Clustering provides a powerful technique for data analysis and data interpretation in the current complex background. Fuzzy clustering has gained significant attention in both research and applications due to its effectiveness in capturing the inherent uncertainty of real-world data. Among these methods, fuzzy C-means (FCM) stands out as one of the most representative and widely used approaches. This study develops a novel nonlinear transformation strategy to restructure data in order to improve the classification performance of FCM, and the transformed data structure, achieved through the developed nonlinear techniques, exhibits highly effective in enhancing the performance of FCM-based classifiers. In the proposed scheme, the original dataset is first partitioned into multiple subsets (matrix blocks) based on the original labels, with distinct weights assigned to each feature within these subsets. This process constructs a more separable dataset, referred to as the "expected high-performance dataset." Then, multiple nonlinear transformation models are constructed for the original dataset and for each feature of the constructed "expected high-performance dataset" with the support vector regression (SVR) method. During these operations, weight optimization is performed using particle swarm optimization (PSO), ultimately enhancing intraclass compactness by amplifying the similarity among samples within the same class. A comprehensive analysis of the proposed method was conducted, and experimental results on public datasets demonstrate its effectiveness and feasibility. The classification accuracy of the proposed method on multiple datasets has been improved by varying degrees compared with FCM, with an average improvement of 16.029% and a maximum improvement of 57.365%.

The accurate separation of leaves from woody material in individual-tree point clouds is crucial for the precise estimation of tree structural parameters. While supervised deep learning methods have demonstrated state-of-the-art performance in this domain, they rely extensively on large volumes of labeled data. However, the process of collecting and annotating tree point cloud data presents significant challenges due to the complexity of the intricate structures of trees, which necessitate substantial human resources and expertise. These constraints highlight the critical need to reduce labeling requirements, a challenge that remains largely unexplored. To address this, the present study first systematically analyzes the model performance under limited data annotation. This analysis is divided into two scenarios, with limited trees and limited point annotations per tree. In addition, based on the aforementioned analysis, we propose a specified weakly supervised framework that integrates consistency regularization, contrastive learning, and prototype learning to further improve performance under limited labeling. A series of experiments conducted on a variety of tree species have indicated that the diversity of tree samples is preferable to the use of more labeled points in the context of limited data annotations. The proposed weakly supervised framework demonstrated a mean intersection over union of 82.0% under the extreme scenario ofone point per class per tree(i.e., one leaf point and one wood point per tree) annotation. This result is nearly on par with the 84.3% mIoU achieved by a fully supervised model. This study offers significant insights into the improvement of label efficiency in the context of learning-based tree leaf-wood separation, paving the way for the development of efficient and scalable methodologies for 3D structural analyses in forestry and subsequent practical applications. The implementation code is available on [will be released if accepted].

Granular computing (GrC) embraces a spectrum of concepts, methodologies, methods, and applications, which dwells upon information granules and their processing. Fuzzy C-means (FCM) based encoding and decoding (granulation-degranulation) mechanism plays a visible role in granular computing. Fuzzy decoding mechanism, also known as the reconstruction (degranulation) problem, has become an intensively studied category in recent years. This study mainly focuses on the improvement of the fuzzy decoding mechanism, and an augmented version achieved through constructing perturbation matrices of prototypes is put forward. Particle swarm optimization is employed to determine a group of optimal perturbation matrices to optimize the prototype matrix and obtain an optimal partition matrix. A series of experiments are carried out to show the enhancement of the proposed method. The experimental results are consistent with the theoretical analysis and demonstrate that the developed method outperforms the traditional FCM-based decoding mechanism.

The multiple signal classification (MUSIC) algorithm based on the orthogonality between the signal subspace and noise subspace is one of the most frequently used methods in the estimation of direction of arrival (DOA), and its performance of DOA estimation mainly depends on the accuracy of the noise subspace. In the most existing researches, the noise subspace is formed by (defined as) the eigenvectors corresponding to all small eigenvalues of the array output covariance matrix. However, we found that the estimation of DOA through the noise subspace in the traditional formation is not optimal in almost all cases, and using a partial noise subspace can always obtain optimal estimation results. In other words, the subspace spanned by the eigenvectors corresponding to a part of the small eigenvalues is more representative of the noise subspace. We demonstrate this conclusion through a number of experiments. Thus, it seems that which and how many eigenvectors should be selected to form the partial noise subspace would be an interesting issue. In addition, this research poses a much general problem: how to select eigenvectors to determine an optimal noise subspace?

In a direction-finding process, high-resolution subspace-based algorithms are the most popular ones. It is well-known that their performance of direction of arrival estimation mainly depends on the accuracy of the signal subspace. However, the traditional methods of capturing the signal subspace do not mine the information hidden in the array output in depth, which may restrict their application to some extent. In this study, we elaborate on a novel scheme to extract the signal subspace through refinement of the correlation matrix of the array output. In the developed scheme, a collection of spatial temporal correlation matrices is firstly established. Then, we define a weighting vector for the correlation matrices, and take the weighted average of the correlation matrices as the covariance matrix of the array output. It is clear that this covariance matrix is more general than the traditional covariance matrix, and the signal subspace can be optimized through adjustment of the weighting vector. In this study, we present an optimal weighting vector by adopting the particle swarm optimization. Simulation results demonstrate that the proposed approach has better performance in root mean square error compared to the existing schemes.

Light detection and ranging (LiDAR) technology has revolutionized forest analysis in past two decades. The increase of available LiDAR data volume is accelerating in recent years. However, the dense and large-volume point clouds may constitute challenges for proper data storage and processing. Point subsampling is often a prerequisite in this circumstance. Nonetheless, the commonly used uniform and random subsampling methods fail to preserve the topological details of branching structures, as they essentially drop points globally. This generates problems for studies on detailed branching structures, and currently there are no point subsampling methods designed for trees. In this letter, a structure-aware subsampling (SAS) method is proposed to tackle this issue. SAS relies on skeleton-adaptive clustering to subsample points locally and maintains the global integrity simultaneously. The proposed method was tested and compared with uniform and random subsampling for retrieving key tree parameters including height, diameter at breast height (DBH), crown area, and wood volume based on geometrical reconstructions. Three datasets from terrestrial, mobile, and unmanned aerial vehicles (UAV) LiDAR platforms were tested. Results showed that SAS was able to achieve similar accuracies of structural parameters compared to the full-resolution data, even with a subsampling rate (SR) of over 90%. More importantly, at the same sampling rate, SAS faithfully preserved more points of thin branches compared to uniform and random subsampling. These results imply that the proposed method maintains the complex tree topology while significantly reduces the data size. This study provides a crucial advancement in LiDAR and forest applications, where data reduction still remains widely unexplored.

This article would like to provide an optimal beam steering control method for high-speed maneuvering platform synthetic aperture radar (SAR) imaging. A corresponding imaging algorithm with 3-D spatial-variation correction is proposed. First, the coordinates of beam footprint are calculated by the transition rule in each pulse repetition time (PRT). The transition rule is designed to get a unified image resolution and minimize the Doppler bandwidth. By the proposed imaging algorithm, 2-D spatial-variation envelop is corrected by azimuth keystone transform and range chirp scaling. Then the space-variant (SV) Doppler terms are compensated by frequency domain perturbation and time-domain resampling. The SV components in both the second- and third-order terms are removed. Finally, the proposed beam steering method and the imaging algorithm are verified by simulated SAR data.

Clustering offers a general methodology and comes with a remarkably rich conceptual and algorithmic framework for data analysis and data interpretation. As one of the most representative algorithms of fuzzy clustering, fuzzy C-means (FCM) is a widely used objective function-based clustering method exploited in various applications. In this study, a virtual-based fuzzy clustering algorithm is proposed to improve the classification performance coming as a result of using fuzzy clustering. This improvement is achieved by forming a virtual space based on the original data space. First, we construct a piecewise linear transformation function to modify the similarity matrix of the original data and build the so-called virtual similarity matrix (VSM). Considering the VSM, the effect of closeness becomes amplified; in other words, high similarity values (say, larger than α which is a cutoff value of the large and small similarity in this paper) present in the original similarity matrix are made higher, whereas lower similarity levels (say, smaller than α) are further reduced. In addition, data with high similarity (say, larger than a certain threshold value) observed in the original space will overlap (the attributes of the samples are exactly the same) significantly in the virtual space; the overlapping samples can be treated as one sample. This modification makes possible easier to identify clusters. Second, we build a relationship matrix between the original dataset and the determined similarity values and present two closed-form solutions to the problem of building the relationship matrix. Subsequently, a virtual space of the original data space is derived through the modified similarity matrix and the introduced relationship matrix. We offer a thorough analysis behind the developed clustering algorithm. The experimental results are in agreement with the underlying conceptual basis. Furthermore, the resulting classification performance is significantly improved compared with the results produced by the FCM and the kernel-based fuzzy C-means.