across the neocortex and demonstrate an analytical framework for investigating time-varying functional connectivity in neural networks.

Discrete and Balanced Spectral Clustering With Scalability

Spectral Clustering (SC) has been the main subject of intensive research due to its remarkable clustering performance. Despite its successes, most existing SC methods suffer from several critical issues. First, they typically involve two independent stages, i.e., learning the continuous relaxation matrix followed by the discretization of the cluster indicator matrix. This two-stage approach can result in suboptimal solutions that negatively impact the clustering performance. Second, these methods are hard to maintain the balance property of clusters inherent in many real-world data, which restricts their practical applicability. Finally, these methods are computationally expensive and hence unable to handle large-scale datasets. In light of these limitations, we present a novel Discrete and Balanced Spectral Clustering with Scalability (DBSC) model that integrates the learning the continuous relaxation matrix and the discrete cluster indicator matrix into a single step. Moreover, the proposed model also maintains the size of each cluster approximately equal, thereby achieving soft-balanced clustering. What's more, the DBSC model incorporates an anchor-based strategy to improve its scalability to large-scale datasets. The experimental results demonstrate that our proposed model outperforms existing methods in terms of both clustering performance and balance performance. Specifically, the clustering accuracy of DBSC on CMUPIE data achieved a 17.93% improvement compared with that of the SOTA methods (LABIN, EBSC, etc.).

TEE-Graph: efficient privacy and ownership protection for cloud-based graph spectral analysis

Introduction

Big graphs like social network user interactions and customer rating matrices require significant computing resources to maintain. Data owners are now using public cloud resources for storage and computing elasticity. However, existing solutions do not fully address the privacy and ownership protection needs of the key involved parties: data contributors and the data owner who collects data from contributors.

Methods

We propose a Trusted Execution Environment (TEE) based solution: TEE-Graph for graph spectral analysis of outsourced graphs in the cloud. TEEs are new CPU features that can enable much more efficient confidential computing solutions than traditional software-based cryptographic ones. Our approach has several unique contributions compared to existing confidential graph analysis approaches. (1) It utilizes the unique TEE properties to ensure contributors' new privacy needs, e.g., the right of revocation for shared data. (2) It implements efficient access-pattern protection with a differentially private data encoding method. And (3) it implements TEE-based special analysis algorithms: the Lanczos method and the Nystrom method for efficiently handling big graphs and protecting confidentiality from compromised cloud providers.

Results

The TEE-Graph approach is much more efficient than software crypto approaches and also immune to access-pattern-based attacks. Compared with the best-known software crypto approach for graph spectral analysis, PrivateGraph, we have seen that TEE-Graph has 103-105 times lower computation, storage, and communication costs. Furthermore, the proposed access-pattern protection method incurs only about 10%-25% of the overall computation cost.

Discussion

Our experimentation showed that TEE-Graph performs significantly better and has lower costs than typical software approaches. It also addresses the unique ownership and access-pattern issues that other TEE-related graph analytics approaches have not sufficiently studied. The proposed approach can be extended to other graph analytics problems with strong ownership and access-pattern protection.

FIESTA: Autoencoders for accurate fiber segmentation in tractography

White matter bundle segmentation is a cornerstone of modern tractography to study the brain's structural connectivity in domains such as neurological disorders, neurosurgery, and aging. In this study, we present FIESTA (FIbEr Segmentation in Tractography using Autoencoders), a reliable and robust, fully automated, and easily semi-automatically calibrated pipeline based on deep autoencoders that can dissect and fully populate white matter bundles. This pipeline is built upon previous works that demonstrated how autoencoders can be used successfully for streamline filtering, bundle segmentation, and streamline generation in tractography. Our proposed method improves bundle segmentation coverage by recovering hard-to-track bundles with generative sampling through the latent space seeding of the subject bundle and the atlas bundle. A latent space of streamlines is learned using autoencoder-based modeling combined with contrastive learning. Using an atlas of bundles in standard space (MNI), our proposed method segments new tractograms using the autoencoder latent distance between each tractogram streamline and its closest neighbor bundle in the atlas of bundles. Intra-subject bundle reliability is improved by recovering hard-to-track streamlines, using the autoencoder to generate new streamlines that increase the spatial coverage of each bundle while remaining anatomically correct. Results show that our method is more reliable than state-of-the-art automated virtual dissection methods such as RecoBundles, RecoBundlesX, TractSeg, White Matter Analysis and XTRACT. Our framework allows for the transition from one anatomical bundle definition to another with marginal calibration efforts. Overall, these results show that our framework improves the practicality and usability of current state-of-the-art bundle segmentation framework.

SnapATAC2: a fast, scalable and versatile tool for analysis of single-cell omics data

Single-cell omics technologies have ushered in a new era for the study of dynamic gene regulation in complex tissues during development and disease pathogenesis. A major computational challenge in analyzing these datasets is to project the large-scale and high dimensional data into low-dimensional space while retaining the relative relationships between cells in order to decompose the cellular heterogeneity and reconstruct cell-type-specific gene regulatory programs. Conventional dimensionality reduction methods suffer from computational inefficiency, difficulty to capture the full spectrum of cellular heterogeneity, or inability to apply across diverse molecular modalities. Here, we report a fast and nonlinear dimensionality reduction algorithm that not only more accurately captures the heterogeneities of single-cell omics data, but also features runtime and memory usage that is computational efficient and linearly proportional to cell numbers. We implement this algorithm in a Python package named SnapATAC2, and demonstrate its superior performance, remarkable scalability and general adaptability using an array of single-cell omics data types, including single-cell ATAC-seq, single-cell RNA-seq, single-cell Hi-C, and single-cell multiomics datasets.

Multiscale Laplacian Learning

Machine learning has greatly influenced many fields, including science. However, despite of the tremendous accomplishments of machine learning, one of the key limitations of most existing machine learning approaches is their reliance on large labeled sets, and thus, data with limited labeled samples remains a challenge. Moreover, the performance of machine learning methods often severely hindered in case of diverse data, usually associated with smaller data sets or data associated with areas of study where the size of the data sets is constrained by high experimental cost and/or ethics. These challenges call for innovative strategies for dealing with these types of data. In this work, the aforementioned challenges are addressed by integrating graph-based frameworks, semi-supervised techniques, multiscale structures, and modified and adapted optimization procedures. This results in two innovative multiscale Laplacian learning (MLL) approaches for machine learning tasks, such as data classification, and for tackling data with limited samples, diverse data, and small data sets. The first approach, multikernel manifold learning (MML), integrates manifold learning with multikernel information and incorporates a warped kernel regularizer using multiscale graph Laplacians. The second approach, the multiscale MBO (MMBO) method, introduces multiscale Laplacians to the modification of the famous classical Merriman-Bence-Osher (MBO) scheme, and makes use of fast solvers. We demonstrate the performance of our algorithms experimentally on a variety of benchmark data sets, and compare them favorably to the state-of-art approaches.

Geodesic-Based Bayesian Coherent Point Drift

Coherent point drift is a well-known algorithm for non-rigid registration, i.e., a procedure for deforming a shape to match another shape. Despite its prevalence, the algorithm has a major drawback that remains unsolved: It unnaturally deforms the different parts of a shape, e.g., human legs, when they are neighboring each other. The inappropriate deformations originate from a proximity-based deformation constraint, called motion coherence. This study proposes a non-rigid registration method that addresses the drawback. The key to solving the problem is to redefine the motion coherence using a geodesic, i.e., the shortest route between points on a shape's surface. We also propose the accelerated variant of the registration method. In numerical studies, we demonstrate that the algorithms can circumvent the drawback of coherent point drift. We also show that the accelerated algorithm can be applied to shapes comprising several millions of points.

Spectral Clustering With Adaptive Neighbors for Deep Learning

Spectral clustering is a well-known clustering algorithm for unsupervised learning, and its improved algorithms have been successfully adapted for many real-world applications. However, traditional spectral clustering algorithms are still facing many challenges to the task of unsupervised learning for large-scale datasets because of the complexity and cost of affinity matrix construction and the eigen-decomposition of the Laplacian matrix. From this perspective, we are looking forward to finding a more efficient and effective way by adaptive neighbor assignments for affinity matrix construction to address the above limitation of spectral clustering. It tries to learn an affinity matrix from the view of global data distribution. Meanwhile, we propose a deep learning framework with fully connected layers to learn a mapping function for the purpose of replacing the traditional eigen-decomposition of the Laplacian matrix. Extensive experimental results have illustrated the competitiveness of the proposed algorithm. It is significantly superior to the existing clustering algorithms in the experiments of both toy datasets and real-world datasets.

Tensorized Bipartite Graph Learning for Multi-View Clustering

Despite the impressive clustering performance and efficiency in characterizing both the relationship between the data and cluster structure, most existing graph-based multi-view clustering methods still have the following drawbacks. They suffer from the expensive time burden due to both the construction of graphs and eigen-decomposition of Laplacian matrix. Moreover, none of them simultaneously considers the similarity of inter-view and similarity of intra-view. In this article, we propose a variance-based de-correlation anchor selection strategy for bipartite construction. The selected anchors not only cover the whole classes but also characterize the intrinsic structure of data. Following that, we present a tensorized bipartite graph learning for multi-view clustering (TBGL). Specifically, TBGL exploits the similarity of inter-view by minimizing the tensor Schatten p-norm, which well exploits both the spatial structure and complementary information embedded in the bipartite graphs of views. We exploit the similarity of intra-view by using the [Formula: see text]-norm minimization regularization and connectivity constraint on each bipartite graph. So the learned graph not only well encodes discriminative information but also has the exact connected components which directly indicates the clusters of data. Moreover, we solve TBGL by an efficient algorithm which is time-economical and has good convergence. Extensive experimental results demonstrate that TBGL is superior to the state-of-the-art methods. Codes and datasets are available: https://github.com/xdweixia/TBGL-MVC.

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.

Inferring Pathways of Oxidative Folding from Prefolding Free Energy Landscapes of Disulfide-Rich Toxins

Short, cysteine-rich peptides can exist in stable or metastable structural ensembles due to the number of possible patterns of formation of their disulfide bonds. One interesting subset of this peptide group is the conotoxins, which are produced by aquatic snails in the family Conidae. The μ conotoxins, which are antagonists and blockers of the voltage-gated sodium channel, exist in a folding spectrum: on one end of the spectrum are more hirudin-like folders, which form disulfide bonds and then reshuffle them, leading to an ensemble of kinetically trapped isomers, and on the other end are more BPTI-like folders, which form the native disulfide bonds one by one in a particular order, leading to a preponderance of conformations existing in a single stable state. In this Article, we employ the composite diffusion map approach to study the unified free energy surface of prefolding μ-conotoxin equilibrium. We identify the two most important nonlinear collective modes of the unified folding landscape and demonstrate that in the absence of their disulfides, the conotoxins can be thought of as largely disordered polymers. A small increase in the number of hydrophobic residues in the protein shifts the free energy landscape toward hydrophobically collapsed coil conformations responsible for cysteine proximity in hirudin-like folders, compared to semiextended coil conformations with more distal cysteines in BPTI-like folders. Overall, this work sheds important light on the folding processes and free energy landscapes of cysteine-rich peptides and demonstrates the extent to which sequence and length contribute to these landscapes.

Integrating transformer and autoencoder techniques with spectral graph algorithms for the prediction of scarcely labeled molecular data

In molecular and biological sciences, experiments are expensive, time-consuming, and often subject to ethical constraints. Consequently, one often faces the challenging task of predicting desirable properties from small data sets or scarcely-labeled data sets. Although transfer learning can be advantageous, it requires the existence of a related large data set. This work introduces three graph-based models incorporating Merriman-Bence-Osher (MBO) techniques to tackle this challenge. Specifically, graph-based modifications of the MBO scheme are integrated with state-of-the-art techniques, including a home-made transformer and an autoencoder, in order to deal with scarcely-labeled data sets. In addition, a consensus technique is detailed. The proposed models are validated using five benchmark data sets. We also provide a thorough comparison to other competing methods, such as support vector machines, random forests, and gradient boosting decision trees, which are known for their good performance on small data sets. The performances of various methods are analyzed using residue-similarity (R-S) scores and R-S indices. Extensive computational experiments and theoretical analysis show that the new models perform very well even when as little as 1% of the data set is used as labeled data.

LSEC: Large-scale spectral ensemble clustering

A fundamental problem in machine learning is ensemble clustering, that is, combining multiple base clusterings to obtain improved clustering result. However, most of the existing methods are unsuitable for large-scale ensemble clustering tasks owing to efficiency bottlenecks. In this paper, we propose a large-scale spectral ensemble clustering (LSEC) method to balance efficiency and effectiveness. In LSEC, a large-scale spectral clustering-based efficient ensemble generation framework is designed to generate various base clusterings with low computational complexity. Thereafter, all the base clusterings are combined using a bipartite graph partition-based consensus function to obtain improved consensus clustering results. The LSEC method achieves a lower computational complexity than most existing ensemble clustering methods. Experiments conducted on ten large-scale datasets demonstrate the efficiency and effectiveness of the LSEC method. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li-Hongmin/MyPaperWithCode.

Centerless Clustering

Although lots of clustering models have been proposed recently, k-means and the family of spectral clustering methods are both still drawing a lot of attention due to their simplicity and efficacy. We first reviewed the unified framework of k-means and graph cut models, and then proposed a clustering method called k-sums where a k-nearest neighbor ( k-NN) graph is adopted. The main idea of k-sums is to minimize directly the sum of the distances between points in the same cluster. To deal with the situation where the graph is unavailable, we proposed k-sums-x that takes features as input. The computational and memory overhead of k-sums are both O(nk), indicating that it can scale linearly w.r.t. the number of objects to group. Moreover, the costs of computational and memory are Irrelevant to the product of the number of points and clusters. The computational and memory complexity of k-sums-x are both linear w.r.t. the number of points. To validate the advantage of k-sums and k-sums-x on facial datasets, extensive experiments have been conducted on 10 synthetic datasets and 17 benchmark datasets. While having a low time complexity, the performance of k-sums is comparable with several state-of-the-art clustering methods.

Characterizing cis-regulatory elements using single-cell epigenomics

Cell type-specific gene expression patterns and dynamics during development or in disease are controlled by cis-regulatory elements (CREs), such as promoters and enhancers. Distinct classes of CREs can be characterized by their epigenomic features, including DNA methylation, chromatin accessibility, combinations of histone modifications and conformation of local chromatin. Tremendous progress has been made in cataloguing CREs in the human genome using bulk transcriptomic and epigenomic methods. However, single-cell epigenomic and multi-omic technologies have the potential to provide deeper insight into cell type-specific gene regulatory programmes as well as into how they change during development, in response to environmental cues and through disease pathogenesis. Here, we highlight recent advances in single-cell epigenomic methods and analytical tools and discuss their readiness for human tissue profiling.

Structured Graph Learning for Scalable Subspace Clustering: From Single View to Multiview

Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: they encounter the expensive time overhead, they fail to explore the explicit clusters, and cannot generalize to unseen data points. In this work, we propose a scalable graph learning framework, seeking to address the above three challenges simultaneously. Specifically, it is based on the ideas of anchor points and bipartite graph. Rather than building an n×n graph, where n is the number of samples, we construct a bipartite graph to depict the relationship between samples and anchor points. Meanwhile, a connectivity constraint is employed to ensure that the connected components indicate clusters directly. We further establish the connection between our method and the K -means clustering. Moreover, a model to process multiview data is also proposed, which is linearly scaled with respect to n . Extensive experiments demonstrate the efficiency and effectiveness of our approach with respect to many state-of-the-art clustering methods.

A Nyström-Based Low-Complexity Algorithm with Improved Effective Array Aperture for Coherent DOA Estimation in Monostatic MIMO Radar

In this paper, we propose a computationally efficient algorithm with improved effective aperture for coherent angle estimation in a monostatic multiple-input multiple-output (MIMO) radar. First, the direction matrix of MIMO radar is mapped into a low-dimensional matrix of virtual uniform linear array (ULA). Then, an augmented data expansion matrix with improved effective aperture is obtained by exploiting the Vandermonde-like structure of the low-dimensional direction matrix and radar cross section (RCS) matrix to enlarge the aperture of the array. Next, a unitary transformation is used to transform the augmented matrix into a real value and the approximate signal subspace of the augmented matrix is obtained by the Nyström method, which can reduce the computational complexity. The eigenvectors of the approximate signal subspace are used to reconstruct the matrix for direct decorrelation processing. Finally, direction of arrivals (DOAs) can be estimated faster by utilizing the unitary ESPRIT algorithm since the rotation invariance of the extended reconstruction matrix still exists. The proposed algorithm has a lower total computational complexity, and the estimation accuracy is improved by utilizing real values and enlarging the array aperture for estimation. Several theoretical analyses and simulation results confirm the effectiveness and advantages of the proposed method.

A Survey on Multi-View Clustering

Clustering is a machine learning paradigm of dividing sample subjects into a number of groups such that subjects in the same groups are more similar to those in other groups. With advances in information acquisition technologies, samples can frequently be viewed from different angles or in different modalities, generating multi-view data. Multi-view clustering, that clusters subjects into subgroups using multi-view data, has attracted more and more attentions. Although MVC methods have been developed rapidly, there has not been enough survey to summarize and analyze the current progress. Therefore, we propose a novel taxonomy of the MVC approaches. Similar to other machine learning methods, we categorize them into generative and discriminative classes. In discriminative class, based on the way of view integration, we split it further into five groups: Common Eigenvector Matrix, Common Coefficient Matrix, Common Indicator Matrix, Direct Combination and Combination After Projection. Furthermore, we relate MVC to other topics: multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated for practitioners. Some benchmark multi-view datasets are introduced and representative MVC algorithms from each group are empirically evaluated to analyze how they perform on benchmark datasets. To promote future development of MVC approaches, we point out several open problems that may require further investigation and thorough examination.

Learnable Subspace Clustering

This article studies the large-scale subspace clustering (LS²C) problem with millions of data points. Many popular subspace clustering methods cannot directly handle the LS²C problem although they have been considered to be state-of-the-art methods for small-scale data points. A simple reason is that these methods often choose all data points as a large dictionary to build huge coding models, which results in high time and space complexity. In this article, we develop a learnable subspace clustering paradigm to efficiently solve the LS²C problem. The key concept is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces instead of the computationally demanding classical coding models. Moreover, we propose a unified, robust, predictive coding machine (RPCM) to learn the parametric function, which can be solved by an alternating minimization algorithm. Besides, we provide a bounded contraction analysis of the parametric function. To the best of our knowledge, this article is the first work to efficiently cluster millions of data points among the subspace clustering methods. Experiments on million-scale data sets verify that our paradigm outperforms the related state-of-the-art methods in both efficiency and effectiveness.

Automatic oculomotor nerve identification based on data‐driven fiber clustering

The oculomotor nerve (OCN) is the main motor nerve innervating eye muscles and can be involved in multiple flammatory, compressive, or pathologies. The diffusion magnetic resonance imaging (dMRI) tractography is now widely used to describe the trajectory of the OCN. However, the complex cranial structure leads to difficulties in fiber orientation distribution (FOD) modeling, fiber tracking, and region of interest (ROI) selection. Currently, the identification of OCN relies on expert manual operation, resulting in challenges, such as the carries high clinical, time‐consuming, and labor costs. Thus, we propose a method that can automatically identify OCN from dMRI tractography. First, we choose the multi‐shell multi‐tissue constraint spherical deconvolution (MSMT‐CSD) FOD estimation model and deterministic tractography to describe the 3D trajectory of the OCN. Then, we rely on the well‐established computational pipeline and anatomical expertise to create a data‐driven OCN tractography atlas from 40 HCP data. We identify six clusters belonging to the OCN from the atlas, including the structures of three kinds of positional relationships (pass between, pass through, and go around) with the red nuclei and two kinds of positional relationships with medial longitudinal fasciculus. Finally, we apply the proposed OCN atlas to identify the OCN automatically from 40 new HCP subjects and two patients with brainstem cavernous malformation. In terms of spatial overlap and visualization, experiment results show that the automatically and manually identified OCN fibers are consistent. Our proposed OCN atlas provides an effective tool for identifying OCN by avoiding the traditional selection strategy of ROIs.

Segmentation of multi-temporal polarimetric SAR data based on mean-shift and spectral graph partitioning

Polarimetric SAR (PolSAR) image segmentation is a key step in its interpretation. For the targets with time series changes, the single-temporal PolSAR image segmentation algorithm is difficult to provide correct segmentation results for its target recognition, time series analysis and other applications. For this, a new algorithm for multi-temporal PolSAR image segmentation is proposed in this paper. Firstly, the over-segmentation of single-temporal PolSAR images is carried out by the mean-shift algorithm, and the over-segmentation results of single-temporal PolSAR are combined to get the over-segmentation results of multi-temporal PolSAR images. Secondly, the edge detectors are constructed to extract the edge information of single-temporal PolSAR images and fuse them to get the edge fusion results of multi-temporal PolSAR images. Then, the similarity measurement matrix is constructed based on the over-segmentation results and edge fusion results of multi-temporal PolSAR images. Finally, the normalized cut criterion is used to complete the segmentation of multi-temporal PolSAR images. The performance of the proposed algorithm is verified based on three temporal PolSAR images of Radarsat-2, and compared with the segmentation algorithm of single-temporal PolSAR image. Experimental results revealed the following findings: (1) The proposed algorithm effectively realizes the segmentation of multi-temporal PolSAR images, and achieves ideal segmentation results. Moreover, the segmentation details are excellent, and the region consistency is good. The objects which can't be distinguished by the single-temporal PolSAR image segmentation algorithm can be segmented. (2) The segmentation accuracy of the proposed multi-temporal algorithm is up to 86.5%, which is significantly higher than that of the single-temporal PolSAR image segmentation algorithm. In general, the segmentation result of proposed algorithm is closer to the optimal segmentation. The optimal segmentation of farmland parcel objects to meet the needs of agricultural production is realized. This lays a good foundation for the further interpretation of multi-temporal PolSAR image.

Laplacian Welsch Regularization for Robust Semisupervised Learning

Semisupervised learning (SSL) has been widely used in numerous practical applications where the labeled training examples are inadequate while the unlabeled examples are abundant. Due to the scarcity of labeled examples, the performances of the existing SSL methods are often affected by the outliers in the labeled data, leading to the imperfect trained classifier. To enhance the robustness of SSL methods to the outliers, this article proposes a novel SSL algorithm called Laplacian Welsch regularization (LapWR). Specifically, apart from the conventional Laplacian regularizer, we also introduce a bounded, smooth, and nonconvex Welsch loss which can suppress the adverse effect brought by the labeled outliers. To handle the model nonconvexity caused by the Welsch loss, an iterative half-quadratic (HQ) optimization algorithm is adopted in which each subproblem has an ideal closed-form solution. To handle the large datasets, we further propose an accelerated model by utilizing the Nyström method to reduce the computational complexity of LapWR. Theoretically, the generalization bound of LapWR is derived based on analyzing its Rademacher complexity, which suggests that our proposed algorithm is guaranteed to obtain satisfactory performance. By comparing LapWR with the existing representative SSL algorithms on various benchmark and real-world datasets, we experimentally found that LapWR performs robustly to outliers and is able to consistently achieve the top-level results.

A deep manifold-regularized learning model for improving phenotype prediction from multi-modal data

The phenotypes of complex biological systems are fundamentally driven by various multi-scale mechanisms. Multi-modal data, such as single cell multi-omics data, enables a deeper understanding of underlying complex mechanisms across scales for phenotypes. We developed an interpretable regularized learning model, deepManReg, to predict phenotypes from multi-modal data. First, deepManReg employs deep neural networks to learn cross-modal manifolds and then to align multi-modal features onto a common latent space. Second, deepManReg uses cross-modal manifolds as a feature graph to regularize the classifiers for improving phenotype predictions and also for prioritizing the multi-modal features and cross-modal interactions for the phenotypes. We applied deepManReg to (1) an image dataset of handwritten digits with multi-features and (2) single cell multi-modal data (Patch-seq data) including transcriptomics and electrophysiology for neuronal cells in the mouse brain. We show that deepManReg improved phenotype prediction in both datasets, and also prioritized genes and electrophysiological features for the phenotypes of neuronal cells.

Hierarchical spectral clustering reveals brain size and shape changes in asymptomatic carriers of C9orf72

Traditional methods for detecting asymptomatic brain changes in neurodegenerative diseases such as Alzheimer's disease or frontotemporal degeneration typically evaluate changes in volume at a predefined level of granularity, e.g. voxel-wise or in a priori defined cortical volumes of interest. Here, we apply a method based on hierarchical spectral clustering, a graph-based partitioning technique. Our method uses multiple levels of segmentation for detecting changes in a data-driven, unbiased, comprehensive manner within a standard statistical framework. Furthermore, spectral clustering allows for detection of changes in shape along with changes in size. We performed tensor-based morphometry to detect changes in the Genetic Frontotemporal dementia Initiative asymptomatic and symptomatic frontotemporal degeneration mutation carriers using hierarchical spectral clustering and compared the outcome to that obtained with a more conventional voxel-wise tensor- and voxel-based morphometric analysis. In the symptomatic groups, the hierarchical spectral clustering-based method yielded results that were largely in line with those obtained with the voxel-wise approach. In asymptomatic C9orf72 expansion carriers, spectral clustering detected changes in size in medial temporal cortex that voxel-wise methods could only detect in the symptomatic phase. Furthermore, in the asymptomatic and the symptomatic phases, the spectral clustering approach detected changes in shape in the premotor cortex in C9orf72. In summary, the present study shows the merit of hierarchical spectral clustering for data-driven segmentation and detection of structural changes in the symptomatic and asymptomatic stages of monogenic frontotemporal degeneration.

Large Graph Clustering With Simultaneous Spectral Embedding and Discretization

Spectral clustering methods are gaining more and more interests and successfully applied in many fields because of their superior performance. However, there still exist two main problems to be solved: 1) spectral clustering methods consist of two successive optimization stages-spectral embedding and spectral rotation, which may not lead to globally optimal solutions, 2) and it is known that spectral methods are time-consuming with very high computational complexity. There are methods proposed to reduce the complexity for data vectors but not for graphs that only have information about similarity matrices. In this paper, we propose a new method to solve these two challenging problems for graph clustering. In the new method, a new framework is established to perform spectral embedding and spectral rotation simultaneously. The newly designed objective function consists of both terms of embedding and rotation, and we use an improved spectral rotation method to make it mathematically rigorous for the optimization. To further accelerate the algorithm, we derive a low-dimensional representation matrix from a graph by using label propagation, with which, in return, we can reconstruct a double-stochastic and positive semidefinite similarity matrix. Experimental results demonstrate that our method has excellent performance in time cost and accuracy.

GPU-Based Supervoxel Generation With a Novel Anisotropic Metric

Video over-segmentation into supervoxels is an important pre-processing technique for many computer vision tasks. Videos are an order of magnitude larger than images. Most existing methods for generating supervovels are either memory- or time-inefficient, which limits their application in subsequent video processing tasks. In this paper, we present an anisotropic supervoxel method, which is memory-efficient and can be executed on the graphics processing unit (GPU). Therefore, our algorithm achieves good balance among segmentation quality, memory usage and processing time. In order to provide accurate segmentation for moving objects in video, we use the optical flow information to design a brand new non-Euclidean metric to calculate the anisotropic distances between seeds and voxels. To efficiently compute the anisotropic metric, we adjust the classic jump flooding algorithm (which is designed for parallel execution on the GPU) to generate anisotropic Voronoi tessellation in the combined color and spatio-temporal space. We evaluate our method and the representative supervoxel algorithms for their capability on segmentation performance, computation speed and memory efficiency. We also apply supervoxel results to the application of foreground propagation in videos to test the performance on solving practical problems. Experiments show that our algorithm is much faster than the existing methods, and achieves good balance on segmentation quality and efficiency.

Nonlinear manifold learning in functional magnetic resonance imaging uncovers a low-dimensional space of brain dynamics

Large-scale brain dynamics are believed to lie in a latent, low-dimensional space. Typically, the embeddings of brain scans are derived independently from different cognitive tasks or resting-state data, ignoring a potentially large-and shared-portion of this space. Here, we establish that a shared, robust, and interpretable low-dimensional space of brain dynamics can be recovered from a rich repertoire of task-based functional magnetic resonance imaging (fMRI) data. This occurs when relying on nonlinear approaches as opposed to traditional linear methods. The embedding maintains proper temporal progression of the tasks, revealing brain states and the dynamics of network integration. We demonstrate that resting-state data embeds fully onto the same task embedding, indicating similar brain states are present in both task and resting-state data. Our findings suggest analysis of fMRI data from multiple cognitive tasks in a low-dimensional space is possible and desirable.

Feature-Aware Uniform Tessellations on Video Manifold for Content-Sensitive Supervoxels

Over-segmenting a video into supervoxels has strong potential to reduce the complexity of downstream computer vision applications. Content-sensitive supervoxels (CSSs) are typically smaller in content-dense regions (i.e., with high variation of appearance and/or motion) and larger in content-sparse regions. In this paper, we propose to compute feature-aware CSSs (FCSSs) that are regularly shaped 3D primitive volumes well aligned with local object/region/motion boundaries in video. To compute FCSSs, we map a video to a 3D manifold embedded in a combined color and spatiotemporal space, in which the volume elements of video manifold give a good measure of the video content density. Then any uniform tessellation on video manifold can induce CSS in the video. Our idea is that among all possible uniform tessellations on the video manifold, FCSS finds one whose cell boundaries well align with local video boundaries. To achieve this goal, we propose a novel restricted centroidal Voronoi tessellation method that simultaneously minimizes the tessellation energy (leading to uniform cells in the tessellation) and maximizes the average boundary distance (leading to good local feature alignment). Theoretically our method has an optimal competitive ratio O(1), and its time and space complexities are O(NK) and O(N+K) for computing K supervoxels in an N-voxel video. We also present a simple extension of FCSS to streaming FCSS for processing long videos that cannot be loaded into main memory at once. We evaluate FCSS, streaming FCSS and ten representative supervoxel methods on four video datasets and two novel video applications. The results show that our method simultaneously achieves state-of-the-art performance with respect to various evaluation criteria.

Approximate spectral clustering using both reference vectors and topology of the network generated by growing neural gas

Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious drawbacks: the significant increases in the time complexity derived from the computation of eigenvectors and the memory space complexity to store the similarity matrix. To address the issues, I develop a new approximate spectral clustering using the network generated by growing neural gas (GNG), called ASC with GNG in this study. ASC with GNG uses not only reference vectors for vector quantization but also the topology of the network for extraction of the topological relationship between data points in a dataset. ASC with GNG calculates the similarity matrix from both the reference vectors and the topology of the network generated by GNG. Using the network generated from a dataset by GNG, ASC with GNG achieves to reduce the computational and space complexities and improve clustering quality. In this study, I demonstrate that ASC with GNG effectively reduces the computational time. Moreover, this study shows that ASC with GNG provides equal to or better clustering performance than SC.

Fast and Effective Active Clustering Ensemble Based on Density Peak

Semisupervised clustering methods improve performance by randomly selecting pairwise constraints, which may lead to redundancy and instability. In this context, active clustering is proposed to maximize the efficacy of annotations by effectively using pairwise constraints. However, existing methods lack an overall consideration of the querying criteria and repeatedly run semisupervised clustering to update labels. In this work, we first propose an active density peak (ADP) clustering algorithm that considers both representativeness and informativeness. Representative instances are selected to capture data patterns, while informative instances are queried to reduce the uncertainty of clustering results. Meanwhile, we design a fast-update-strategy to update labels efficiently. In addition, we propose an active clustering ensemble framework that combines local and global uncertainties to query the most ambiguous instances for better separation between the clusters. A weighted voting consensus method is introduced for better integration of clustering results. We conducted experiments by comparing our methods with state-of-the-art methods on real-world data sets. Experimental results demonstrate the effectiveness of our methods.

Novel Feature-Extraction Methods for the Estimation of Above-Ground Biomass in Rice Crops

Traditional methods to measure spatio-temporal variations in above-ground biomass dynamics (AGBD) predominantly rely on the extraction of several vegetation-index features highly associated with AGBD variations through the phenological crop cycle. This work presents a comprehensive comparison between two different approaches for feature extraction for non-destructive biomass estimation using aerial multispectral imagery. The first method is called GFKuts, an approach that optimally labels the plot canopy based on a Gaussian mixture model, a Montecarlo-based K-means, and a guided image filtering for the extraction of canopy vegetation indices associated with biomass yield. The second method is based on a Graph-Based Data Fusion (GBF) approach that does not depend on calculating vegetation-index image reflectances. Both methods are experimentally tested and compared through rice growth stages: vegetative, reproductive, and ripening. Biomass estimation correlations are calculated and compared against an assembled ground-truth biomass measurements taken by destructive sampling. The proposed GBF-Sm-Bs approach outperformed competing methods by obtaining biomass estimation correlation of 0.995 with R2=0.991 and RMSE=45.358 g. This result increases the precision in the biomass estimation by around 62.43% compared to previous works.

Reduced Hippocampal Glutamate and Posterior Cingulate N-Acetyl Aspartate in Mild Cognitive Impairment and Alzheimer's Disease Is Associated with Episodic Memory Performance and White Matter Integrity in the Cingulum: A Pilot Study

Identification of biological changes underlying the early symptoms of Alzheimer's disease (AD) will help to identify and stage individuals prior to symptom onset. The limbic system, which supports episodic memory and is impaired early in AD, is a primary target. In this study, brain metabolism and microstructure evaluated by high field (7 Tesla) proton magnetic resonance spectroscopy (1H-MRS) and diffusion tensor imaging (DTI) were evaluated in the limbic system of eight individuals with mild cognitive impairment (MCI), nine with AD, and sixteen normal elderly controls (NEC). Left hippocampal glutamate and posterior cingulate N-acetyl aspartate concentrations were reduced in MCI and AD compared to NEC. Differences in DTI metrics indicated volume and white matter loss along the cingulum in AD compared to NEC. Metabolic and microstructural changes were associated with episodic memory performance assessed using Craft Story 21 Recall and Benson Complex Figure Copy. The current study suggests that metabolite concentrations measured using 1H-MRS may provide insight into the underlying metabolic and microstructural processes of episodic memory impairment.

Linear-time cluster ensembles of large-scale single-cell RNA-seq and multimodal data

A fundamental task in single-cell RNA-seq (scRNA-seq) analysis is the identification of transcriptionally distinct groups of cells. Numerous methods have been proposed for this problem, with a recent focus on methods for the cluster analysis of ultralarge scRNA-seq data sets produced by droplet-based sequencing technologies. Most existing methods rely on a sampling step to bridge the gap between algorithm scalability and volume of the data. Ignoring large parts of the data, however, often yields inaccurate groupings of cells and risks overlooking rare cell types. We propose method Specter that adopts and extends recent algorithmic advances in (fast) spectral clustering. In contrast to methods that cluster a (random) subsample of the data, we adopt the idea of landmarks that are used to create a sparse representation of the full data from which a spectral embedding can then be computed in linear time. We exploit Specter's speed in a cluster ensemble scheme that achieves a substantial improvement in accuracy over existing methods and identifies rare cell types with high sensitivity. Its linear-time complexity allows Specter to scale to millions of cells and leads to fast computation times in practice. Furthermore, on CITE-seq data that simultaneously measures gene and protein marker expression, we show that Specter is able to use multimodal omics measurements to resolve subtle transcriptomic differences between subpopulations of cells.

Creation of a novel trigeminal tractography atlas for automated trigeminal nerve identification

Diffusion MRI (dMRI) tractography has been successfully used to study the trigeminal nerves (TGNs) in many clinical and research applications. Currently, identification of the TGN in tractography data requires expert nerve selection using manually drawn regions of interest (ROIs), which is prone to inter-observer variability, time-consuming and carries high clinical and labor costs. To overcome these issues, we propose to create a novel anatomically curated TGN tractography atlas that enables automated identification of the TGN from dMRI tractography. In this paper, we first illustrate the creation of a trigeminal tractography atlas. Leveraging a well-established computational pipeline and expert neuroanatomical knowledge, we generate a data-driven TGN fiber clustering atlas using tractography data from 50 subjects from the Human Connectome Project. Then, we demonstrate the application of the proposed atlas for automated TGN identification in new subjects, without relying on expert ROI placement. Quantitative and visual experiments are performed with comparison to expert TGN identification using dMRI data from two different acquisition sites. We show highly comparable results between the automatically and manually identified TGNs in terms of spatial overlap and visualization, while our proposed method has several advantages. First, our method performs automated TGN identification, and thus it provides an efficient tool to reduce expert labor costs and inter-operator bias relative to expert manual selection. Second, our method is robust to potential imaging artifacts and/or noise that can prevent successful manual ROI placement for TGN selection and hence yields a higher successful TGN identification rate.

Graph-Based Data Fusion Applied to: Change Detection and Biomass Estimation in Rice Crops

The complementary nature of different modalities and multiple bands used in remote sensing data is helpful for tasks such as change detection and the prediction of agricultural variables. Nonetheless, correctly processing a multi-modal dataset is not a simple task, owing to the presence of different data resolutions and formats. In the past few years, graph-based methods have proven to be a useful tool in capturing inherent data similarity, in spite of different data formats, and preserving relevant topological and geometric information. In this paper, we propose a graph-based data fusion algorithm for remotely sensed images applied to (i) data-driven semi-unsupervised change detection and (ii) biomass estimation in rice crops. In order to detect the change, we evaluated the performance of four competing algorithms on fourteen datasets. To estimate biomass in rice crops, we compared our proposal in terms of root mean squared error (RMSE) concerning a recent approach based on vegetation indices as features. The results confirm that the proposed graph-based data fusion algorithm outperforms state-of-the-art methods for change detection and biomass estimation in rice crops.