Correntropy Induced L2 Graph for Robust Subspace Clustering

Subspace clustering has important and wide applications in computer vision and pattern recognition. It is a challenging task to learn low-dimensional subspace structures due to the possible errors (e.g., noise and corruptions) existing in high-dimensional data. Recent subspace clustering methods usually assume a sparse representation of corrupted errors and correct the errors iteratively. However large corruptions in real-world applications can not be well addressed by these methods. A novel optimization model for robust subspace clustering is proposed in this paper. The objective function of our model mainly includes two parts. The first part aims to achieve a sparse representation of each high-dimensional data point with other data points. The second part aims to maximize the correntropy between a given data point and its low-dimensional representation with other points. Correntropy is a robust measure so that the influence of large corruptions on subspace clustering can be greatly suppressed. An extension of our method with explicit introduction of representation error terms into the model is also proposed. Half-quadratic minimization is provided as an efficient solution to the proposed robust subspace clustering formulations. Experimental results on Hopkins 155 dataset and Extended Yale Database B demonstrate that our method outperforms state-of-the-art subspace clustering methods.

Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-of-the-art approaches are designed by following the model of spectral clustering-based method. These methods pay much attention to learn the representation matrix to construct a suitable similarity matrix and overlook the influence of the noise term on subspace clustering. However, the real data are always contaminated by the noise and the noise usually has a complicated statistical distribution. To alleviate this problem, in this paper, we propose a subspace clustering method based on Cauchy loss function (CLF). Particularly, it uses CLF to penalize the noise term for suppressing the large noise mixed in the real data. This is due to that the CLF's influence function has an upper bound that can alleviate the influence of a single sample, especially the sample with a large noise, on estimating the residuals. Furthermore, we theoretically prove the grouping effect of our proposed method, which means that highly correlated data can be grouped together. Finally, experimental results on five real data sets reveal that our proposed method outperforms several representative clustering methods.

Attention reweighted sparse subspace clustering

Subspace clustering-based band selection (BS) have achieved significant progress. However, traditional approaches focus solely on the linear relationships among bands, neglecting important nonlinear information. Moreover, single-view data inherently limits the exploitation of complementary latent features across different views. To address the above issues, this paper proposes a novel multi-view multi-level robust deep subspace clustering method for BS (MRDSC). First, we construct spectral, spatial, and texture views to provide rich and complementary feature representations for subspace clustering. Further, a multi-level deep subspace clustering network is employed to deeply capture both global and local nonlinear relationships within the self-representation coefficient matrix of each view, while Robust Principal Component Analysis is applied to obtain a clean coefficient matrix. Finally, a self-aligned contrastive learning mechanism is introduced to enhance the consistency of positive samples and the discriminability of negative samples, effectively integrating complementary information across views and reinforcing feature consistency. Experimental results on three public datasets demonstrate that the proposed method exhibits high stability and effectiveness.

Clustering is an unsupervised learning approach that explores data and seeks groups of similar objects. Many classical clustering models such as k-means and DBSCAN are based on heuristics algorithms and suffer from local optimal solutions and numerical instability. Recently convex clustering has received increasing attentions, which leverages the sparsity inducing norms and enjoys many attractive theoretical properties. However, convex clustering is based on Euclidean distance and is thus not robust against outlier features. Since the outlier features are very common especially when dimensionality is high, the vulnerability has greatly limited the applicability of convex clustering to analyze many real-world datasets. In this paper, we address the challenge by proposing a novel robust convex clustering method that simultaneously performs convex clustering and identifies outlier features. Specifically, the proposed method learns to decompose the data matrix into a clustering structure component and a group sparse component that captures feature outliers. We develop a block coordinate descent algorithm which iteratively performs convex clustering after outliers features are identified and eliminated. We also propose an efficient algorithm for solving the convex clustering by exploiting the structures on its dual problem. Moreover, to further illustrate the statistical stability, we present the theoretical performance bound of the proposed clustering method. Empirical studies on synthetic data and real-world data demonstrate that the proposed robust convex clustering can detect feature outliers as well as improve cluster quality.

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

In many real applications, the collected data is usually high dimensionality of feature space and no labels are given, which will result in the “curse of dimensionality” problem and bring the challenge for the feature selection. Although tremendous efforts have been made in unsupervised feature selection, the existing methods neglect the robustness of jointly feature selection and clustering. In this paper, we present a robust simultaneous feature selection and clustering method. By introducing a robust loss function, the unsupervised linear discriminant analysis methods with two different strategies (the ratio trace and the trace ratio) are incorporated into this loss function, which can guarantee the selected features with robustness. Then two novel simultaneous unsupervised feature selection and clustering objective functions are presented by the proposed loss function equipped with $\ell_{2,1}$-norm. Two alternative iterative optimization algorithms are developed to solve these two objective functions. The comparative experimental results conducted on eight UCI datasets show that the proposed methods are better than other competing methods.

Popular de novo amplicon clustering methods suffer from two fundamental flaws: arbitrary global clustering thresholds, and input-order dependency induced by centroid selection. Swarm was developed to address these issues by first clustering nearly identical amplicons iteratively using a local threshold, and then by using clusters' internal structure and amplicon abundances to refine its results. This fast, scalable, and input-order independent approach reduces the influence of clustering parameters and produces robust operational taxonomic units, improving the amount of meaningful biological information that can be extracted from amplicon-based studies.

The purpose of this correspondence is to report on some nxasurements of output SNR (signal-to-noise ratio or S/N), characteristics for a square-law detector extracting signals from non-Gaussian noise, specifically, impulsive noise. Non-Garlssian noise arises in varioas communication media such as the atmosphere, wire lines, and under water. In experimental and theoretical investigations of the effects of non-Gaussian noise on various communications systems, a simple correlator is often considered because it is possible to obtain theoretical predictions of the (S/N), for signal and additive non-Gaussian noise at the correlator input if an appropriate noise model is available for calculating the required fourth-order moment. Middleton (1962), in his analysis of correlator performance in non-Gaussian background noise, employed the so-called Poisson impulse noise model. His theoretical predictions reveal that impulsive noise always degrades the (S/N), as compared with Gaussian noise backgrounds having the same spectral distribution for a given input SNR. However, his theoretical formulas are rather difficult to check experimentally in their full generality and assess the relative importance of various parameters. We compare a study restricted to the case of a square-law detector with Middleton's results.

Subspace clustering using a symmetric low-rank representation

Robust adaptive sparse channel estimation problem has been attracted highly attention in the next-generation wireless communications systems. Re-weighted L1-norm penalized sign least mean square error (RL1-SLMS) algorithm is considered as one of attractive methods to estimate unknown sparse system as well as to mitigate impulsive noises. However, the convergence performance of RL1-SLMS is very ambiguous comparing with its preliminary version. This paper provides comprehensive convergence analysis for the RL1-SLMS algorithm under non-Gaussian impulsive noise environment. Numerical simulations are given to show the fast convergence and robustness with respect to system sparsity as well as non-Gaussian noise.

Outer-Points shaver: Robust graph-based clustering via node cutting

We propose an original learning approach for image classification problems. Recognizing semantic events in video requires to preliminary learn the different classes of events. This first stage is crucial since it conditions the further classification results. In video content analysis, the task is especially difficult due to the high infra-class variability and to noisy measurements. We then represent each class by the centers of several sub-classes (or clusters) thanks to a robust partitional clustering algorithm which can be applied in parallel to a (non-predefined) number of classes. Our clustering technique overcome three main limitations of standard K-means methods: sensitivity to initialization, choice of the number of clusters and influence of outliers. Moreover, it can process the training data in an incremental way. Experimental results on sports videos are reported.

High-dimensional data is usually drawn from the union of multiple low-dimensional subspaces. The task of subspace clustering is to cluster high-dimensional data into their corresponding subspace. Subspace clustering algorithm based on spectral clustering is one of the important methods of subspace clustering. This method is proposed by the spectral clustering framework. This type of method is usually divided into two steps, namely learning the affinity matrix and obtaining the segmentation matrix by spectral clustering. However, the results obtained this way are often sub-optimal. Meanwhile many state-of-the-art algorithms do not consider consistency of correlation data, resulting in the affinity matrix either too dense to make the algorithm contain a lot of erroneous information, or too sparse to make the algorithm lose correlation information. In this paper, we propose Correlation Structured Low-Rank Subspace Clustering (CSLRSC). The CSLRSC is based on the model of low rank representation by adding new $l_{1}$ norm to solve the problem that the affinity matrix established by the previous method is too dense. Adding the structured norm to the model can integrate affinity matrix learning and spectral clustering into one step to obtain an approximate optimal solution of the algorithm. The experimental results that we obtain on Extended Yale B face dataset, MINIST hand-write dataset, and ORL dataset show that our algorithm is superior to others.

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.