Low-rank kernel learning for graph-based clustering

Extended clustering algorithm based on cluster shape boundary

Based on the shape characteristics of the sample distribution in the clustering problem, this paper proposes an extended clustering algorithm based on cluster shape boundary (ECBSB). The algorithm automatically determines the number of clusters and classification discrimination boundaries by finding the boundary closures of the clusters from a global perspective of the sample distribution. Since ECBSB is insensitive to local features of the sample distribution, it can accurately identify clusters on complex shape and uneven density distribution. ECBSB first detects the shape boundary points of the cluster in the sample set with edge noise points eliminated, and then generates boundary closures around the cluster based on the boundary points. Finally, the cluster labels of the boundary are propagated to the entire sample set by a nearest neighbor search. The proposed method is evaluated on multiple benchmark datasets. Exhaustive experimental results show that the proposed method achieves highly accurate and robust clustering results, and is superior to the classical clustering baselines on most of the test data.

A Survey on Multi-View Clustering

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

Multiview Clustering: A Scalable and Parameter-Free Bipartite Graph Fusion Method

Multiview clustering partitions data into different groups according to their heterogeneous features. Most existing methods degenerate the applicability of models due to their intractable hyper-parameters triggered by various regularization terms. Moreover, traditional spectral based methods always encounter the expensive time overheads and fail in exploring the explicit clusters from graphs. In this paper, we present a scalable and parameter-free graph fusion framework for multiview clustering, seeking for a joint graph compatible across multiple views in a self-supervised weighting manner. Our formulation coalesces multiple view-wise graphs straightforward and learns the weights as well as the joint graph interactively, which could actively release the model from any weight-related hyper-parameters. Meanwhile, we manipulate the joint graph by a connectivity constraint such that the connected components indicate clusters directly. The designed algorithm is initialization-independent and time-economical which obtains the stable performance and scales well with the data size. Substantial experiments on toy data as well as real datasets are conducted that verify the superiority of the proposed method compared to the state-of-the-arts over the clustering performance and time expenditure.

Smoothness Regularized Multiview Subspace Clustering With Kernel Learning

Multiview subspace clustering has attracted an increasing amount of attention in recent years. However, most of the existing multiview subspace clustering methods assume linear relations between multiview data points when learning the affinity representation by means of the self-expression or fail to preserve the locality property of the original feature space in the learned affinity representation. To address the above issues, in this article, we propose a new multiview subspace clustering method termed smoothness regularized multiview subspace clustering with kernel learning (SMSCK). To capture the nonlinear relations between multiview data points, the proposed model maps the concatenated multiview observations into a high-dimensional kernel space, in which the linear relations reflect the nonlinear relations between multiview data points in the original space. In addition, to explicitly preserve the locality property of the original feature space in the learned affinity representation, the smoothness regularization is deployed in the subspace learning in the kernel space. Theoretical analysis has been provided to ensure that the optimal solution of the proposed model meets the grouping effect. The unique optimal solution of the proposed model can be obtained by an optimization strategy and the theoretical convergence analysis is also conducted. Extensive experiments are conducted on both image and document data sets, and the comparison results with state-of-the-art methods demonstrate the effectiveness of our method.

Consensus Affinity Graph Learning for Multiple Kernel Clustering

Significant attention to multiple kernel graph-based clustering (MKGC) has emerged in recent years, primarily due to the superiority of multiple kernel learning (MKL) and the outstanding performance of graph-based clustering. However, many existing MKGC methods design a fat model that poses challenges for computational cost and clustering performance, as they learn both an affinity graph and an extra consensus kernel cumbersomely. To tackle this challenging problem, this article proposes a new MKGC method to learn a consensus affinity graph directly. By using the self-expressiveness graph learning and an adaptive local structure learning term, the local manifold structure of the data in kernel space is preserved for learning multiple candidate affinity graphs from a kernel pool first. After that, these candidate affinity graphs are synthesized to learn a consensus affinity graph via a thin autoweighted fusion model, in which a self-tuned Laplacian rank constraint and a top- k neighbors sparse strategy are introduced to improve the quality of the consensus affinity graph for accurate clustering purposes. The experimental results on ten benchmark datasets and two synthetic datasets show that the proposed method consistently and significantly outperforms the state-of-the-art methods.

δ-Norm-Based Robust Regression With Applications to Image Analysis

Up to now, various matrix norms (e.g., l₁ -norm, l₂ -norm, l_2,1 -norm, etc.) have been widely leveraged to form the loss function of different regression models, and have played an important role in image analysis. However, the previous regression models adopting the existing norms are sensitive to outliers and, thus, often bring about unsatisfactory results on the heavily corrupted images. This is because their adopted norms for measuring the data residual can hardly suppress the negative influence of noisy data, which will probably mislead the regression process. To address this issue, this paper proposes a novel δ (delta)-norm to count the nonzero blocks around an element in a vector or matrix, which weakens the impacts of outliers and also takes the structure property of examples into account. After that, we present the δ -norm-based robust regression (DRR) in which the data examples are mapped to the kernel space and measured by the proposed δ -norm. By exploring an explicit kernel function, we show that DRR has a closed-form solution, which suggests that DRR can be efficiently solved. To further handle the influences from mixed noise, DRR is extended to a multiscale version. The experimental results on image classification and background modeling datasets validate the superiority of the proposed approach to the existing state-of-the-art robust regression models.

An Inception Convolutional Autoencoder Model for Chinese Healthcare Question Clustering

Healthcare question answering (HQA) system plays a vital role in encouraging patients to inquire for professional consultation. However, there are some challenging factors in learning and representing the question corpus of HQA datasets, such as high dimensionality, sparseness, noise, nonprofessional expression, etc. To address these issues, we propose an inception convolutional autoencoder model for Chinese healthcare question clustering (ICAHC). First, we select a set of kernels with different sizes using convolutional autoencoder networks to explore both the diversity and quality in the clustering ensemble. Thus, these kernels encourage to capture diverse representations. Second, we design four ensemble operators to merge representations based on whether they are independent, and input them into the encoder using different skip connections. Third, it maps features from the encoder into a lower-dimensional space, followed by clustering. We conduct comparative experiments against other clustering algorithms on a Chinese healthcare dataset. Experimental results show the effectiveness of ICAHC in discovering better clustering solutions. The results can be used in the prediction of patients' conditions and the development of an automatic HQA system.

Scaled Simplex Representation for Subspace Clustering

The self-expressive property of data points, that is, each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering (SC) methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the data. Besides, the affine constraint used in these methods is not flexible enough for practical applications. To overcome these problems, in this article, we introduce a scaled simplex representation (SSR) for the SC problem. Specifically, the non-negative constraint is used to make the coefficient matrix physically meaningful, and the coefficient vector is constrained to be summed up to a scalar to make it more discriminative. The proposed SSR-based SC (SSRSC) model is reformulated as a linear equality-constrained problem, which is solved efficiently under the alternating direction method of multipliers framework. Experiments on benchmark datasets demonstrate that the proposed SSRSC algorithm is very efficient and outperforms the state-of-the-art SC methods on accuracy. The code can be found at https://github.com/csjunxu/SSRSC.

Nonlocal Low-Rank Tensor Completion for Visual Data

In this paper, we propose a novel nonlocal patch tensor-based visual data completion algorithm and analyze its potential problems. Our algorithm consists of two steps: the first step is initializing the image with triangulation-based linear interpolation and the second step is grouping similar nonlocal patches as a tensor then applying the proposed tensor completion technique. Specifically, with treating a group of patch matrices as a tensor, we impose the low-rank constraint on the tensor through the recently proposed tensor nuclear norm. Moreover, we observe that after the first interpolation step, the image gets blurred and, thus, the similar patches we have found may not exactly match the reference. We name the problem "Patch Mismatch," and then in order to avoid the error caused by it, we further decompose the patch tensor into a low-rank tensor and a sparse tensor, which means the accepted horizontal strips in mismatched patches. Furthermore, our theoretical analysis shows that the error caused by Patch Mismatch can be decomposed into two components, one of which can be bounded by a reasonable assumption named local patch similarity, and the other part is lower than that using matrix completion. Extensive experimental results on real-world datasets verify our method's superiority to the state-of-the-art tensor-based image inpainting methods.

Deep clustering with a Dynamic Autoencoder: From reconstruction towards centroids construction

In unsupervised learning, there is no apparent straightforward cost function that can capture the significant factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static. The absence of concrete supervision suggests that smooth dynamics should be integrated during the training process. Compared to classical static cost functions, dynamic objective functions allow to better make use of the gradual and uncertain knowledge acquired through pseudo-supervision. In this paper, we propose Dynamic Autoencoder (DynAE), a novel model for deep clustering that addresses a clustering-reconstruction trade-off, by gradually and smoothly eliminating the reconstruction objective function in favor of a construction one. Experimental evaluations on benchmark datasets show that our approach achieves state-of-the-art results compared to the most relevant deep clustering methods.

Multiple Kernel k-Means with Incomplete Kernels

Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernel matrices to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are first imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel matrix over all the samples. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Robust Graph Learning From Noisy Data

Learning graphs from data automatically have shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from the real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust principle component analysis (RPCA), where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption and 2) improved graph construction by exploiting clean data recovered by RPCA. Thus, it boosts the clustering, semisupervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.

LABIN: Balanced Min Cut for Large-Scale Data

Although many spectral clustering algorithms have been proposed during the past decades, they are not scalable to large-scale data due to their high computational complexities. In this paper, we propose a novel spectral clustering method for large-scale data, namely, large-scale balanced min cut (LABIN). A new model is proposed to extend the self-balanced min-cut (SBMC) model with the anchor-based strategy and a fast spectral rotation with linear time complexity is proposed to solve the new model. Extensive experimental results show the superior performance of our proposed method in comparison with the state-of-the-art methods including SBMC.