Pairwise Relationships Research Articles

BMT independence

We introduce the notion of BMT independence, enabling the study of arbitrary mixtures of Boolean, monotone, and tensor independence and generalizing the notion of BM independence of J. Wysoczanski. pairwise independence relations are encoded through a directed graph, which in turn determines the way mixed moments must be computed. Corresponding Central and Poisson-Type Limit Theorems are provided along with an explicit construction to realize BMT independent random variables as bounded operators on the tensor product of Hilbert spaces.

A Review of Hypergraph Neural Networks

In recent years, Graph Neural Networks (GNNs) have seen notable success in fields such as recommendation systems and natural language processing, largely due to the availability of vast amounts of data and powerful computational resources. GNNs are primarily designed to work with graph data that involve pairwise relationships. However, in many real-world networks, the relationships between entities are complex and go beyond simple pairwise connections, as seen in scientific collaboration networks, protein networks, and similar domains. If these complex relationships are directly represented as pairwise relationships using graph structures, it can lead to information loss. A hypergraph, as a special kind of graph-structured data, can represent higher-order relationships that cannot be fully captured by graphs, thereby addressing the limitations of graphs. In light of this, researchers have begun to focus on how to design neural networks on hypergraphs, leading to the proposal of hypergraph neural network (HGNN) models for downstream tasks. Therefore, this paper reviews the existing hypergraph neural network models. The review is conducted from two perspectives: spectral analysis methods and neural network methods on hypergraphs, discussing both unfolded and non-unfolded methods, and further subdividing them based on their algorithm characteristics and application scenarios. Subsequently, the design concepts of various algorithms are analyzed and compared, and the advantages and disadvantages of each type of algorithm are summarized based on experimental results. Finally, potential future research directions in hypergraph learning are discussed.

HAGMN-UQ: Hyper association graph matching network with uncertainty quantification for coronary artery semantic labeling

Coronary artery disease (CAD) is one of the leading causes of death worldwide. Accurate extraction of individual arterial branches from invasive coronary angiograms (ICA) is critical for CAD diagnosis and detection of stenosis. Generating semantic segmentation for coronary arteries through deep learning-based models presents challenges due to the morphological similarity among different types of coronary arteries, making it difficult to maintain high accuracy while keeping low computational complexity. To address this challenge, we propose an innovative approach using the hyper association graph-matching neural network with uncertainty quantification (HAGMN-UQ) for coronary artery semantic labeling on ICAs. The graph-matching procedure maps the arterial branches between two individual graphs, so that the unlabeled arterial segments are classified by the labeled segments, and the coronary artery semantic labeling is achieved. Leveraging hypergraphs not only extends representation capabilities beyond pairwise relationships, but also improves the robustness and accuracy of the graph matching by enabling the modeling of higher-order associations. In addition, employing the uncertainty quantification to determine the trustworthiness of graph matching reduces the required number of comparisons, so as to accelerate the inference speed. Consequently, our model achieved an accuracy of 0.9211 for coronary artery semantic labeling with a fast inference speed, leading to an effective and efficient prediction in real-time clinical decision-making scenarios.

Diffusion process with structural changes for subspace clustering

Spectral clustering-based methods have gained significant popularity in subspace clustering due to their ability to capture the underlying data structure effectively. Standard spectral clustering focuses on only pairwise relationships between data points, neglecting interactions among high-order neighboring points. Integrating the diffusion process can address this limitation by leveraging a Markov random walk. However, ensuring that diffusion methods capture sufficient information while maintaining stability against noise remains challenging. In this paper, we propose the Diffusion Process with Structural Changes (DPSC) method, a novel affinity learning framework that enhances the robustness of the diffusion process. Our approach broadens the scope of nearest neighbors and leverages the dropout idea to generate random transition matrices. Furthermore, inspired by the structural changes model, we use two transition matrices to optimize the iteration rule. The resulting affinity matrix undergoes self-supervised learning and is subsequently integrated back into the diffusion process for refinement. Notably, the convergence of the proposed DPSC is theoretically proven. Extensive experiments on benchmark datasets demonstrate that the proposed method outperforms existing subspace clustering methods. The code of our proposed DPSC is available at https://github.com/zhudafa/DPSC.

Learning accurate neighborhood- and self-information for higher-order relation prediction in Heterogeneous Information Networks

Heterogeneous Information Networks (HINs) are commonly employed to model complex real-world scenarios with diverse node and edge types. However, due to constraints in data collection and processing, constructed networks often lack certain relations. Consequently, various methods have emerged, particularly recently, leveraging heterogeneous graph neural networks (HGNNs) to predict missing relations. Nevertheless, these methods primarily focus on pairwise relations between two nodes. Real-world interactions, however, often involve multiple nodes and diverse types, extending beyond simple pairwise relations. For instance, academic collaboration networks may entail interactions among authors, papers, and conferences simultaneously. Despite their prevalence, higher-order relations are often overlooked. While HGNNs are effective at learning network structures, they may suffer from over-smoothing, resulting in similar representations for nodes and their neighbors. The learned inaccurate proximity among nodes impedes the discernment of higher-order relations. Furthermore, observed edges among a target group of nodes can provide valuable evidence for predicting higher-order relations. To address these challenges, we propose a novel model called Accurate Neighborhood- and Self-information Enhanced Heterogeneous Graph Neural Network (ANSE-HGN). Building upon HGNNs to encode network structure and attributes, we introduce a relation-based neighborhood encoder to capture information within multi-hop neighborhoods in heterogeneous higher-order relations. This enables the calculation of accurate proximity among target groups of nodes, thereby enhancing prediction accuracy. Additionally, we leverage self-information from observed higher-order relations as an auxiliary loss to reinforce the learning process. Extensive experiments on four real-world datasets demonstrate the superiority of our proposed method in higher-order relation prediction tasks.

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.

FamLink2 – A comprehensive tool for likelihood computations in pedigrees analyses involving linked DNA markers accounting for genotype uncertainties

There is an increasing demand for software that can handle an arbitrary number of linked markers in forensic genetics; primarily with application to inference of relationships and direct matching but also in applications such as ancestry inference and mixture interpretation. With the emergence of sequencing technologies, denser sets of SNP markers are generated and analyzed. Additionally, sequence data of low quality and quantity DNA generate uncertainty about the underlying true genotype. We provide an efficient implementation of a general model for pedigree likelihood computations with genetic marker data using a three-layered approach. The top and first layer is the population model where allele frequencies and population substructure are accounted for. The second layer is the inheritance model which efficiently handles linked markers using an IBD model. The third and bottom layer is the observational level where we model the likelihood of the true genotype given underlying reads as well as parameters for errors. We exemplify the utility of our implementation as well as provide validation according to guidelines established by the ISFG using a combination of two published SNP panels. We demonstrate that computations are feasible for panels encompassing 10,000 markers and we argue that, due to the properties of the underlying algorithm, extending the number of markers will result in a linear increase in computation time. In addition we study the impact of parameters used in our model and suggest some guidelines pertaining to their values. The results demonstrate that a probabilistic model for low coverage sequence read data is needed instead of relying on an a threshold based genotype and applying our general model for inference of relationships on a real case can be superior, i.e. higher information content, to other methods relying on either fixed genotypes with low quality sequence data or simple pair wise relationship tests. In summary, the implementation, FamLink2 (freely available at https://famlink.se), can jointly handle genetic linkage, genotype uncertainty and population substructure for an arbitrary pedigree with data for any number of individuals. Whereas the current study will focus on calculations disregarding mutations, FamLink2 has the ability to model mutations for certain built-in pedigrees.

Spontaneous Brain Activity Emerges from Pairwise Interactions in the Larval Zebrafish Brain

Brain activity is characterized by brainwide spatiotemporal patterns that emerge from synapse-mediated interactions between individual neurons. Calcium imaging provides access to recordings of whole-brain activity at single-neuron resolution and, therefore, allows the study of how large-scale brain dynamics emerge from local activity. In this study, we use a statistical mechanics approach—the pairwise maximum entropy model—to infer microscopic network features from collective patterns of activity in the larval zebrafish brain and relate these features to the emergence of observed whole-brain dynamics. Our findings indicate that the pairwise interactions between neural populations and their intrinsic activity states are sufficient to explain observed whole-brain dynamics. In fact, the pairwise relationships between neuronal populations estimated with the maximum entropy model strongly correspond to observed structural connectivity patterns. Model simulations also demonstrated how tuning pairwise neuronal interactions drives transitions between observed physiological regimes and pathologically hyperexcitable whole-brain regimes. Finally, we use virtual resection to identify the brain structures that are important for maintaining the brain in a physiological dynamic regime. Together, our results indicate that whole-brain activity emerges from a complex dynamical system that transitions between basins of attraction whose strength and topology depend on the connectivity between brain areas. Published by the American Physical Society 2024

CORRECTING MODEL MISSPECIFICATION IN RELATIONSHIP ESTIMATES.

The datasets of large genotyping biobanks and direct-to-consumer genetic testing companies contain many related individuals. Until now, it has been widely accepted that the most distant relationships that can be detected are around fifteen degrees (approximately 8 th cousins) and that practical relationship estimates have a ceiling around ten degrees (approximately 5 th cousins). However, we show that these assumptions are incorrect and that they are due to a misapplication of relationship estimators. In particular, relationship estimators are applied almost exclusively to putative relatives who have been identified because they share detectable tracts of DNA identically by descent (IBD). However, no existing relationship estimator conditions on the event that two individuals share at least one detectable segment of IBD anywhere in the genome. As a result, the relationship estimates obtained using existing estimators are dramatically biased for distant relationships, inferring all sufficiently distant relationships to be around ten degrees regardless of the depth of the true relationship. Existing relationship estimators are derived under a model that assumes that each pair of related individuals shares a single common ancestor (or mating pair of ancestors). This model breaks down for relationships beyond 10 generations in the past because individuals share many thousands of cryptic common ancestors due to pedigree collapse. We first derive a corrected likelihood that conditions on the event that at least one segment is observed between a pair of putative relatives and we demonstrate that the corrected likelihood largely eliminates the bias in estimates of pairwise relationships and provides a more accurate characterization of the uncertainty in these estimates. We then reformulate the relationship inference problem to account for the fact that individuals share many common ancestors, not just one. We demonstrate that the most distant relationship that can be inferred using IBD may be 200 degrees or more, rather than ten, extending the time-to-common ancestor from approximately 300 years in the past to approximately 3,000 years in the past or more. This dramatic increase in the range of relationship estimators makes it possible to infer relationships whose common ancestors lived before historical events such as European settlement of the Americas, the Transatlantic Slave Trade, and the rise and fall of the Roman Empire.

Generalized Einstein relations between absorption and emission spectra at thermodynamic equilibrium

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive.

Multispecies interactions and the community context of the evolution of virulence.

Pairwise host-parasite relationships are typically embedded in broader networks of ecological interactions, which have the potential to shape parasite evolutionary trajectories. Understanding this 'community context' of pathogen evolution is vital for wildlife, agricultural and human systems alike, as pathogens typically infect more than one host-and these hosts may have independent ecological relationships. Here, we introduce an eco-evolutionary model examining ecological feedback across a range of host-host interactions. Specifically, we analyse a model of the evolution of virulence of a parasite infecting two hosts exhibiting competitive, mutualistic or exploitative relationships. We first find that parasite specialism is necessary for inter-host interactions to impact parasite evolution. Furthermore, we find generally that increasing competition between hosts leads to higher shared parasite virulence while increasing mutualism leads to lower virulence. In exploitative host-host interactions, the particular form of parasite specialization is critical-for instance, specialization in terms of onward transmission, host tolerance or intra-host pathogen growth rate lead to distinct evolutionary outcomes under the same host-host interactions. Our work provides testable hypotheses for multi-host disease systems, predicts how changing interaction networks may impact virulence evolution and broadly demonstrates the importance of looking beyond pairwise relationships to understand evolution in realistic community contexts.

Improving unsupervised pedestrian re‐identification with enhanced feature representation and robust clustering

AbstractPedestrian re‐identification (re‐ID) is an important research direction in computer vision, with extensive applications in pattern recognition and monitoring systems. Due to uneven data distribution, and the need to solve clustering standards and similarity evaluation problems, the performance of unsupervised methods is limited. To address these issues, an improved unsupervised re‐ID method, called Enhanced Feature Representation and Robust Clustering (EFRRC), which combines EFRRC is proposed. First, a relation network that considers the relations between each part of the pedestrian's body and other parts is introduced, thereby obtaining more discriminative feature representations. The network makes the feature at the single‐part level also contain partial information of other body parts, making it more discriminative. A global contrastive pooling (GCP) module is introduced to obtain the global features of the image. Second, a dispersion‐based clustering method, which can effectively evaluate the quality of clustering and discover potential patterns in the data is designed. This approach considers a wider context of sample‐level pairwise relationships for robust cluster affinity assessment. It effectively addresses challenges posed by imbalanced data distributions in complex situations. The above structures are connected through a clustering contrastive learning framework, which not only improves the discriminative power of features and the accuracy of clustering, but also solves the problem of inconsistent clustering updates. Experimental results on three public datasets demonstrate the superiority of our method over existing unsupervised re‐ID methods.

Context-embedded hypergraph attention network and self-attention for session recommendation

Modeling user intention with limited evidence in short-term historical sequences is a major challenge in session recommendation. In this domain, research exploration extends from traditional methods to deep learning. However, most of them solely concentrate on the sequential dependence or pairwise relations within the session, disregarding the inherent consistency among items. Additionally, there is a lack of research on context adaptation in session intention learning. To this end, we propose a novel session-based model named C-HAN, which consists of two parallel modules: the context-embedded hypergraph attention network and self-attention. These modules are designed to capture the inherent consistency and sequential dependencies between items. In the hypergraph attention network module, the different types of interaction contexts are introduced to enhance the model’s contextual awareness. Finally, the soft-attention mechanism efficiently integrates the two types of information, collaboratively constructing the representation of the session. Experimental validation on three real-world datasets demonstrates the superior performance of C-HAN compared to state-of-the-art methods. The results show that C-HAN achieves an average improvement of 6.55%, 5.91%, and 6.17% over the runner-up baseline method on Precision@K, Recall@K, and MRR evaluation metrics, respectively.

A comparative analysis of mutual information methods for pairwise relationship detection in metagenomic data

BackgroundConstruction of co-occurrence networks in metagenomic data often employs correlation to infer pairwise relationships between microbes. However, biological systems are complex and often display qualities non-linear in nature. Therefore, the reliance on correlation alone may overlook important relationships and fail to capture the full breadth of intricacies presented in underlying interaction networks. It is of interest to incorporate metrics that are not only robust in detecting linear relationships, but non-linear ones as well.ResultsIn this paper, we explore the use of various mutual information (MI) estimation approaches for quantifying pairwise relationships in biological data and compare their performances against two traditional measures–Pearson’s correlation coefficient, r, and Spearman’s rank correlation coefficient, ρ. Metrics are tested on both simulated data designed to mimic pairwise relationships that may be found in ecological systems and real data from a previous study on C. diff infection. The results demonstrate that, in the case of asymmetric relationships, mutual information estimators can provide better detection ability than Pearson’s or Spearman’s correlation coefficients. Specifically, we find that these estimators have elevated performances in the detection of exploitative relationships, demonstrating the potential benefit of including them in future metagenomic studies.ConclusionsMutual information (MI) can uncover complex pairwise relationships in biological data that may be missed by traditional measures of association. The inclusion of such relationships when constructing co-occurrence networks can result in a more comprehensive analysis than the use of correlation alone.

The biomedical relationship corpus of the BioRED track at the BioCreative VIII challenge and workshop.

The automatic recognition of biomedical relationships is an important step in the semantic understanding of the information contained in the unstructured text of the published literature. The BioRED track at BioCreative VIII aimed to foster the development of such methods by providing the participants the BioRED-BC8 corpus, a collection of 1000 PubMed documents manually curated for diseases, gene/proteins, chemicals, cell lines, gene variants, and species, as well as pairwise relationships between them which are disease-gene, chemical-gene, disease-variant, gene-gene, chemical-disease, chemical-chemical, chemical-variant, and variant-variant. Furthermore, relationships are categorized into the following semantic categories: positive correlation, negative correlation, binding, conversion, drug interaction, comparison, cotreatment, and association. Unlike most of the previous publicly available corpora, all relationships are expressed at the document level as opposed to the sentence level, and as such, the entities are normalized to the corresponding concept identifiers of the standardized vocabularies, namely, diseases and chemicals are normalized to MeSH, genes (and proteins) to National Center for Biotechnology Information (NCBI) Gene, species to NCBI Taxonomy, cell lines to Cellosaurus, and gene/protein variants to Single Nucleotide Polymorphism Database. Finally, each annotated relationship is categorized as 'novel' depending on whether it is a novel finding or experimental verification in the publication it is expressed in. This distinction helps differentiate novel findings from other relationships in the same text that provides known facts and/or background knowledge. The BioRED-BC8 corpus uses the previous BioRED corpus of 600 PubMed articles as the training dataset and includes a set of newly published 400 articles to serve as the test data for the challenge. All test articles were manually annotated for the BioCreative VIII challenge by expert biocurators at the National Library of Medicine, using the original annotation guidelines, where each article is doubly annotated in a three-round annotation process until full agreement is reached between all curators. This manuscript details the characteristics of the BioRED-BC8 corpus as a critical resource for biomedical named entity recognition and relation extraction. Using this new resource, we have demonstrated advancements in biomedical text-mining algorithm development. Database URL: https://codalab.lisn.upsaclay.fr/competitions/16381.

White matter microstructure mediates the pairwise relationship between childhood maltreatment, microRNA-9, and the severity of major depressive disorder.

White matter microstructure mediates the pairwise relationship between childhood maltreatment, microRNA-9, and the severity of major depressive disorder.

Constructing sympatry networks to assess potential introgression pathways within the major oak sections in the contiguous US states

Societal Impact StatementIncreasing evidence indicates gene flow commonly occurs between closely related species in diverse plant genera and can involve numerous species. Here, we present a simple method to quantify and characterize the potential for gene flow among “sympatric” species (they share some part of their geographic distribution), using oaks as a case study. The resulting sympatry networks provide insight into potential interspecific gene flow, from the perspective of each species and across the entire suite of interfertile species. In a rapidly changing world, interspecific gene flow will play an increasingly important role in the conservation of endangered species, both positive and negative.Summary We provide a simple method, using geographic distribution data, to quantify and characterize sympatry networks among a suite of interfertile species to assess potential routes for introgressive hybridization (IH). Sympatry is a necessary condition for IH and is easily determined from widely available geographic distribution data. Oaks, famous for hybridization, present an excellent case study. We use county‐level data for 94 oak species in the contiguous US states to determine patterns of sympatry of species within the four sections, assumed to be interfertile. The pairwise sympatry relationships can generate species‐centric local networks or a syngameon‐wide network. Two different measures of sympatry are used: proportional and relative. Most oak species are exposed to IH from many species, with red oaks having slightly higher local levels of sympatry (5.7 vs. 3.8 spp per county) than white oaks but lower total numbers of sympatric species (13.7 vs. 14.8). The nature of potential IH generally differs for threatened species, which are often embedded in the much larger distributions of widespread species. Potential IH within oak sections is widespread and disproportionately affects rare species. Given that IH has potentially positive or negative impacts on species cohesion, persistence, and adaptation, the geographic connections among species and the ‘local sympatry effect’ can serve as a springboard for hypothesis generation and genetic investigation of introgression patterns.

Identifying the hierarchical emotional areas in the human brain through information fusion

The brain basis of emotion has consistently received widespread attention, attracting a large number of studies to explore this cutting-edge topic. However, the methods employed in these studies typically only model the pairwise relationship between two brain regions, while neglecting the interactions and information fusion among multiple brain regions—one of the key ideas of the psychological constructionist hypothesis. To overcome the limitations of traditional methods, this study provides an in-depth theoretical analysis of how to maximize interactions and information fusion among brain regions. Building on the results of this analysis, we propose to identify the hierarchical emotional areas in the human brain through multi-source information fusion and graph machine learning methods. Comprehensive experiments reveal that the identified hierarchical emotional areas, from lower to higher levels, primarily facilitate the fundamental process of emotion perception, the construction of basic psychological operations, and the coordination and integration of these operations. Overall, our findings provide unique insights into the brain mechanisms underlying specific emotions based on the psychological constructionist hypothesis.

Cross-Modal Federated Human Activity Recognition.

Federated human activity recognition (FHAR) has attracted much attention due to its great potential in privacy protection. Existing FHAR methods can collaboratively learn a global activity recognition model based on unimodal or multimodal data distributed on different local clients. However, it is still questionable whether existing methods can work well in a more common scenario where local data are from different modalities, e.g., some local clients may provide motion signals while others can only provide visual data. In this article, we study a new problem of cross-modal federated human activity recognition (CM-FHAR), which is conducive to promote the large-scale use of the HAR model on more local devices. CM-FHAR has at least three dedicated challenges: 1) distributive common cross-modal feature learning, 2) modality-dependent discriminate feature learning, 3) modality imbalance issue. To address these challenges, we propose a modality-collaborative activity recognition network (MCARN), which can comprehensively learn a global activity classifier shared across all clients and multiple modality-dependent private activity classifiers. To produce modality-agnostic and modality-specific features, we learn an altruistic encoder and an egocentric encoder under the constraint of a separation loss and an adversarial modality discriminator collaboratively learned in hyper-sphere. To address the modality imbalance issue, we propose an angular margin adjustment scheme to improve the modality discriminator on modality-imbalanced data by enhancing the intra-modality compactness of the dominant modality and increase the inter-modality discrepancy. Moreover, we propose a relation-aware global-local calibration mechanism to constrain class-level pairwise relationships for the parameters of the private classifier. Finally, through decentralized optimization with alternative steps of adversarial local updating and modality-aware global aggregation, the proposed MCARN obtains state-of-the-art performance on both modality-balanced and modality-imbalanced data.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.