Multiple Kernel k-Means with Incomplete Kernels

Incomplete Data Meets Uncoupled Case: A Challenging Task of Multiview Clustering

Incomplete multiview clustering (IMC) methods have achieved remarkable progress by exploring the complementary information and consensus representation of incomplete multiview data. However, to our best knowledge, none of the existing methods attempts to handle the uncoupled and incomplete data simultaneously, which affects their generalization ability in real-world scenarios. For uncoupled incomplete data, the unclear and partial cross-view correlation introduces the difficulty to explore the complementary information between views, which results in the unpromising clustering performance for the existing multiview clustering methods. Besides, the presence of hyperparameters limits their applications. To fill these gaps, a novel uncoupled IMC (UIMC) method is proposed in this article. Specifically, UIMC develops a joint framework for feature inferring and recoupling. The high-order correlations of all views are explored by performing a tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN) on recoupled and inferred self-representation matrices. Moreover, all hyperparameters of the UIMC method are updated in an exploratory manner. Extensive experiments on six widely used real-world datasets have confirmed the superiority of the proposed method in handling the uncoupled incomplete multiview data compared with the state-of-the-art methods.

Low-Rank Graph Completion-Based Incomplete Multiview Clustering

In order to reduce the negative effect of missing data on clustering, incomplete multiview clustering (IMVC) has become an important research content in machine learning. At present, graph-based methods are widely used in IMVC, but these methods still have some defects. First, some of the methods overlook potential relationships across views. Second, most of the methods depend on local structure information and ignore the global structure information. Third, most of the methods cannot use both global structure information and potential information across views to adaptively recover the incomplete relationship structure. To address the above issues, we propose a unified optimization framework to learn reasonable affinity relationships, called low-rank graph completion-based IMVC (LRGR_IMVC). 1) Our method introduces adaptive graph embedding to effectively explore the potential relationship among views; 2) we append a low-rank constraint to adequately exploit the global structure information among views; and 3) this method unites related information within views, potential information across views, and global structure information to adaptively recover the incomplete graph structure and obtain complete affinity relationships. Experimental results on several commonly used datasets show that the proposed method achieves better clustering performance significantly than some of the most advanced methods.

Circulating tumor DNA- and cancer tissue-based next-generation sequencing reveals comparable consistency in targeted gene mutations for advanced or metastatic non-small cell lung cancer

BACKGROUND

Molecular subtyping is an essential complementarity after pathological analyses for targeted therapy. This study aimed to investigate the consistency of next-generation sequencing (NGS) results between circulating tumor DNA (ctDNA)-based and tissue-based in non-small cell lung cancer (NSCLC) and identify the patient characteristics that favor ctDNA testing.

METHODS

Patients who diagnosed with NSCLC and received both ctDNA- and cancer tissue-based NGS before surgery or systemic treatment in Lung Cancer Center, Sichuan University West China Hospital between December 2017 and August 2022 were enrolled. A 425-cancer panel with a HiSeq 4000 NGS platform was used for NGS. The unweighted Cohen's kappa coefficient was employed to discriminate the high-concordance group from the low-concordance group with a cutoff value of 0.6. Six machine learning models were used to identify patient characteristics that relate to high concordance between ctDNA-based and tissue-based NGS.

RESULTS

A total of 85 patients were enrolled, of which 22.4% (19/85) had stage III disease and 56.5% had stage IV disease. Forty-four patients (51.8%) showed consistent gene mutation types between ctDNA-based and tissue-based NGS, while one patient (1.2%) tested negative in both approaches. Advanced diseases and metastases to other organs would be fit for the ctDNA-based NGS, and the generalized linear model showed that T stage, M stage, and tumor mutation burden were the critical discriminators to predict the consistency of results between ctDNA-based and tissue-based NGS.

CONCLUSION

ctDNA-based NGS showed comparable detection performance in the targeted gene mutations compared with tissue-based NGS, and it could be considered in advanced or metastatic NSCLC.

Memory and Communication Efficient Federated Kernel k-Means

A federated kernel k -means (FedKKM) algorithm is developed in this article to conduct distributed clustering with low memory consumption on user devices. In FedKKM, a federated eigenvector approximation (FEA) algorithm is designed to iteratively determine the low-dimensional approximate vectors of the transformed feature vectors, using only low-dimensional random feature vectors. To maintain high communication efficiency in each iteration of FEA, a communication-efficient Lanczos algorithm (CELA) is further designed in FEA to reduce the communication cost. Based on the low-dimensional approximate vectors, the clustering result is obtained by leveraging a distributed linear k -means algorithm. A theoretical analysis shows that: 1) FEA has a convergence rate of O(1/T) , where T is the number of iterations; 2) the scalability of FedKKM is not affected by the dataset size since the communication cost of FedKKM is independent of the number of users' data; and 3) FedKKM is a (1+ϵ) approximation algorithm. The experimental results show that FedKKM achieves the comparable clustering quality to that of a centralized kernel k -means. Compared with state-of-the-art schemes, FedKKM reduces the memory consumption on user devices by up to 94% and also reduces the communication cost by more than 40%.

Incomplete Multiple Kernel Alignment Maximization for Clustering

Multiple kernel alignment (MKA) maximization criterion has been widely applied into multiple kernel clustering (MKC) and many variants have been recently developed. Though demonstrating superior clustering performance in various applications, it is observed that none of them can effectively handle incomplete MKC, where parts or all of the pre-specified base kernel matrices are incomplete. To address this issue, we propose to integrate the imputation of incomplete kernel matrices and MKA maximization for clustering into a unified learning framework. The clustering of MKA maximization guides the imputation of incomplete kernel elements, and the completed kernel matrices are in turn combined to conduct the subsequent MKC. These two procedures are alternately performed until convergence. By this way, the imputation and MKC processes are seamlessly connected, with the aim to achieve better clustering performance. Besides theoretically analyzing the clustering generalization error bound, we empirically evaluate the clustering performance on several multiple kernel learning (MKL) benchmark datasets, and the results indicate the superiority of our algorithm over existing state-of-the-art counterparts. Our codes and data are publicly available at https://xinwangliu.github.io/.

Refining Graph Structure for Incomplete Multi-View Clustering

As a challenging problem, incomplete multi-view clustering (MVC) has drawn much attention in recent years. Most of the existing methods contain the feature recovering step inevitably to obtain the clustering result of incomplete multi-view datasets. The extra target of recovering the missing feature in the original data space or common subspace is difficult for unsupervised clustering tasks and could accumulate mistakes during the optimization. Moreover, the biased error is not taken into consideration in the previous graph-based methods. The biased error represents the unexpected change of incomplete graph structure, such as the increase in the intra-class relation density and the missing local graph structure of boundary instances. It would mislead those graph-based methods and degrade their final performance. In order to overcome these drawbacks, we propose a new graph-based method named Graph Structure Refining for Incomplete MVC (GSRIMC). GSRIMC avoids recovering feature steps and just fully explores the existing subgraphs of each view to produce superior clustering results. To handle the biased error, the biased error separation is the core step of GSRIMC. In detail, GSRIMC first extracts basic information from the precomputed subgraph of each view and then separates refined graph structure from biased error with the help of tensor nuclear norm. Besides, cross-view graph learning is proposed to capture the missing local graph structure and complete the refined graph structure based on the complementary principle. Extensive experiments show that our method achieves better performance than other state-of-the-art baselines.

Local Sample-Weighted Multiple Kernel Clustering With Consensus Discriminative Graph

Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proven to be of vital significance in applications since the unreliable distant-distance similarity estimation would degrade clustering performance. Although existing localized MKC algorithms exhibit improved performance compared with globally designed competitors, most of them widely adopt the KNN mechanism to localize kernel matrix by accounting for τ -nearest neighbors. However, such a coarse manner follows an unreasonable strategy that the ranking importance of different neighbors is equal, which is impractical in applications. To alleviate such problems, this article proposes a novel local sample-weighted MKC (LSWMKC) model. We first construct a consensus discriminative affinity graph in kernel space, revealing the latent local structures. Furthermore, an optimal neighborhood kernel for the learned affinity graph is output with naturally sparse property and clear block diagonal structure. Moreover, LSWMKC implicitly optimizes adaptive weights on different neighbors with corresponding samples. Experimental results demonstrate that our LSWMKC possesses better local manifold representation and outperforms existing kernel or graph-based clustering algorithms. The source code of LSWMKC can be publicly accessed from https://github.com/liliangnudt/LSWMKC.

Fast Self-Guided Multi-View Subspace Clustering

Multi-view subspace clustering is an important topic in cluster analysis. Its aim is to utilize the complementary information conveyed by multiple views of objects to be clustered. Recently, view-shared anchor learning based multi-view clustering methods have been developed to speed up the learning of common data representation. Although widely applied to large-scale scenarios, most of the existing approaches are still faced with two limitations. First, they do not pay sufficient consideration on the negative impact caused by certain noisy views with unclear clustering structures. Second, many of them only focus on the multi-view consistency, yet are incapable of capturing the cross-view diversity. As a result, the learned complementary features may be inaccurate and adversely affect clustering performance. To solve these two challenging issues, we propose a Fast Self-guided Multi-view Subspace Clustering (FSMSC) algorithm which skillfully integrates the view-shared anchor learning and global-guided-local self-guidance learning into a unified model. Such an integration is inspired by the observation that the view with clean clustering structures will play a more crucial role in grouping the clusters when the features of all views are concatenated. Specifically, we first learn a locally-consistent data representation shared by all views in the local learning module, then we learn a globally-discriminative data representation from multi-view concatenated features in the global learning module. Afterwards, a feature selection matrix constrained by the l2,1 -norm is designed to construct a guidance from global learning to local learning. In this way, the multi-view consistent and diverse information can be simultaneously utilized and the negative impact caused by noisy views can be overcame to some extent. Extensive experiments on different datasets demonstrate the effectiveness of our proposed fast self-guided learning model, and its promising performance compared to both, the state-of-the-art non-deep and deep multi-view clustering algorithms. The code of this paper is available at https://github.com/chenzhe207/FSMSC.

A simulation study on missing data imputation for dichotomous variables using statistical and machine learning methods

The problem of missing data, particularly for dichotomous variables, is a common issue in medical research. However, few studies have focused on the imputation methods of dichotomous data and their performance, as well as the applicability of these imputation methods and the factors that may affect their performance. In the arrangement of application scenarios, different missing mechanisms, sample sizes, missing rates, the correlation between variables, value distributions, and the number of missing variables were considered. We used data simulation techniques to establish a variety of different compound scenarios for missing dichotomous variables and conducted real-data validation on two real-world medical datasets. We comprehensively compared the performance of eight imputation methods (mode, logistic regression (LogReg), multiple imputation (MI), decision tree (DT), random forest (RF), k-nearest neighbor (KNN), support vector machine (SVM), and artificial neural network (ANN)) in each scenario. Accuracy and mean absolute error (MAE) were applied to evaluating their performance. The results showed that missing mechanisms, value distributions and the correlation between variables were the main factors affecting the performance of imputation methods. Machine learning-based methods, especially SVM, ANN, and DT, achieved relatively high accuracy with stable performance and were of potential applicability. Researchers should explore the correlation between variables and their distribution pattern in advance and prioritize machine learning-based methods for practical applications when encountering dichotomous missing data.

Hyper-Laplacian Regularized Multi-View Clustering with Exclusive L21 Regularization and Tensor Log-Determinant Minimization Approach

Multi-view clustering aims to capture the multiple views inherent information by identifying the data clustering that reflects distinct features of datasets. Being a consensus in literature that different views of a dataset share a common latent structure, most existing multi-view subspace learning methods rely on the nuclear norm to seek the low-rank representation of the underlying subspace. However, the nuclear norm often fails to distinguish the variance of features for each cluster due to its convexity nature and data tends to fall in multiple non-linear subspaces for multi-dimensional datasets. To address these problems, we propose a new and novel multi-view clustering method (HL-L21-TLD-MSC) that unifies the Hyper-Laplacian (HL) and exclusive ℓ 2, 1 (L21) regularization with Tensor Log-Determinant Rank Minimization (TLD) setting. Specifically, the hyper-Laplacian regularization maintains the local geometrical structure that makes the estimation prune to nonlinearities, and the mixed ℓ 2, 1 and ℓ 1, 2 regularization provides the joint sparsity within-cluster as well as the exclusive sparsity between-cluster. Furthermore, a log-determinant function is used as a tighter tensor rank approximation to discriminate the dimension of features. An efficient alternating algorithm is then derived to optimize the proposed model, and the construction of a convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments are conducted on ten well-known datasets to demonstrate that the proposed approach outperforms the existing state-of-the-art approaches with various scenarios, in which, six of them achieve perfect results under our framework developed in this paper, demonstrating highly effectiveness for the proposed approach.

Performance Analysis and Applications of Finite-Time ZNN Models With Constant/Fuzzy Parameters for TVQPEI

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value.

Multiview Subspace Clustering via Co-Training Robust Data Representation

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

Community Detection in Semantic Networks: A Multi-View Approach

The semantic social network is a complex system composed of nodes, links, and documents. Traditional semantic social network community detection algorithms only analyze network data from a single view, and there is no effective representation of semantic features at diverse levels of granularity. This paper proposes a multi-view integration method for community detection in semantic social network. We develop a data feature matrix based on node similarity and extract semantic features from the views of word frequency, keyword, and topic, respectively. To maximize the mutual information of each view, we use the robustness of L21-norm and F-norm to construct an adaptive loss function. On this foundation, we construct an optimization expression to generate the unified graph matrix and output the community structure with multiple views. Experiments on real social networks and benchmark datasets reveal that in semantic information analysis, multi-view is considerably better than single-view, and the performance of multi-view community detection outperforms traditional methods and multi-view clustering algorithms.

Model Selection Using K-Means Clustering Algorithm for the Symmetrical Segmentation of Remote Sensing Datasets

The importance of unsupervised clustering methods is well established in the statistics and machine learning literature. Many sophisticated unsupervised classification techniques have been made available to deal with a growing number of datasets. Due to its simplicity and efficiency in clustering a large dataset, the k-means clustering algorithm is still popular and widely used in the machine learning community. However, as with other clustering methods, it requires one to choose the balanced number of clusters in advance. This paper’s primary emphasis is to develop a novel method for finding the optimum number of clusters, k, using a data-driven approach. Taking into account the cluster symmetry property, the k-means algorithm is applied multiple times to a range of k values within which the balanced optimum k value is expected. This is based on the uniqueness and symmetrical nature among the centroid values for the clusters produced, and we chose the final k value as the one for which symmetry is observed. We evaluated the proposed algorithm’s performance on different simulated datasets with controlled parameters and also on real datasets taken from the UCI machine learning repository. We also evaluated the performance of the proposed method with the aim of remote sensing, such as in deforestation and urbanization, using satellite images of the Islamabad region in Pakistan, taken from the Sentinel-2B satellite of the United States Geological Survey. From the experimental results and real data analysis, it is concluded that the proposed algorithm has better accuracy and minimum root mean square error than the existing methods.

Parameter-Free and Scalable Incomplete Multiview Clustering With Prototype Graph

Multiview clustering (MVC) seamlessly combines homogeneous information and allocates data samples into different communities, which has shown significant effectiveness for unsupervised tasks in recent years. However, some views of samples may be incomplete due to unfinished data collection or storage failure in reality, which refers to the so-called incomplete multiview clustering (IMVC). Despite many IMVC pioneer frameworks have been introduced, the majority of their approaches are limited by the cubic time complexity and quadratic space complexity which heavily prevent them from being employed in large-scale IMVC tasks. Moreover, the massively introduced hyper-parameters in existing methods are not practical in real applications. Inspired by recent unsupervised multiview prototype progress, we propose a novel parameter-free and scalable incomplete multiview clustering framework with the prototype graph termed PSIMVC-PG to solve the aforementioned issues. Different from existing full pair-wise graph studying, we construct an incomplete prototype graph to flexibly capture the relations between existing instances and discriminate prototypes. Moreover, PSIMVC-PG can directly obtain the prototype graph without pre-process of searching hyper-parameters. We conduct massive experiments on various incomplete multiview tasks, and the performances show clear advantages over existing methods. The code of PSIMVC-PG can be publicly downloaded at https://github.com/wangsiwei2010/PSIMVC-PG.

A Novel 2D Clustering Algorithm Based on Recursive Topological Data Structure

In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric space and takes into account the local and global topological properties of the data to be clustered. Taking into account cluster symmetry property, from a metric and mathematical-topological point of view, the analysis was carried out only in the positive region, reducing the number of calculations in the clustering process. The new clustering theory is inspired by the thermodynamics principle of energy. Thus, both topologies are recursively taken into account. The proposed model is based on the interaction of particles defined through measuring homogeneous-energy criterion. Based on the energy concept, both general and local topologies are taken into account for clustering. The effect of the integration of a new element into the cluster on homogeneous-energy criterion is analyzed. If the new element does not alter the homogeneous-energy of a group, then it is added; otherwise, a new cluster is created. The mathematical-topological theory and the results of its application on public benchmark datasets are presented.

Discrete and Parameter-Free Multiple Kernel k-Means

The multiple kernel k -means (MKKM) and its variants utilize complementary information from different sources, achieving better performance than kernel k -means (KKM). However, the optimization procedures of most previous works comprise two stages, learning the continuous relaxation matrix and obtaining the discrete one by extra discretization procedures. Such a two-stage strategy gives rise to a mismatched problem and severe information loss. Even worse, most existing MKKM methods overlook the correlation among prespecified kernels, which leads to the fusion of mutually redundant kernels and bad effects on the diversity of information sources, finally resulting in unsatisfying results. To address these issues, we elaborate a novel Discrete and Parameter-free Multiple Kernel k -means (DPMKKM) model solved by an alternative optimization method, which can directly obtain the cluster assignment results without subsequent discretization procedure. Moreover, DPMKKM can measure the correlation among kernels by implicitly introducing a regularization term, which is able to enhance kernel fusion by reducing redundancy and improving diversity. Noteworthily, the time complexity of optimization algorithm is successfully reduced, through masterly utilizing of coordinate descent technique, which contributes to higher algorithm efficiency and broader applications. What's more, our proposed model is parameter-free avoiding intractable hyperparameter tuning, which makes it feasible in practical applications. Lastly, extensive experiments conducted on a number of real-world datasets illustrated the effectiveness and superiority of the proposed DPMKKM model.

Unsupervised labelling of remote sensing images based on force field clustering

Remote sensing image segmentation provides technical support for decision making in many areas of environmental resource management. But, the quality of the remote sensing images obtained from different channels can vary considerably, and manually labeling a mass amount of image data is too expensive and inefficiently. In this paper, we propose a point density force field clustering (PDFC) process. According to the spectral information from different ground objects, remote sensing superpixel points are divided into core and edge data points. The differences in the densities of core data points are used to form the local peak. The center of the initial cluster can be determined by the weighted density and position of the local peak. An iterative nebular clustering process is used to obtain the result, and a proposed new objective function is used to optimize the model parameters automatically to obtain the global optimal clustering solution. The proposed algorithm can cluster the area of different ground objects in remote sensing images automatically, and these categories are then labeled by humans simply.

High-Order Correlation Preserved Incomplete Multi-View Subspace Clustering

Incomplete multi-view clustering aims to exploit the information of multiple incomplete views to partition data into their clusters. Existing methods only utilize the pair-wise sample correlation and pair-wise view correlation to improve the clustering performance but neglect the high-order correlation of samples and that of views. To address this issue, we propose a high-order correlation preserved incomplete multi-view subspace clustering (HCP-IMSC) method which effectively recovers the missing views of samples and the subspace structure of incomplete multi-view data. Specifically, multiple affinity matrices constructed from the incomplete multi-view data are treated as a third-order low rank tensor with a tensor factorization regularization which preserves the high-order view correlation and sample correlation. Then, a unified affinity matrix can be obtained by fusing the view-specific affinity matrices in a self-weighted manner. A hypergraph is further constructed from the unified affinity matrix to preserve the high-order geometrical structure of the data with incomplete views. Then, the samples with missing views are restricted to be reconstructed by their neighbor samples under the hypergraph-induced hyper-Laplacian regularization. Furthermore, the learning of view-specific affinity matrices as well as the unified one, tensor factorization, and hyper-Laplacian regularization are integrated into a unified optimization framework. An iterative algorithm is designed to solve the resultant model. Experimental results on various benchmark datasets indicate the superiority of the proposed method. The code is implemented by using MATLAB R2018a and MindSpore library: https://github.com/ChangTang/HCP-IMSC.

Robust Matrix Factorization With Spectral Embedding

Nonnegative matrix factorization (NMF) and spectral clustering are two of the most widely used clustering techniques. However, NMF cannot deal with the nonlinear data, and spectral clustering relies on the postprocessing. In this article, we propose a Robust Matrix factorization with Spectral embedding (RMS) approach for data clustering, which inherits the advantages of NMF and spectral clustering, while avoiding their shortcomings. In addition, to cluster the data represented by multiple views, we present the multiview version of RMS (M-RMS), and the weights of different views are self-tuned. The main contributions of this research are threefold: 1) by integrating spectral clustering and matrix factorization, the proposed methods are able to capture the nonlinear data structure and obtain the cluster indicator directly; 2) instead of using the squared Frobenius-norm, the objectives are developed with the l_2,1 -norm, such that the effects of the outliers are alleviated; and 3) the proposed methods are totally parameter-free, which increases the applicability for various real-world problems. Extensive experiments on several single-view/multiview data sets demonstrate the effectiveness of our methods and verify their superior clustering performance over the state of the arts.

Kernel Probabilistic K-Means Clustering

Kernel fuzzy c-means (KFCM) is a significantly improved version of fuzzy c-means (FCM) for processing linearly inseparable datasets. However, for fuzzification parameter m=1, the problem of KFCM (kernel fuzzy c-means) cannot be solved by Lagrangian optimization. To solve this problem, an equivalent model, called kernel probabilistic k-means (KPKM), is proposed here. The novel model relates KFCM to kernel k-means (KKM) in a unified mathematic framework. Moreover, the proposed KPKM can be addressed by the active gradient projection (AGP) method, which is a nonlinear programming technique with constraints of linear equalities and linear inequalities. To accelerate the AGP method, a fast AGP (FAGP) algorithm was designed. The proposed FAGP uses a maximum-step strategy to estimate the step length, and uses an iterative method to update the projection matrix. Experiments demonstrated the effectiveness of the proposed method through a performance comparison of KPKM with KFCM, KKM, FCM and k-means. Experiments showed that the proposed KPKM is able to find nonlinearly separable structures in synthetic datasets. Ten real UCI datasets were used in this study, and KPKM had better clustering performance on at least six datsets. The proposed fast AGP requires less running time than the original AGP, and it reduced running time by 76-95% on real datasets.

Incomplete multi-modal representation learning for Alzheimer's disease diagnosis

Alzheimers disease (AD) is a complex neurodegenerative disease. Its early diagnosis and treatment have been a major concern of researchers. Currently, the multi-modality data representation learning of this disease is gradually becoming an emerging research field, attracting widespread attention. However, in practice, data from multiple modalities are only partially available, and most of the existing multi-modal learning algorithms can not deal with the incomplete multi-modality data. In this paper, we propose an Auto-Encoder based Multi-View missing data Completion framework (AEMVC) to learn common representations for AD diagnosis. Specifically, we firstly map the original complete view to a latent space using an auto-encoder network framework. Then, the latent representations measuring statistical dependence learned from the complete view are used to complement the kernel matrix of the incomplete view in the kernel space. Meanwhile, the structural information of original data and the inherent association between views are maintained by graph regularization and Hilbert-Schmidt Independence Criterion (HSIC) constraints. Finally, a kernel based multi-view method is applied to the learned kernel matrix for the acquisition of common representations. Experimental results achieved on Alzheimers Disease Neuroimaging Initiative (ADNI) datasets validate the effectiveness of the proposed method.

Consensus guided incomplete multi-view spectral clustering

Incomplete multi-view clustering which aims to solve the difficult clustering challenge on incomplete multi-view data collected from diverse domains with missing views has drawn considerable attention in recent years. In this paper, we propose a novel method, called consensus guided incomplete multi-view spectral clustering (CGIMVSC), to address the incomplete clustering problem. Specifically, CGIMVSC seeks to explore the local information within every single-view and the semantic consistent information shared by all views in a unified framework simultaneously, where the local structure is adaptively obtained from the incomplete data rather than pre-constructed via a k-nearest neighbor approach in the existing methods. Considering the semantic consistency of multiple views, CGIMVSC introduces a co-regularization constraint to minimize the disagreement between the common representation and the individual representations with respect to different views, such that all views will obtain a consensus clustering result. Experimental comparisons with some state-of-the-art methods on seven datasets validate the effectiveness of the proposed method on incomplete multi-view clustering.

Real-Time Pattern-Recognition of GPR Images with YOLO v3 Implemented by Tensorflow

Artificial intelligence (AI) is widely used in pattern recognition and positioning. In most of the geological exploration applications, it needs to locate and identify underground objects according to electromagnetic wave characteristics from the ground-penetrating radar (GPR) images. Currently, a few robust AI approach can detect targets by real-time with high precision or automation for GPR images recognition. This paper proposes an approach that can be used to identify parabolic targets with different sizes and underground soil or concrete structure voids based on you only look once (YOLO) v3. With the TensorFlow 1.13.0 developed by Google, we construct YOLO v3 neural network to realize real-time pattern recognition of GPR images. We propose the specific coding method for the GPR image samples in Yolo V3 to improve the prediction accuracy of bounding boxes. At the same time, K-means algorithm is also applied to select anchor boxes to improve the accuracy of positioning hyperbolic vertex. For some instances electromagnetic-vacillated signals may occur, which refers to multiple parabolic electromagnetic waves formed by strong conductive objects among soils or overlapping waveforms. This paper deals with the vacillating signal similarity intersection over union (IoU) (V-IoU) methods. Experimental result shows that the V-IoU combined with non-maximum suppression (NMS) can accurately frame targets in GPR image and reduce the misidentified boxes as well. Compared with the single shot multi-box detector (SSD), YOLO v2, and Faster-RCNN, the V-IoU YOLO v3 shows its superior performance even when implemented by CPU. It can meet the real-time output requirements by an average 12 fps detected speed. In summary, this paper proposes a simple and high-precision real-time pattern recognition method for GPR imagery, and promoted the application of artificial intelligence or deep learning in the field of the geophysical science.

An Adaptive Ellipse Distance Density Peak Fuzzy Clustering Algorithm Based on the Multi-target Traffic Radar

In the multi-target traffic radar scene, the clustering accuracy between vehicles with close driving distance is relatively low. In response to this problem, this paper proposes a new clustering algorithm, namely an adaptive ellipse distance density peak fuzzy (AEDDPF) clustering algorithm. Firstly, the Euclidean distance is replaced by adaptive ellipse distance, which can more accurately describe the structure of data obtained by radar measurement vehicles. Secondly, the adaptive exponential function curve is introduced in the decision graph of the fast density peak search algorithm to accurately select the density peak point, and the initialization of the AEDDPF algorithm is completed. Finally, the membership matrix and the clustering center are calculated through successive iterations to obtain the clustering result.The time complexity of the AEDDPF algorithm is analyzed. Compared with the density-based spatial clustering of applications with noise (DBSCAN), k-means, fuzzy c-means (FCM), Gustafson-Kessel (GK), and adaptive Euclidean distance density peak fuzzy (Euclid-ADDPF) algorithms, the AEDDPF algorithm has higher clustering accuracy for real measurement data sets in certain scenarios. The experimental results also prove that the proposed algorithm has a better clustering effect in some close-range vehicle scene applications. The generalization ability of the proposed AEDDPF algorithm applied to other types of data is also analyzed.

A Novel Model on Reinforce K-Means Using Location Division Model and Outlier of Initial Value for Lowering Data Cost

Today, semi-structured and unstructured data are mainly collected and analyzed for data analysis applicable to various systems. Such data have a dense distribution of space and usually contain outliers and noise data. There have been ongoing research studies on clustering algorithms to classify such data (outliers and noise data). The K-means algorithm is one of the most investigated clustering algorithms. Researchers have pointed out a couple of problems such as processing clustering for the number of clusters, K, by an analyst through his or her random choices, producing biased results in data classification through the connection of nodes in dense data, and higher implementation costs and lower accuracy according to the selection models of the initial centroids. Most K-means researchers have pointed out the disadvantage of outliers belonging to external or other clusters instead of the concerned ones when K is big or small. Thus, the present study analyzed problems with the selection of initial centroids in the existing K-means algorithm and investigated a new K-means algorithm of selecting initial centroids. The present study proposed a method of cutting down clustering calculation costs by applying an initial center point approach based on space division and outliers so that no objects would be subordinate to the initial cluster center for dependence lower from the initial cluster center. Since data containing outliers could lead to inappropriate results when they are reflected in the choice of a center point of a cluster, the study proposed an algorithm to minimize the error rates of outliers based on an improved algorithm for space division and distance measurement. The performance experiment results of the proposed algorithm show that it lowered the execution costs by about 13-14% compared with those of previous studies when there was an increase in the volume of clustering data or the number of clusters. It also recorded a lower frequency of outliers, a lower effectiveness index, which assesses performance deterioration with outliers, and a reduction of outliers by about 60%.

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Learning Hybrid Representation by Robust Dictionary Learning in Factorized Compressed Space

In this paper, we investigate the robust dictionary learning (DL) to discover the hybrid salient low-rank and sparse representation in a factorized compressed space. A Joint Robust Factorization and Projective Dictionary Learning (J-RFDL) model is presented. The setting of J-RFDL aims at improving the data representations by enhancing the robustness to outliers and noise in data, encoding the reconstruction error more accurately and obtaining hybrid salient coefficients with accurate reconstruction ability. Specifically, J-RFDL performs the robust representation by DL in a factorized compressed space to eliminate the negative effects of noise and outliers on the results, which can also make the DL process efficient. To make the encoding process robust to noise in data, J-RFDL clearly uses sparse L2, 1-norm that can potentially minimize the factorization and reconstruction errors jointly by forcing rows of the reconstruction errors to be zeros. To deliver salient coefficients with good structures to reconstruct given data well, J-RFDL imposes the joint low-rank and sparse constraints on the embedded coefficients with a synthesis dictionary. Based on the hybrid salient coefficients, we also extend J-RFDL for the joint classification and propose a discriminative J-RFDL model, which can improve the discriminating abilities of learnt coefficients by minimizing the classification error jointly. Extensive experiments on public datasets demonstrate that our formulations can deliver superior performance over other state-of-the-art methods.

Adaptive Sample-level Graph Combination for Partial Multiview Clustering

Multiview clustering explores complementary information among distinct views to enhance clustering performance under the assumption that all samples have complete information in all available views. However, this assumption does not hold in many real applications, where the information of some samples in one or more views may be missing, leading to partial multiview clustering problems. In this case, significant performance degeneration is usually observed. A collection of partial multiview clustering algorithms has been proposed to address this issue and most treat all different views equally during clustering. In fact, because different views provide features collected from different angles/feature spaces, they might play different roles in the clustering process. With the diversity of different views considered, in this study, a novel adaptive method is proposed for partial multiview clustering by automatically adjusting the contributions of different views. The samples are divided into complete and incomplete sets, while a joint learning mechanism is established to facilitate the connection between them and thereby improve clustering performance. More specifically, the method is characterized by a joint optimization model comprising two terms. The first term mines the underlying cluster structure from both complete and incomplete samples by adaptively updating their importance in all available views. The second term is designed to group all data with the aid of the cluster structure modeled in the first term. These two terms seamlessly integrate the complementary information among multiple views and enhance the performance of partial multiview clustering. Experimental results on real-world datasets illustrate the effectiveness and efficiency of our proposed method.

Partition level multiview subspace clustering

Multiview clustering has gained increasing attention recently due to its ability to deal with multiple sources (views) data and explore complementary information between different views. Among various methods, multiview subspace clustering methods provide encouraging performance. They mainly integrate the multiview information in the space where the data points lie. Hence, their performance may be deteriorated because of noises existing in each individual view or inconsistent between heterogeneous features. For multiview clustering, the basic premise is that there exists a shared partition among all views. Therefore, the natural space for multiview clustering should be all partitions. Orthogonal to existing methods, we propose to fuse multiview information in partition level following two intuitive assumptions: (i) each partition is a perturbation of the consensus clustering; (ii) the partition that is close to the consensus clustering should be assigned a large weight. Finally, we propose a unified multiview subspace clustering model which incorporates the graph learning from each view, the generation of basic partitions, and the fusion of consensus partition. These three components are seamlessly integrated and can be iteratively boosted by each other towards an overall optimal solution. Experiments on four benchmark datasets demonstrate the efficacy of our approach against the state-of-the-art techniques.