Geometric visualization of clusters obtained from fuzzy clustering algorithms

Fuzzy-clustering methods, such as fuzzy k-means and expectation maximization, allow an object to be assigned to multiple clusters with different degrees of membership. However, the memberships that result from fuzzy-clustering algorithms are difficult to be analyzed and visualized. The memberships, usually converted to 0-1 values, are visualized using parallel coordinates or different color shades. In this paper, we propose a new approach to visualize fuzzy-clustered data. The scheme is based on a geometric visualization, and works by grouping the objects with similar cluster memberships towards the vertices of a hyper-tetrahedron. The proposed method shows clear advantages over the existing methods, demonstrating its capabilities for viewing and navigating inter-cluster relationships in a spatial manner.     

Novel fuzzy clustering scheme for 3D wireless sensor networks

In this paper, we consider the sensor-energy optimization in 3D Wireless Sensor Networks (WSNs), which determines an optimal topology of sensors to prolong the network lifetime and reduce the energy expenditure. A new mathematical model for clustering in 3D WSN, considering energy consumption, constraints of communication and a 3D energy function, is presented. Using the Lagrange multiplier method, solutions of the model consisting of cluster centres and the membership matrix are computed and used in the new algorithm, called FCM-3 WSN. Experimental validation on real 3D datasets demonstrates that FCM-3 WSN outperforms the relevant methods, namely, Low-Energy Adaptive Clustering Hierarchy (LEACH), Centralized LEACH (LEACH-C), Single-hop Clustering and Energy-Efficient Protocol (SCEEP), Hybrid-Low Energy Adaptive Clustering Hierarchy (H-LEACH), K-Means and Fuzzy C-Means (FCM).     

Classification of turbulent flow patterns with fuzzy clustering

A pattern recognition technique for the identification of critical points in turbulent flows based on fuzzy C-means clustering is presented. The technique deals with, in particular, the problem that experimental data is normally obtained with coarsely spaced sensors making the identification of critical points uncertain. The technique was applied to hot-wire data from two different turbulent flows; one is the highly ordered wake of a mesh strip, while the second is the wake of a circular cylinder, which has a higher level of disorder. Foci and saddle points in the velocity fields were accurately detected and classified.     

利用距离变换实现CT图象中软组织显示

基于距离变换的软组织显示方法，由分割，距离变换，剥皮和体绘制4个步骤组成，为加快运算速度和满足实时交互的需要，在进行三维医学CT图象内部软组织显示时，采用了一种新的三维欧氏距离变换算法和基于体绘制的三维数据场多表面显示方法，实验结果表明，该方法能够清晰地再现皮下血管，肌肉与骨骼的空间解剖关系，在临床医学领域具有重要的应用价值。     

基于信息熵种子点选取的流线可视化

有效的种子点选取方法是影响流线分布洞悉流场特性的关键。在保持流场变化规律与重要特征准确描述前提下,为了解决由过多流线所导致的遮挡与杂乱问题,提出了基于贪婪策略和蒙特卡洛的两种种子点选取方法。基于贪婪策略的种子点选取方法通过流场信息熵的计算,对流场中的关键特征具有高度敏感性。基于蒙特卡洛种子点选取方法根据均匀随机分布函数生成输入,基于信息熵计算输入点影响半径确定流线分布。通过多个数据集对两种选取方法实验,结果表明基于贪婪策略选取方法可高效捕获流场的关键特征,基于蒙特卡洛方法选取流线更加均匀,保持了流场全局变化规律,两种方法的结合得到更优化的流场可视化效果。     

On-line fuzzy modeling via clustering and support vector machines

In this paper, we propose a novel approach to identify unknown nonlinear systems with fuzzy rules and support vector machines. Our approach consists of four steps which are on-line clustering, structure identification, parameter identification and local model combination. The collected data are firstly clustered into several groups through an on-line clustering technique, then structure identification is performed on each group using support vector machines such that the fuzzy rules are automatically generated with the support vectors. Time-varying learning rates are applied to update the membership functions of the fuzzy rules. The modeling errors are proven to be robustly stable with bounded uncertainties by a Lyapunov method and an input-to-state stability technique. Comparisons with other related works are made through a real application of crude oil blending process. The results demonstrate that our approach has good accuracy, and this method is suitable for on-line fuzzy modeling.     

Interactive toothbrushing education by a smart toothbrush system via 3D visualization

The very first step for keeping good dental hygiene is to employ the correct toothbrushing style. Due to the possible occurrence of periodontal disease at an early age, it is critical to begin correct toothbrushing patterns as early as possible. With this aim, we proposed a novel toothbrush monitoring and training system to interactively educate on toothbrushing behavior in terms of the correct brushing motion and grip axis orientation. Our intelligent toothbrush monitoring system first senses a user's brushing pattern by analyzing the waveforms acquired from a built-in accelerometer and magnetic sensor. To discern the inappropriate toothbrushing style, a real-time interactive three dimensional display system, based on an OpenGL 3D surface rendering scheme, is applied to visualize a subject's brushing patterns and subsequently advise on the correct brushing method.     

结合空间信息的模糊聚类侧扫声纳图像分割

目的 针对侧扫声纳图像具有背景复杂、噪声污染重等特点,提出一种结合空间信息的模糊聚类分割算法(FCM),以提高侧扫声纳图像的分割精度和分割速度。方法 采用结合组合邻域中值滤波的FCM算法,首先选取正十字邻域和斜十字邻域,分别计算两个邻域内的像素灰度中值;然后,结合其中的较小值,引入惩罚项,得到融合灰度信息和空间信息的灰度值;最后,对融合后的灰度图像进行FCM分割。结果 利用该算法对不同尺寸和不同目标的侧扫声纳图像进行分割,并将分割结果与其他5种聚类算法的分割结果进行比较,对比分析每种算法的分割精度和运算时间。结合中值滤波的FCM算法的分割精度和运算时间均优于传统的FCM算法和结合均值滤波的FCM算法,其中结合组合邻域中值滤波的FCM算法的运算速度较快,分割精度略高于结合传统中值滤波的FCM算法。结论 结合组合邻域中值滤波的FCM算法在对侧扫声纳图像进行分割时,具有较强的抗噪性、实时性和较强的边缘保持能力。     

Partitioning elements of the Periodic Table via fuzzy clustering technique

In this paper we present fuzzy clustering results of the elements of the Periodic Table according to several physical properties related directly to their electronic structure (ionization potential, cohesion energy, conductivity, atomic number). We find that the resulting classes reproduce the Periods of the Periodic Table. Using additional physical properties not directly related to the electronic structure of the elements (compressibility, density) in the fuzzy clustering procedure, we find that the elements of the Periodic Table are partitioned in another way.The authors are grateful to the referees for their valuable suggestions that contributed to improve the presentation of their work.     

Texture-based visualization of unsteady 3D flow by real-time advection and volumetric illumination

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a 3D graphics processing unit (GPU)-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. We investigate two alternative methods for the volumetric illumination of the result of texture advection: First, gradient-based illumination that employs a real-time computation of gradients, and, second, line-based lighting based on illumination in codimension 2. In addition to the Phong model, perception-guided rendering methods are considered, such as cool/warm shading, halo rendering, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions. GPU implementation aspects, performance measurements, and a discussion of results are included to demonstrate our visualization approach.     

Multi-view clustering via simultaneous weighting on views and features

In big data era, more and more data are collected from multiple views, each of which reflect distinct perspectives of the data. Many multi-view data are accompanied by incompatible views and high dimension, both of which bring challenges for multi-view clustering. This paper proposes a strategy of simultaneous weighting on view and feature to discriminate their importance. Each feature of multi-view data is given bi-level weights to express its importance in feature level and view level, respectively. Furthermore, we implements the proposed weighting method in the classical k-means algorithm to conduct multi-view clustering task. An efficient gradient-based optimization algorithm is embedded into k-means algorithm to compute the bi-level weights automatically. Also, the convergence of the proposed weight updating method is proved by theoretical analysis. In experimental evaluation, synthetic datasets with varied noise and missing-value are created to investigate the robustness of the proposed approach. Then, the proposed approach is also compared with five state-of-the-art algorithms on three real-world datasets. The experiments show that the proposed method compares very favourably against the other methods.     

Intelligent multi-shot 3D visualization interfaces

In next-generation virtual 3D simulation, training, and entertainment environments, intelligent visualization interfaces must respond to user-specified viewing requests so users can follow salient points of the action and monitor the relative locations of objects. Users should be able to indicate which object(s) to view, how each should be viewed, what cinematic style and pace to employ, and how to respond when a single satisfactory view is not possible. When constraints fail, weak constraints can be relaxed or multi-shot solutions can be displayed in sequence or as composite shots with simultaneous viewports. To address these issues, we have developed ConstraintCam, a real-time camera visualization interface for dynamic 3D worlds.     

Collaborative 3D visualization with CSpray

CSpray lets small groups of geographically distributed scientists share data and interactively create visualizations. It features different information-sharing levels, a session manager, and 3D visualization aids     

基于VTK的电磁场三维可视化研究及实现

针对在三维电磁场可视化过程中面临的电磁数据的多样性和数据映射的多样性问题,分析了电磁场三维可视化的主要流程和电磁场数据集,并引入三维可视化类库VTK。利用VTK类库良好的封装性,采用Marching Cube和Hedgehog建模,分别实现了电磁标量场和电磁矢量场的三维可视化。     

3D stereo interactive medical visualization

Our interactive, 3D stereo display helps guide clinicians during endovascular procedures, such as intraoperative needle insertion and stent placement relative to the target organs. We describe a new method of guiding endovascular procedures using interactive 3D stereo visualizations. We use as an example the transjugular intrahepatic portosystemic shunt (TIPS) procedure. Our goal is to increase the speed and safety of endovascular procedures by providing the interventionalist with 3D information as the operation proceeds. Our goal is to provide 3D image guidance of the TIPS procedure so that the interventionalist can readily adjust the needle position and trajectory to reach the target on the first pass. We propose a 3D stereo display of the interventionalist's needle and target vessels. We also add interactivity via head tracking so that the interventionalist gains a better 3D sense of the relationship between the target vessels and the needle during needle advancement.     

Collaborative fuzzy clustering

In this study, we introduce a new clustering architecture in which several subsets of patterns can be processed together with an objective of finding a structure that is common to all of them. To reveal this structure, the clustering algorithms operating on the separate subsets of data collaborate by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns that are directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. A detailed clustering algorithm is developed on a basis of the standard FCM method and illustrated by means of numeric examples.     

Convex-set-based fuzzy clustering

Prototype-based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. We propose a two-level fuzzy clustering method that involves adaptively expanding and merging convex polytopes, where the convex polytopes are considered as a “flexible” prototype. Therefore, the dependency on the use of a specified prototype can be eliminated. Also, the proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. In the first level of our proposed method, each cluster is represented by a convex polytope which is described by its set of vertices. Specifically, nonlinear membership functions are utilized to determine whether an input pattern creates a new cluster or whether an existing cluster should be modified. In the second level, the expandable clusters that are selected by an intercluster distance measure are merged to improve clustering efficiency and to reduce the order dependency of the incoming input patterns. Several experimental results are given to show the validity of our method     

Accelerating fuzzy clustering

This paper extends earlier work [C. Borgelt, R. Kruse, Speeding up fuzzy clustering with neural network techniques, in: Proceedings of the 12th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE’03, St. Louis, MO, USA), IEEE Press, Piscataway, NJ, USA, 2003] on an approach to accelerate fuzzy clustering by transferring methods that were originally developed to speed up the training process of (artificial) neural networks. The core idea is to consider the difference between two consecutive steps of the alternating optimization scheme of fuzzy clustering as providing a gradient. This “gradient” may then be modified in the same way as a gradient is modified in error backpropagation in order to enhance the training. Even though these modifications are, in principle, directly applicable, carefully checking and bounding the update steps can improve the performance and can make the procedure more robust. In addition, this paper provides a new and much more detailed experimental evaluation that is based on fuzzy cluster comparison measures [C. Borgelt, Resampling for fuzzy clustering, Int. J. Uncertainty, Fuzziness Knowledge-based Syst. 15 (5) (2007), 595-614], which can be used nicely to study the convergence speed.