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1.
Brief Bioinform ; 24(4)2023 07 20.
Artículo en Inglés | MEDLINE | ID: mdl-37280190

RESUMEN

Clustering methods have been widely used in single-cell RNA-seq data for investigating tumor heterogeneity. Since traditional clustering methods fail to capture the high-dimension methods, deep clustering methods have drawn increasing attention these years due to their promising strengths on the task. However, existing methods consider either the attribute information of each cell or the structure information between different cells. In other words, they cannot sufficiently make use of all of this information simultaneously. To this end, we propose a novel single-cell deep fusion clustering model, which contains two modules, i.e. an attributed feature clustering module and a structure-attention feature clustering module. More concretely, two elegantly designed autoencoders are built to handle both features regardless of their data types. Experiments have demonstrated the validity of the proposed approach, showing that it is efficient to fuse attributes, structure, and attention information on single-cell RNA-seq data. This work will be further beneficial for investigating cell subpopulations and tumor microenvironment. The Python implementation of our work is now freely available at https://github.com/DayuHuu/scDFC.


Asunto(s)
Algoritmos , Análisis de Expresión Génica de una Sola Célula , Análisis de Secuencia de ARN/métodos , Análisis de la Célula Individual/métodos , Análisis por Conglomerados , Perfilación de la Expresión Génica/métodos
2.
J Environ Manage ; 339: 117899, 2023 Aug 01.
Artículo en Inglés | MEDLINE | ID: mdl-37054592

RESUMEN

Foundry dust is the main refractory solid waste in the foundry industry, and its resource utilization is a top priority for realizing green and cleaner production. The massive amount of coal dust in foundry dust is a potential impediment to the recycling of foundry dust, and the efficient separation of coal dust is crucial to solving the above problems. In this paper, the flotation separation of coal dust from foundry dust enhanced by pre-soaking assisted mechanical stirring was reported. The influence of pre-soaking, stirring speed, and stirring time on the flotation results of foundry dust was systematically studied, and the enhancement mechanism was analyzed based on the microstructure and hydrophobicity of foundry dust. Flotation kinetics experiments with different stirring time were conducted to clarify the flotation process of foundry dust. The results indicate that the pre-soaking of foundry dust is beneficial for the water-absorbing swelling of clay minerals coated on the surface of coal dust, and the subsequent mechanical stirring pretreatment promotes the monomer dissociation of foundry dust, which increases the contact angle of foundry dust and considerably improves the flotation results. The optimal stirring speed and stirring time were 2400 rpm and 30 min, respectively. The classical first-order model presented the highest degree of fitting with the flotation data among the five flotation kinetics models. Therefore, the pre-soaking assisted mechanical stirring is a promising method for promoting flotation separation and the complete recycling of foundry dust.


Asunto(s)
Carbón Mineral , Polvo , Residuos Sólidos/análisis , Minerales , Reciclaje/métodos
3.
Expert Syst Appl ; 213: 118885, 2023 Mar 01.
Artículo en Inglés | MEDLINE | ID: mdl-36188673

RESUMEN

With the amount of medical waste rapidly increasing since the corona virus disease 2019 (COVID-19) pandemic, medical waste treatment risk evaluation has become an important task. The transportation of medical waste is an essential process of medical waste treatment. This paper aims to develop an integrated model to evaluate COVID-19 medical waste transportation risk by integrating an extended type-2 fuzzy total interpretive structural model (TISM) with a Bayesian network (BN). First, an interval type-2 fuzzy based transportation risk rating scale is introduced to help experts express uncertain evaluation information, in which a new double alpha-cut method is developed for the defuzzification of the interval type-2 fuzzy numbers (IT2FNs). Second, TISM is combined with IT2FNs to construct a hierarchical structural model of COVID-19 medical waste transportation risk factors under a high uncertain environment; a new bidirectional extraction method is proposed to describe the hierarchy of risk factors more reasonably and accurately. Third, the BN is integrated with IT2FNs to make a comprehensive medical waste transportation risk evaluation, including identifying the sensitive factors and diagnosing the event's causation. Then, a case study of COVID-19 medical waste transportation is displayed to demonstrate the effectiveness of the proposed model. Further, a comparison of the proposed model with the traditional TISM and BN model is conducted to stress the advantages of the proposed model.

4.
Environ Chem Lett ; 20(1): 119-129, 2022.
Artículo en Inglés | MEDLINE | ID: mdl-34512224

RESUMEN

The coronavirus disease 2019 (COVID-19) pandemic is still spreading all over the world. Although China quickly brought the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) under control in 2020, sporadic outbreaks have recurred from time to time. Outbreaks since June 2020 have suggested that the imported cold food supply chain is a major cause for the recurrence and spread of COVID-19. Here we review recurrent outbreaks in China from June 2020 to March 2021, and we analyse the main causes for recurrence and transmission by the supply of imported cold food from port to fork. Contaminated cold food or food packaging material can transmit the virus through 'person-to-thing-to-person', by contrast with the classical 'person-to-person' pathway. We decribe safety precautions for the food system, operating environment and people along the cold chain logistics. Surface disinfection and nucleic acid inspection are needed in each stage of the logistics of imported cold food supply.

5.
Entropy (Basel) ; 22(12)2020 Dec 15.
Artículo en Inglés | MEDLINE | ID: mdl-33333933

RESUMEN

This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation. In order to overcome the drawbacks of current FMEA, this paper proposes a novel risk prioritization method based on cumulative prospect theory and type-2 intuitionistic fuzzy VIKOR approach. Type-2 intuitionistic VIKOR handles the combination of the risk factors with their entropy weight. Triangular fuzzy number intuitionistic fuzzy numbers (TFNIFNs) applied as type-2 intuitionistic fuzzy numbers (Type-2 IFNs) are adopted to depict the uncertainty in the risk analysis. Then, cumulative prospect theory is employed to deal with the FMEA team member's risk sensitiveness and decision-making psychological behavior. Finally, a numerical example of the railway train bogie system is selected to illustrate the application and feasibility of the proposed extended FMEA model in this paper, and a comparison study is also performed to validate the practicability and effectiveness of the novel FMEA model. On this basis, this study can provide guidance for the risk prioritization of railway trains and indicate a direction for further research of risk management of rail traffic.

6.
Sensors (Basel) ; 19(19)2019 Sep 24.
Artículo en Inglés | MEDLINE | ID: mdl-31554333

RESUMEN

Video anomaly detection is widely applied in modern society, which is achieved by sensors such as surveillance cameras. This paper learns anomalies by exploiting videos under the fully unsupervised setting. To avoid massive computation caused by back-prorogation in existing methods, we propose a novel efficient three-stage unsupervised anomaly detection method. In the first stage, we adopt random projection instead of autoencoder or its variants in previous works. Then we formulate the optimization goal as a least-square regression problem which has a closed-form solution, leading to less computational cost. The discriminative reconstruction losses of normal and abnormal events encourage us to roughly estimate normality that can be further sifted in the second stage with one-class support vector machine. In the third stage, to eliminate the instability caused by random parameter initializations, ensemble technology is performed to combine multiple anomaly detectors' scores. To the best of our knowledge, it is the first time that unsupervised ensemble technology is introduced to video anomaly detection research. As demonstrated by the experimental results on several video anomaly detection benchmark datasets, our algorithm robustly surpasses the recent unsupervised methods and performs even better than some supervised approaches. In addition, we achieve comparable performance contrast with the state-of-the-art unsupervised method with much less running time, indicating the effectiveness, efficiency, and robustness of our proposed approach.

7.
J Org Chem ; 80(8): 3737-44, 2015 Apr 17.
Artículo en Inglés | MEDLINE | ID: mdl-25710256

RESUMEN

A new route from benzylic imines permits the synthesis of 1,2-borazaronaphthalenes in good yields. The reaction involves formation of the enamidyl dibromoborane, which undergoes base-promoted borylation of the nearby aromatic C-H bond. Electrophilic attack of the boron species onto the benzylic arene is supported by the slow borylation of arenes substituted with electron-withdrawing groups. The resultant boron bromides can be easily substituted with lithium reagents to provide a range of products. The electronic properties of these 1,2-borazaronaphthalene derivatives have been investigated by UV-vis and fluorescence spectroscopy.

8.
Appl Opt ; 54(11): 3478-83, 2015 Apr 10.
Artículo en Inglés | MEDLINE | ID: mdl-25967340

RESUMEN

In this paper, a metamaterial terahertz (THz) switch based on a split-ring resonator embedded with photoconductive silicon is presented and numerically investigated. Simulation results show that the switch works at two different resonant modes with different pump light powers and that the response time of the switch is less than 1 ps. By defining the switching window as the frequency range where the transmission magnitude of the ON state is one order of magnitude higher than the OFF state, a switching window ranging from 1.26 to 1.49 THz is obtained. The large modulation depth of the switch is due to the large separations of the maximum and minimum transmissions, which are 0.89 and 0.01, respectively. Particularly, the switch is frequency tunable by changing the thickness and permittivity of the dielectric layer.

9.
Artículo en Inglés | MEDLINE | ID: mdl-38215316

RESUMEN

With the development of various applications, such as recommendation systems and social network analysis, graph data have been ubiquitous in the real world. However, graphs usually suffer from being absent during data collection due to copyright restrictions or privacy-protecting policies. The graph absence could be roughly grouped into attribute-incomplete and attribute-missing cases. Specifically, attribute-incomplete indicates that a portion of the attribute vectors of all nodes are incomplete, while attribute-missing indicates that all attribute vectors of partial nodes are missing. Although various graph imputation methods have been proposed, none of them is custom-designed for a common situation where both types of graph absence exist simultaneously. To fill this gap, we develop a novel graph imputation network termed revisiting initializing then refining (RITR), where both attribute-incomplete and attribute-missing samples are completed under the guidance of a novel initializing-then-refining imputation criterion. Specifically, to complete attribute-incomplete samples, we first initialize the incomplete attributes using Gaussian noise before network learning, and then introduce a structure-attribute consistency constraint to refine incomplete values by approximating a structure-attribute correlation matrix to a high-order structure matrix. To complete attribute-missing samples, we first adopt structure embeddings of attribute-missing samples as the embedding initialization, and then refine these initial values by adaptively aggregating the reliable information of attribute-incomplete samples according to a dynamic affinity structure. To the best of our knowledge, this newly designed method is the first end-to-end unsupervised framework dedicated to handling hybrid-absent graphs. Extensive experiments on six datasets have verified that our methods consistently outperform the existing state-of-the-art competitors. Our source code is available at https://github.com/WxTu/RITR.

10.
Artículo en Inglés | MEDLINE | ID: mdl-38889020

RESUMEN

Since the rapid progress in multimedia and sensor technologies, multiview clustering (MVC) has become a prominent research area within machine learning and data mining, experiencing significant advancements over recent decades. MVC is distinguished from single-view clustering by its ability to integrate complementary information from multiple distinct data perspectives and enhance clustering performance. However, the efficacy of MVC methods is predicated on the availability of complete views for all samples-an assumption that frequently fails in practical scenarios where data views are often incomplete. To surmount this challenge, various approaches to incomplete MVC (IMVC) have been proposed, with deep neural networks emerging as a favored technique for their representation learning ability. Despite their promise, previous methods commonly adopt sample-level (e.g., features) or affinity-level (e.g., graphs) guidance, neglecting the discriminative label-level guidance (i.e., pseudo-labels). In this work, we propose a novel deep IMVC method termed pseudo-label propagation for deep IMVC (PLP-IMVC), which integrates high-quality pseudo-labels from the complete subset of incomplete data with deep label propagation networks to obtain improved clustering results. In particular, we first design a local model (PLP-L) that leverages pseudo-labels to their fullest extent. Then, we propose a global model (PLP-G) that exploits manifold regularization to mitigate the label noises, promote view-level information fusion, and learn discriminative unified representations. Experimental results across eight public benchmark datasets and three evaluation metrics prove our method's efficacy, demonstrating superior performance compared to 18 advanced baseline methods.

11.
IEEE Trans Image Process ; 33: 2995-3008, 2024.
Artículo en Inglés | MEDLINE | ID: mdl-38640047

RESUMEN

Multi-view clustering (MVC) has attracted broad attention due to its capacity to exploit consistent and complementary information across views. This paper focuses on a challenging issue in MVC called the incomplete continual data problem (ICDP). Specifically, most existing algorithms assume that views are available in advance and overlook the scenarios where data observations of views are accumulated over time. Due to privacy considerations or memory limitations, previous views cannot be stored in these situations. Some works have proposed ways to handle this problem, but all of them fail to address incomplete views. Such an incomplete continual data problem (ICDP) in MVC is difficult to solve since incomplete information with continual data increases the difficulty of extracting consistent and complementary knowledge among views. We propose Fast Continual Multi-View Clustering with Incomplete Views (FCMVC-IV) to address this issue. Specifically, the method maintains a scalable consensus coefficient matrix and updates its knowledge with the incoming incomplete view rather than storing and recomputing all the data matrices. Considering that the given views are incomplete, the newly collected view might contain samples that have yet to appear; two indicator matrices and a rotation matrix are developed to match matrices with different dimensions. In addition, we design a three-step iterative algorithm to solve the resultant problem with linear complexity and proven convergence. Comprehensive experiments conducted on various datasets demonstrate the superiority of FCMVC-IV over the competing approaches. The code is publicly available at https://github.com/wanxinhang/FCMVC-IV.

12.
Artículo en Inglés | MEDLINE | ID: mdl-38717883

RESUMEN

While humans can excel at image classification tasks by comparing a few images, existing metric-based few-shot classification methods are still not well adapted to novel tasks. Performance declines rapidly when encountering new patterns, as feature embeddings cannot effectively encode discriminative properties. Moreover, existing matching methods inadequately utilize support set samples, focusing only on comparing query samples to category prototypes without exploiting contrastive relationships across categories for discriminative features. In this work, we propose a method where query samples select their most category-representative features for matching, making feature embeddings adaptable and category-related. We introduce a category alignment mechanism (CAM) to align query image features with different categories. CAM ensures features chosen for matching are distinct and strongly correlated to intra-and inter-contrastive relationships within categories, making extracted features highly related to their respective categories. CAM is parameter-free, requires no extra training to adapt to new tasks, and adjusts features for matching when task categories change. We also implement a cross-validation-based feature selection technique for support samples, generating more discriminative category prototypes. We implement two versions of inductive and transductive inference and conduct extensive experiments on six datasets to demonstrate the effectiveness of our algorithm. The results indicate that our method consistently yields performance improvements on benchmark tasks and surpasses the current state-of-the-art methods.

13.
Artículo en Inglés | MEDLINE | ID: mdl-38236668

RESUMEN

The success of multiview raw data mining relies on the integrity of attributes. However, each view faces various noises and collection failures, which leads to a condition that attributes are only partially available. To make matters worse, the attributes in multiview raw data are composed of multiple forms, which makes it more difficult to explore the structure of the data especially in multiview clustering task. Due to the missing data in some views, the clustering task on incomplete multiview data confronts the following challenges, namely: 1) mining the topology of missing data in multiview is an urgent problem to be solved; 2) most approaches do not calibrate the complemented representations with common information of multiple views; and 3) we discover that the cluster distributions obtained from incomplete views have a cluster distribution unaligned problem (CDUP) in the latent space. To solve the above issues, we propose a deep clustering framework based on subgraph propagation and contrastive calibration (SPCC) for incomplete multiview raw data. First, the global structural graph is reconstructed by propagating the subgraphs generated by the complete data of each view. Then, the missing views are completed and calibrated under the guidance of the global structural graph and contrast learning between views. In the latent space, we assume that different views have a common cluster representation in the same dimension. However, in the unsupervised condition, the fact that the cluster distributions of different views do not correspond affects the information completion process to use information from other views. Finally, the complemented cluster distributions for different views are aligned by contrastive learning (CL), thus solving the CDUP in the latent space. Our method achieves advanced performance on six benchmarks, which validates the effectiveness and superiority of our SPCC.

14.
Artículo en Inglés | MEDLINE | ID: mdl-38557633

RESUMEN

Multi-View clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity, preventing them from being applied to large-scale tasks. Multi-View clustering via matrix factorization is a representative to address this issue. However, most of them map the data matrices into a fixed dimension, limiting the model's expressiveness. Moreover, a range of methods suffers from a two-step process, i.e., multimodal learning and the subsequent k -means, inevitably causing a suboptimal clustering result. In light of this, we propose a one-step multi-view clustering with diverse representation (OMVCDR) method, which incorporates multi-view learning and k -means into a unified framework. Specifically, we first project original data matrices into various latent spaces to attain comprehensive information and auto-weight them in a self-supervised manner. Then, we directly use the information matrices under diverse dimensions to obtain consensus discrete clustering labels. The unified work of representation learning and clustering boosts the quality of the final results. Furthermore, we develop an efficient optimization algorithm with proven convergence to solve the resultant problem. Comprehensive experiments on various datasets demonstrate the promising clustering performance of our proposed method. The code is publicly available at https://github.com/wanxinhang/OMVCDR.

15.
Artículo en Inglés | MEDLINE | ID: mdl-38648135

RESUMEN

Temporal graph learning aims to generate high-quality representations for graph-based tasks with dynamic information, which has recently garnered increasing attention. In contrast to static graphs, temporal graphs are typically organized as node interaction sequences over continuous time rather than an adjacency matrix. Most temporal graph learning methods model current interactions by incorporating historical neighborhood. However, such methods only consider first-order temporal information while disregarding crucial high-order structural information, resulting in suboptimal performance. To address this issue, we propose a self-supervised method called S2T for temporal graph learning, which extracts both temporal and structural information to learn more informative node representations. Notably, the initial node representations combine first-order temporal and high-order structural information differently to calculate two conditional intensities. An alignment loss is then introduced to optimize the node representations, narrowing the gap between the two intensities and making them more informative. Concretely, in addition to modeling temporal information using historical neighbor sequences, we further consider structural knowledge at both local and global levels. At the local level, we generate structural intensity by aggregating features from high-order neighbor sequences. At the global level, a global representation is generated based on all nodes to adjust the structural intensity according to the active statuses on different nodes. Extensive experiments demonstrate that the proposed model S2T achieves at most 10.13% performance improvement compared with the state-of-the-art competitors on several datasets.

16.
Artículo en Inglés | MEDLINE | ID: mdl-38602855

RESUMEN

Existing multiple kernel clustering (MKC) algorithms have two ubiquitous problems. From the theoretical perspective, most MKC algorithms lack sufficient theoretical analysis, especially the consistency of learned parameters, such as the kernel weights. From the practical perspective, the high complexity makes MKC unable to handle large-scale datasets. This paper tries to address the above two issues. We first make a consistency analysis of an influential MKC method named Simple Multiple Kernel k-Means (SimpleMKKM). Specifically, suppose that ∧γn are the kernel weights learned by SimpleMKKM from the training samples. We also define the expected version of SimpleMKKM and denote its solution as γ*. We establish an upper bound of ||∧γn-γ*||∞ in the order of ~O(1/√n), where n is the sample number. Based on this result, we also derive its excess clustering risk calculated by a standard clustering loss function. For the large-scale extension, we replace the eigen decomposition of SimpleMKKM with singular value decomposition (SVD). Consequently, the complexity can be decreased to O(n) such that SimpleMKKM can be implemented on large-scale datasets. We then deduce several theoretical results to verify the approximation ability of the proposed SVD-based method. The results of comprehensive experiments demonstrate the superiority of the proposed method. The code is publicly available at https://github.com/weixuan-liang/SVD-based-SimpleMKKM.

17.
Artículo en Inglés | MEDLINE | ID: mdl-38315591

RESUMEN

Few-shot relation reasoning on knowledge graphs (FS-KGR) is an important and practical problem that aims to infer long-tail relations and has drawn increasing attention these years. Among all the proposed methods, self-supervised learning (SSL) methods, which effectively extract the hidden essential inductive patterns relying only on the support sets, have achieved promising performance. However, the existing SSL methods simply cut down connections between high-frequency and long-tail relations, which ignores the fact, i.e., the two kinds of information could be highly related to each other. Specifically, we observe that relations with similar contextual meanings, called aliasing relations (ARs), may have similar attributes. In other words, the ARs of the target long-tail relation could be in high-frequency, and leveraging such attributes can largely improve the reasoning performance. Based on the interesting observation above, we proposed a novel Self-supervised learning model by leveraging Aliasing Relations to assist FS-KGR, termed . Specifically, we propose a graph neural network (GNN)-based AR-assist module to encode the ARs. Besides, we further provide two fusion strategies, i.e., simple summation and learnable fusion, to fuse the generated representations, which contain extra abundant information underlying the ARs, into the self-supervised reasoning backbone for performance enhancement. Extensive experiments on three few-shot benchmarks demonstrate that achieves state-of-the-art (SOTA) performance compared with other methods in most cases.

18.
Artículo en Inglés | MEDLINE | ID: mdl-38941209

RESUMEN

Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the usage of KGs in many AI applications, such as question answering, recommendation systems, and etc. According to the graph types, existing KGR models can be roughly divided into three categories, i.e., static models, temporal models, and multi-modal models. Early works in this domain mainly focus on static KGR, and recent works try to leverage the temporal and multi-modal information, which are more practical and closer to real-world. However, no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a first survey for knowledge graph reasoning tracing from static to temporal and then to multi-modal KGs. Concretely, the models are reviewed based on bi-level taxonomy, i.e., top-level (graph types) and base-level (techniques and scenarios). Besides, the performances, as well as datasets, are summarized and presented. Moreover, we point out the challenges and potential opportunities to enlighten the readers. The corresponding open-source repository is shared on GitHub https://github.com/LIANGKE23/Awesome-Knowledge-Graph-Reasoning.

19.
IEEE Trans Pattern Anal Mach Intell ; 45(4): 5174-5186, 2023 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-35969570

RESUMEN

We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. To optimize it, we equivalently rewrite the minimization-maximization formulation as a minimization of an optimal value function, prove its differenentiablity, and design a reduced gradient descent algorithm to decrease it. Furthermore, we prove that the resultant solution of SimpleMKKM is the global optimum. We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error. After that, we develop extensive experiments to investigate the proposed SimpleMKKM from the perspectives of clustering accuracy, advantage on the formulation and optimization, variation of the learned consensus clustering matrix with iterations, clustering performance with varied number of samples and base kernels, analysis of the learned kernel weight, the running time and the global convergence. The experimental study demonstrates the effectiveness of the proposed SimpleMKKM by considerably and consistently outperforming state of the art multiple kernel clustering alternatives. In addition, the ablation study shows that the improved clustering performance is contributed by both the novel formulation and new optimization. Our work provides a more effective approach to integrate multi-view data for clustering, and this could trigger novel research on multiple kernel clustering. The source code and data for SimpleMKKM are available at https://github.com/xinwangliu/SimpleMKKMcodes/.

20.
IEEE Trans Pattern Anal Mach Intell ; 45(7): 8566-8576, 2023 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-37018308

RESUMEN

The newly proposed localized simple multiple kernel k-means (SimpleMKKM) provides an elegant clustering framework which sufficiently considers the potential variation among samples. Although achieving superior clustering performance in some applications, we observe that it is required to pre-specify an extra hyperparameter, which determines the size of the localization. This greatly limits its availability in practical applications since there is a little guideline to set a suitable hyperparameter in clustering tasks. To overcome this issue, we firstly parameterize a neighborhood mask matrix as a quadratic combination of a set of pre-computed base neighborhood mask matrices, which corresponds to a group of hyperparameters. We then propose to jointly learn the optimal coefficient of these neighborhood mask matrices together with the clustering tasks. By this way, we obtain the proposed hyperparameter-free localized SimpleMKKM, which corresponds to a more intractable minimization-minimization-maximization optimization problem. We rewrite the resultant optimization as a minimization of an optimal value function, prove its differentiability, and develop a gradient based algorithm to solve it. Furthermore, we theoretically prove that the obtained optimum is the global one. Comprehensive experimental study on several benchmark datasets verifies its effectiveness, comparing with several state-of-the-art counterparts in the recent literature. The source code for hyperparameter-free localized SimpleMKKM is available at https://github.com/xinwangliu/SimpleMKKMcodes/.

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