The study is concerned with the fundamentals of granular computing and its application to neural networks. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (embracing a number of individual entitites) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information granulation are discussed including several alternatives such as fuzzy sets, interval analysis, rough sets, and probability. The notion of granularity itself is defined and quantified. A design agenda of granular computing is formulated and the key design problems are raised. A number of granular architectures are also discussed with an objective of dealinating the fundamental algorithmic and conceptual challenges. It is shown that the use of information granules of different size (granularity) lends itself to general pyramid architectures of information processing. The role of encoding and decoding mechanisms visible in this setting is also discussed in detail along with some particular solutions. Neural networks are primarily involved at the level of numeric optimization. Granularity of information introduces another dimension to the neurocomputing. We discuss the role of granular constructs in the design of neural networks and knowledge representation therein. The intent of this paper is to elaborate on the fundamentals and put the entire area in a certain perspective while not moving into specific algorithmic details.
Although spatial information of images usually enhance the robustness of the Fuzzy C-Means (FCM) algorithm, it greatly increases the computational costs for image segmentation. To achieve a sound trade-off between the segmentation performance and the speed of clustering, we come up with a Kullback-Leibler (KL) divergence-based FCM algorithm by incorporating a tight wavelet frame transform and a morphological reconstruction operation. To enhance FCM's robustness, an observed image is first filtered by using the morphological reconstruction. A tight wavelet frame system is employed to decompose the observed and filtered images so as to form their feature sets. Considering these feature sets as data of clustering, an modified FCM algorithm is proposed, which introduces a KL divergence term in the partition matrix into its objective function. The KL divergence term aims to make membership degrees of each image pixel closer to those of its neighbors, which brings that the membership partition becomes more suitable and the parameter setting of FCM becomes simplified. On the basis of the obtained partition matrix and prototypes, the segmented feature set is reconstructed by minimizing the inverse process of the modified objective function. To modify abnormal features produced in the reconstruction process, each reconstructed feature is reassigned to the closest prototype. As a result, the segmentation accuracy of KL divergence-based FCM is further improved. What's more, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Finally, supporting experiments coping with synthetic, medical and color images are reported. Experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other comparative algorithms. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.
