Capsules are fundamental informative units that are introduced into capsule networks to manipulate the hierarchical presentation of patterns. The part-hole relationship of an entity is learned through capsule layers, using a routing-by-agreement mechanism that is approximated by a voting procedure. Nevertheless, existing routing methods are computationally inefficient. We address this issue by proposing a novel routing mechanism, namely “shortcut routing”, that directly learns to activate global capsules from local capsules. In our method, the number of operations in the routing procedure is reduced by omitting the capsules in intermediate layers, resulting in lighter routing. To further address the computational problem, we investigate an attention-based approach, and propose fuzzy coefficients, which have been found to be efficient than mixture coefficients from EM routing. Our method achieves on-par classification results on the Mnist (99.52%), smallnorb (93.91%), and affNist (89.02%) datasets. Compared to EM routing, our fuzzy-based and attention-based routing methods attain reductions of 1.42 and 2.5 in terms of the number of calculations.

In this paper, we propose a hybrid fuzzy geometric active contour method, which embeds the spatial fuzzy clustering into the evolution of geometric active contour. In every iteration, the evolving curve works as a spatial constraint on the fuzzy clustering, and the clustering result is utilized to construct the fuzzy region force. On one hand, the fuzzy region force provides a powerful capability to avoid the leakages at weak boundaries and enhances the robustness to various noises. On the other hand, the local information obtained from the gradient feature map contributes to locating the object boundaries accurately and improves the performance on the images with heterogeneous foreground or background. Experimental results on synthetic and real images have shown that our model can precisely extract object boundaries and perform better than the existing representative hybrid active contour approaches.

In this paper, we propose a new 3D sound rendering method for multiple sound sources with limited computational resources. The method is based on fuzzy clustering, which achieves dual benefits of two general methods based on amplitude-panning and hard clustering. In embedded systems where the number of reproducible sound sources is restricted, the general methods suffer from localization errors and/or serious quality degradation, whereas the proposed method settles the problems by executing clustering-process and amplitude-panning simultaneously. Computational cost evaluation based on DSP implementation and subjective listening test have been performed to demonstrate the applicability for embedded systems and the effectiveness of the proposed method.

This letter presents a new inter-cluster proximity index for fuzzy partitions obtained from the fuzzy c-means algorithm. It is defined as the average proximity of all possible pairs of clusters. The proximity of each pair of clusters is determined by the overlap and the separation of the two clusters. The former is quantified by using concepts of Fuzzy Rough sets theory and the latter by computing the distance between cluster centroids. Experimental results indicate the efficiency of the proposed index.

This paper deals with statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtain the Fermi-Dirac distribution function as a membership function by regularizing the fuzzy c-means with fuzzy entropy. Then we formulate it as a direct annealing clustering, and examine the meanings of Fermi-Dirac function and fuzzy entropy from a statistical mechanical point of view, and show that this fuzzy clustering method is none other than the Fermi-Dirac statistics.

We present a TSK (Takagi-Sugeno-Kang)-based Linguistic Fuzzy Model (TSK-LFM) with uncertain model output. Based on the Linguistic Model (LM) proposed by Pedrycz, we develop a comprehensive design framework. The main design process is composed of the automatic generation of the contexts, fuzzy rule extraction by Context-based Fuzzy C-Means (CFCM) clustering, connection of bias term, and combination of TSK and linguistic context. Finally, we contrast the performance of the presented models with other models for coagulant dosing process in a water purification plant.

In this paper, we present the method for identifying an Adaptive Neuro-Fuzzy Networks (ANFN) with Takagi-Sugeno-Kang (TSK) fuzzy type based on fuzzy granulation. We also develop a systematic approach to generating fuzzy if-then rules from a given input-output data. The proposed ANFN is designed by the use of fuzzy granulation realized via context-based fuzzy clustering. This clustering technique builds information granules in the form of fuzzy sets and develops clusters by preserving the homogeneity of the clustered patterns associated with the input and output space. The experimental results reveal that the proposed model yields a better performance in comparison with Linguistic Models (LM) and Radial Basis Function Networks (RBFN) based on context-based fuzzy clustering introduced in the previous literature for Box-Jenkins gas furnace data and automobile MPG prediction.

In this paper, conventional validity indexes are reviewed and the shortcomings of the fuzzy cluster validation index based on inter-cluster proximity are examined. Based on these considerations, a new cluster validity index is proposed for fuzzy partitions obtained from the fuzzy c-means algorithm. The proposed validity index is defined as the average value of the relative intersections of all possible pairs of fuzzy clusters in the system. It computes the overlap between two fuzzy clusters by considering the intersection of each data point in the overlap. The optimal number of clusters is obtained by minimizing the validity index with respect to c. Experiments in which the proposed validity index and several conventional validity indexes were applied to well known data sets highlight the superior qualities of the proposed index.

In this paper, a novel variable-rate vector quantizer (VQ) design algorithm using fuzzy clustering technique is presented. The algorithm, termed fuzzy entropy-constrained VQ (FECVQ) design algorithm, has a better rate-distortion performance than that of the usual entropy-constrained VQ (ECVQ) algorithm for variable-rate VQ design. When performing the fuzzy clustering, the FECVQ algorithm considers both the usual squared-distance measure, and the length of channel index associated with each codeword so that the average rate of the VQ can be controlled. In addition, the membership function for achieving the optimal clustering for the design of FECVQ are derived. Simulation results demonstrate that the FECVQ can be an effective alternative for the design of variable-rate VQs.

An adaptive algorithm is presented for fuzzy clustering of data. Partitioning is fuzzified by addition of an entropy term to objective functions. The proposed method produces more convex membership functions than those given by the fuzzy c-means algorithm.