Kernel Fuzzy Similarity Measure-Based Spectral Clustering for Image Segmentation

Simulated annealing spectral clustering algorithm for image segmentation

Over the years, research on fuzzy clustering algorithms has attracted the attention of many researchers, and they have been applied to various areas, such as image segmentation and data clustering. Various fuzzy clustering algorithms have been put forward based on the initial Fuzzy C-Means clustering (FCM) with Euclidean distance. However, the existing fuzzy clustering approaches ignore two problems. Firstly, clustering algorithms based on Euclidean distance have a high error rate, and are more sensitive to noise and outliers. Secondly, the parameters of the fuzzy clustering algorithms are hard to determine. In practice, they are often determined by the user’s experience, which results in poor performance of the clustering algorithm. Therefore, considering the above deficiencies, this paper proposes a novel fuzzy clustering algorithm by combining the Gaussian kernel function and Grey Wolf Optimizer (GWO), called Kernel-based Picture Fuzzy C-Means clustering with Grey Wolf Optimizer (KPFCM-GWO). In KPFCM-GWO, the Gaussian kernel function is used as a symmetrical measure of distance between data points and cluster centers, and the GWO is utilized to determine the parameter values of PFCM. To verify the validity of KPFCM-GWO, a comparative study was conducted. The experimental results indicate that KPFCM-GWO outperforms other clustering methods, and the improvement of KPFCM-GWO is mainly attributed to the combination of the Gaussian kernel function and the parameter optimization capability of the GWO. What is more, the paper applies KPFCM-GWO to analyzes the value of an airline’s customers, and five levels of customer categories are defined.

Spectral clustering has recently achieved a plenty of successful applications in the fields of image processing and object pattern recognition. However, it is a frequent challenging problem that many spectral clustering algorithms suffer from the sensitivity in the selection of the parameters for their Gaussian kernel functions and K-means partitioning processes. To alleviate this situation, we first construct a distance matrix and project the data points into the eigen-space spanned by the selected eigenvectors, then we apply the proposed partitioning algorithm inspired by the continuity of data distribution. In order to partition the data points projected on the eigenvectors, we formulate a cost function with quadratic data-fidelity and L 0 gradient constraint, and the optimal solution can be obtained with the use of alternating direction method of multipliers (ADMM). The proposed approach has been tested for the image segmentation problems. The experiments on the benchmark image datasets showed that the proposal was able to achieve efficient and effective results with the help of the superpixels.

Spectral clustering requires the time-consuming decomposition of the Laplacian matrix of the similarity graph, thus limiting its applicability to large datasets. To improve the efficiency of spectral clustering, a top-down approach was recently proposed, which first divides the data into several micro-clusters (granular-balls), then splits these micro-clusters when they are not ``compact'', and finally uses these micro-clusters as nodes to construct a similarity graph for more efficient spectral clustering. However, this top-down approach is challenging to adapt to unevenly distributed or structurally complex data. This is because constructing micro-clusters as a rough ball struggles to capture the shape and structure of data in a local range, and the simplistic splitting rule that solely targets ``compactness'' is susceptible to noise and variations in data density and leads to micro-clusters with varying shapes, making it challenging to accurately measure the similarity between them. To resolve these issues and improve spectral clustering, this paper first proposes to start from local structures to obtain micro-clusters, such that the complex structural information inside local neighborhoods is well captured by them. Moreover, by noting that Euclidean distance is more suitable for convex sets, this paper further proposes a data splitting rule that couples local density and data manifold structures, so that the similarities of the obtained micro-clusters can be easily characterized. A novel similarity measure between micro-clusters is then proposed for the final spectral clustering. A series of experiments based on synthetic and real-world datasets demonstrate that the proposed method has better adaptability to structurally complex data than granular-ball based methods.

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k $$ k $$ -nearest neighbor graph with only one parameter k $$ k $$ , that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F $$ F $$ -measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

Summary. Pattern recognition has as its objective to classify objects into different categories and classes. It is a fundamental component of artificial intelligence and computer vision. This chapter investigates the application of an efficient optimization method, known as Particle Swarm Optimization (PSO), to the field of pattern recognition and image processing. First a clustering method that is based on PSO is discussed. The application of the proposed clustering algorithm to the problem of unsupervised classification and segmentation of images is investigated. Then PSObased approaches that tackle the color image quantization and spectral unmixing problems are discussed.

Since the 21st century, with the rapid development of China’s domestic economy and the continuous improvement of people’s living standards, the development and construction of urban infrastructure are also faster and faster, and the requirements for the stability of foundations such as buildings, roads and bridges, subway, and high-speed railway are also higher and higher. In the southwest of China, due to the influence of terrain conditions, there are a large number of soil rock mixtures with uneven particle size change and complex particle composition. Understanding the mechanical properties of soil rock mixture and effectively measuring the strength and deformation parameters of soil rock mixture are one of the most important research topics. At the same time, in order to identify the soil rock mixture, the conventional Gauss Euclidean distance calculation method cannot fully reflect the structure of soil rock mixture, so an improved Gauss kernel function multiclass support vector machine (MSVM) method is proposed. On the basis of Gaussian radial, Gaussian kernel function is used to replace Euclidean distance in ranging. The attitude kernel function of Gaussian kernel function is established according to ranging. Many types of support vector machines (SVM) are constructed by a binary tree method to complete classification. The experimental results show that, based on the improved Gaussian kernel function, this paper discusses the high-intensity interval training, so as to achieve a good recognition effect, whether it has a promoting effect on improving the physical quality of college boys, and designs the training scheme to carry out experimental intervention on college boys, so as to provide a new training theoretical reference for school physical education teaching. It also provides a training method for college boys to improve their physical fitness.

Since the 21st century, with the rapid development of China’s domestic economy and the continuous improvement of people’s living standards, the development and construction of urban infrastructure are also faster and faster, and the requirements for the stability of foundations such as buildings, roads and bridges, subway, and high-speed railway are also higher and higher. In the southwest of China, due to the influence of terrain conditions, there are a large number of soil rock mixtures with uneven particle size change and complex particle composition. Understanding the mechanical properties of soil rock mixture and effectively measuring the strength and deformation parameters of soil rock mixture are one of the most important research topics. At the same time, in order to identify the soil rock mixture, the conventional Gauss Euclidean distance calculation method cannot fully reflect the structure of soil rock mixture, so an improved Gauss kernel function multiclass support vector machine (MSVM) method is proposed. On the basis of Gaussian radial, Gaussian kernel function is used to replace Euclidean distance in ranging. The attitude kernel function of Gaussian kernel function is established according to ranging. Many types of support vector machines (SVM) are constructed by a binary tree method to complete classification. The experimental results show that, based on the improved Gaussian kernel function, this paper discusses the high-intensity interval training, so as to achieve a good recognition effect, whether it has a promoting effect on improving the physical quality of college boys, and designs the training scheme to carry out experimental intervention on college boys, so as to provide a new training theoretical reference for school physical education teaching. It also provides a training method for college boys to improve their physical fitness.

Fuzzy spectral clustering with robust spatial information for image segmentation

Spectral clustering has become one of the most popular clustering methods due to its superior performance compared to the traditional clustering methods. However, the performance of spectral clustering would be limited by complex data, such as a huge number of samples and high dimensionality. To address this problem, some existing methods apply deep learning to learn the lower-dimensional representations, spectral clustering is then applied to the representations. Different from the existing methods that separate the two stages of feature representation learning and spectral clustering, in this paper, we propose Spectral Clustering Joint Deep Embedding (SCJDE), a method that simultaneously learns the feature representations and the spectral embedding of spectral clustering via a deep autoencoder. Moreover, a sparsity constraint is imposed to generate better spectral embedding for spectral clustering. Finally, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> -means is performed on the spectral embedding to obtain clustering result. The proposed method can learn a good spectral embedding for spectral clustering by deep learning to obtain better clustering results. The experimental results on both synthetic and real-world datasets demonstrate the effectiveness of the proposed method.

This paper presents a new method of nonlinear finetwork with Gaussian kernel functions. In practice, signal enhancement filters are usually adopted as a preprocessor of signal processing system. For this purpose, an approach of nonlinear filtering using a network with Gaussian kernel functions is proposed for the efficient enhancement of noisy signals. In this method, the condition for signal enhancement is obtained by using the phase space analysis of signal time series. Then, from this analysis, the structure of nonlinear filter is determined and a network with Gaussian kernel functions is trained in such a way of obtaining the clean signal. This procedure can be repeated to obtain the multilayer (or deep) structure of nonlinear filters. As a result, the proposed nonlinear filter has demonstrated significant merits in signal enhancement compared with other conventional preprocessing filters.

Spectral Clustering (SC) is an effective clustering method for its excellent performance in partitioning non-linearly distributed data. On the other hand, Ensemble Clustering (EC), a different clustering technology, can promote cluster quality by ensembling the results of base clusterings. In this work, we concentrate on an EC framework that utilizes SC as the base method. Nevertheless, SC suffers from scalability due to its high computational complexity in constructing the Laplacian graph and computing the corresponding eigendecomposition. In the past decades, many efforts have been made to it. However, SC suffers from the scalability issue in processing extensive data, especially in web-scale scenarios. Additionally, EC requires multiple clustering results as the ensemble bases, which further aggravates resource consumption. To address this issue, LiteWSEC, a simple yet efficient Lightweight Framework for Web-scale Spectral Ensemble Clustering, is proposed to cluster web-scale data with limited resource requirements. It adopts the Web-scale Spectral Clustering (WSC) as the base method, which has minimal space overhead without computing overall embedding explicitly. LiteWSEC is highly flexible in the memory requirement, which is adaptive to the available resource. It can partition web-scale data (e.g., <inline-formula><tex-math notation="LaTeX">$n $</tex-math></inline-formula> = 8,000 k) in an resource-limited host (e.g., memory is restricted to 1 GB). Experiments on real-world, large-scale, and web-scale datasets demonstrate both the efficiency and effectiveness of LiteWSEC over state-of-the-art SC and EC methods.

A robust adaptive clustering analysis method for automatic identification of clusters

Fast adaptively balanced min-cut clustering

Introduction: Macroeconomic problems such as inflation and exchange rates are often highlighted as benchmarks for achieving economic progress. The stability of both must be monitored by the government in order to control the inflation rate and exchange rate. This instability is a phenomenon of fluctuation, namely the phenomenon of the rise and fall of the exchange rate of a currency based on demand and supply. Given the large impact of exchange rate fluctuations on the economy, the prediction of the wage exchange rate against the US dollar is considered necessary because it is useful to anticipate and minimize bad possibilities that arise. Method: Methods that can be used to analyze fluctuating currency exchange rate data are nonparametric regression, Nadaraya-Watson estimator, Gaussian kernel function, and Local Polynomial Regression. Results and Discussion: The results of a nonparametric regression comparison between the Nadaraya-Watson estimator, Gaussian kernel function, and local polynomial regression were obtained by MAPE of 2.508% and 0.179%, respectively. This shows that the best model uses the local polynomial regression method and predicted USD exchange rate data against IDR using the best model, namely Local polynomial Regression where the MAPE value is less than 10%, which means the prediction rate is very good. Conclusion: The nonparametric regression method of the Nadaraya-Watrson estimator, Gaussian kernel function, and local polynomial regression shows that the best model uses the local polynomial regression method.