Building the fundamentals of granular computing: A principle of justifiable granularity

The study introduces and discusses a principle of justifiable granularity, which supports a coherent way of designing information granules in presence of experimental evidence (either of numerical or granular character). The term “justifiable” pertains to the construction of the information granule, which is formed in such a way that it is (a) highly legitimate (justified) in light of the experimental evidence, and (b) specific enough meaning it comes with a well-articulated semantics (meaning). The design process associates with a well-defined optimization problem with the two requirements of experimental justification and specificity. A series of experiments is provided as well as a number of constructs carried for various formalisms of information granules (intervals, fuzzy sets, rough sets, and shadowed sets) are discussed as well.     

Fuzzy rough granular neural networks, fuzzy granules, and classification

We introduce a fuzzy rough granular neural network (FRGNN) model based on the multilayer perceptron using a back-propagation algorithm for the fuzzy classification of patterns. We provide the development strategy of the network mainly based upon the input vector, initial connection weights determined by fuzzy rough set theoretic concepts, and the target vector. While the input vector is described in terms of fuzzy granules, the target vector is defined in terms of fuzzy class membership values and zeros. Crude domain knowledge about the initial data is represented in the form of a decision table, which is divided into subtables corresponding to different classes. The data in each decision table is converted into granular form. The syntax of these decision tables automatically determines the appropriate number of hidden nodes, while the dependency factors from all the decision tables are used as initial weights. The dependency factor of each attribute and the average degree of the dependency factor of all the attributes with respect to decision classes are considered as initial connection weights between the nodes of the input layer and the hidden layer, and the hidden layer and the output layer, respectively. The effectiveness of the proposed FRGNN is demonstrated on several real-life data sets.     

Granular neural networks: A study of optimizing allocation of information granularity in input space

In this paper, we develop a granular input space for neural networks, especially for multilayer perceptrons (MLPs). Unlike conventional neural networks, a neural network with granular input is an augmented study on a basis of a well learned numeric neural network. We explore an efficient way of forming granular input variables so that the corresponding granular outputs of the neural network achieve the highest values of the criteria of specificity (and support). When we augment neural networks through distributing information granularities across input variables, the output of a network has different levels of sensitivity on different input variables. Capturing the relationship between input variables and output result becomes of a great help for mining knowledge from the data. And in this way, important features of the data can be easily found. As an essential design asset, information granules are considered in this construct. The quantification of information granules is viewed as levels of granularity which is given by the expert. The detailed optimization procedure of allocation of information granularity is realized by an improved partheno genetic algorithm (IPGA). The proposed algorithm is testified effective by some numeric studies completed for synthetic data and data coming from the machine learning and StatLib repositories. Moreover, the experimental studies offer a deep insight into the specificity of input features.     

Optimal allocation of information granularity in system modeling through the maximization of information specificity: A development of granular input space

In this study, we introduce a concept of a granular input space in system modeling, in particular in fuzzy rule-based modeling. The underlying problem can be succinctly formulated in the following way: given is a numeric model, develop an efficient way of forming granular input variables so that the corresponding granular outputs of the model achieve the highest level of specificity. The rationale behind the formulation of the problem is offered along with several illustrative examples. In conjunction with the underlying idea, developed is an algorithmic framework supporting an optimization of the specificity of the model exposed to granular inputs (data). It is dwelled upon one of the principles of Granular Computing, namely an optimal allocation of information granularity. For illustrative purposes, the study is focused on information granules formalized in terms of intervals (however the proposed approach becomes equally relevant for other formalism of information granules). Some comparative analysis with the existing idea of global sensitivity analysis is also carried out by contrasting the essential differences among the two approaches and analyzing the results of computational experiments.     

Semisupervised self-learning granular neural networks for remote sensing image classification

Accuracy of a pattern classification model mostly depends on ample number of training samples, which is the major bottleneck for classifying land cover of remote sensing images. Further, the unbalance scenario typically encountered in hyperspectral remote sensing images, i.e., limited number of training samples with more dimensions, makes the decision-making process cumbersome. Under such inevitable constraints, the article aims to develop an improved classification model using semisupervised self-learning granular neural networks (GNNs) for remote sensing images. The proposed semisupervised method has adopted a new strategy for selecting the potential candidate samples from the unlabeled dataset and used GNN as the base classifier. We have considered GNN because of its transparent architecture that leads to improved performance with less computational complexity compared to the conventional neural networks. Performance of the model is further enhanced with fuzzy granulation of features using class belonging information and selection of granulated features using neighborhood rough sets (NRS). The proposed model thus takes the mutual advantages of GNN architecture, fuzzy granulation with class belonging information, NRS-based feature selection and the most important, improved semisupervised self-learning approach. Performance of the model is compared with other similar methods and verified in terms of different performance measurement indexes, using two multispectral and two hyperspectral remote sensing images.     

Feature analysis through information granulation and fuzzy sets

Feature analysis and feature selection are fundamental pursuits in pattern recognition. We revisit and generalize an issue of feature selection by introducing a mechanism of soft (fuzzy) feature selection. The underlying idea is to consider features to be granular rather than numeric. By varying the level of granularity, we modify the level of contribution of the specific feature to the overall feature space. We admit an interval model of the features meaning that their values assume a form of numeric intervals. The intervalization of the features exhibits a clear-cut interpretation. Moreover a contribution of the features to the formation of the feature space can be easily controlled: the broader the interval, the less essential contribution of the feature to the entire feature space. In limit, when the intervals get broad enough, one may view the feature to be completely eliminated (dropped) from the feature space. The quantification of the features in terms of their importance is realized in the setting of the clustering FCM model (namely, a process of the binary or fuzzy feature selection is carried out and numerically quantified in the space of membership values generated by fuzzy clusters). As the focal point of this study concerns an interval-like form of information granules, we reveal how such feature intervalization helps approximate fuzzy sets described by any type of membership function. Detailed computations give rise to a detailed quantification of such granular features. Numerical experiments provide a comprehensive numerical illustration of the problem.     

Evolutionary design of hybrid self-organizing fuzzy polynomial neural networks with the aid of information granulation

We introduce a new architecture of information granulation-based and genetically optimized Hybrid Self-Organizing Fuzzy Polynomial Neural Networks (HSOFPNN). Such networks are based on genetically optimized multi-layer perceptrons. We develop their comprehensive design methodology involving mechanisms of genetic optimization and information granulation. The architecture of the resulting HSOFPNN combines fuzzy polynomial neurons (FPNs) that are located at the first layer of the network with polynomial neurons (PNs) forming the remaining layers of the network. The augmented version of the HSOFPNN, “IG_gHSOFPNN”, for brief, embraces the concept of information granulation and subsequently exhibits higher level of flexibility and leads to simpler architectures and rapid convergence speed to optimal structure in comparison with the HSOFPNNs and SOFPNNs.

The GA-based design procedure being applied at each layer of HSOFPNN leads to the selection of preferred nodes of the network (FPNs or PNs) whose local characteristics (such as the number of input variables, the order of the polynomial, a collection of the specific subset of input variables, the number of membership functions for each input variable, and the type of membership function) can be easily adjusted. In the sequel, two general optimization mechanisms are explored. The structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is afterwards carried out in the setting of a standard least square method-based learning. The obtained results demonstrate a superiority of the proposed networks over the existing fuzzy and neural models.     

A design of granular fuzzy classifier

In this paper, we propose a new design methodology of granular fuzzy classifiers based on a concept of information granularity and information granules. The classifier uses the mechanism of information granulation with the aid of which the entire input space is split into a collection of subspaces. When designing the proposed fuzzy classifier, these information granules are constructed in a way they are made reflective of the geometry of patterns belonging to individual classes. Although the elements involved in the generated information granules (clusters) seem to be homogeneous with respect to the distribution of patterns in the input (feature) space, they still could exhibit a significant level of heterogeneity when it comes to the class distribution within the individual clusters. To build an efficient classifier, we improve the class homogeneity of the originally constructed information granules (by adjusting the prototypes of the clusters) and use a weighting scheme as an aggregation mechanism.     

Design of information granule-oriented RBF neural networks and its application to power supply for high-field magnet

To realize effective modeling and secure accurate prediction abilities of models for power supply for high-field magnet (PSHFM), we develop a comprehensive design methodology of information granule-oriented radial basis function (RBF) neural networks. The proposed network comes with a collection of radial basis functions, which are structurally as well as parametrically optimized with the aid of information granulation and genetic algorithm. The structure of the information granule-oriented RBF neural networks invokes two types of clustering methods such as K-Means and fuzzy C-Means (FCM). The taxonomy of the resulting information granules relates to the format of the activation functions of the receptive fields used in RBF neural networks. The optimization of the network deals with a number of essential parameters as well as the underlying learning mechanisms (e.g., the width of the Gaussian function, the numbers of nodes in the hidden layer, and a fuzzification coefficient used in the FCM method). During the identification process, we are guided by a weighted objective function (performance index) in which a weight factor is introduced to achieve a sound balance between approximation and generalization capabilities of the resulting model. The proposed model is applied to modeling power supply for high-field magnet where the model is developed in the presence of a limited dataset (where the small size of the data is implied by high costs of acquiring data) as well as strong nonlinear characteristics of the underlying phenomenon. The obtained experimental results show that the proposed network exhibits high accuracy and generalization capabilities.     

一种用于非线性函数逼近的小波神经网络

提出一种用于非线性函数逼近的小波神经网络，给出了网络的参数训练方法。从信息熵的概念出发，改进了网络参数训练的目标函数，并利用引入动量项的最速下降法训练网络权值、尺度因子和平移因子。仿真实验表明，该小波神经网络用于非线性函数逼近时优于同等规模的BP网络，且其训练方法亦具有收敛速度快、逼近精度高等优点。     

Non-linear variable selection for artificial neural networks using partial mutual information

Artificial neural networks (ANNs) have been widely used to model environmental processes. The ability of ANN models to accurately represent the complex, non-linear behaviour of relatively poorly understood processes makes them highly suited to this task. However, the selection of an appropriate set of input variables during ANN development is important for obtaining high-quality models. This can be a difficult task when considering that many input variable selection (IVS) techniques fail to perform adequately due to an underlying assumption of linearity, or due to redundancy within the available data.This paper focuses on a recently proposed IVS algorithm, based on estimation of partial mutual information (PMI), which can overcome both of these issues and is considered highly suited to the development of ANN models. In particular, this paper addresses the computational efficiency and accuracy of the algorithm via the formulation and evaluation of alternative techniques for determining the significance of PMI values estimated during selection. Furthermore, this paper presents a rigorous assessment of the PMI-based algorithm and clearly demonstrates the superior performance of this non-linear IVS technique in comparison to linear correlation-based techniques.     

Estimating incomplete information in group decision making: A framework of granular computing

A general assumption in group decision making scenarios is that of all individuals possess accurate knowledge of the entire problem under study, including the abilities to make a distinction of the degree up to which an alternative is better than other one. However, in many real world scenarios, this may be unrealistic, particularly those involving numerous individuals and options to choose from conflicting and dynamics information sources. To manage such a situation, estimation methods of incomplete information, which use own assessments provided by the individuals and consistency criteria to avoid discrepancy, have been widely employed under fuzzy preference relations. In this study, we introduce the information granularity concept to estimate missing values supporting the objective of obtaining complete fuzzy preference relations with higher consistency levels. We use the concept of granular preference relations to form each missing value as a granule of information in place of a crisp number. This offers the flexibility that is required to estimate the missing information so that the consistency levels related to the complete fuzzy preference relations are as higher as possible.     

An information granulation based data mining approach for classifying imbalanced data

Recently, the class imbalance problem has attracted much attention from researchers in the field of data mining. When learning from imbalanced data in which most examples are labeled as one class and only few belong to another class, traditional data mining approaches do not have a good ability to predict the crucial minority instances. Unfortunately, many real world data sets like health examination, inspection, credit fraud detection, spam identification and text mining all are faced with this situation. In this study, we present a novel model called the “Information Granulation Based Data Mining Approach” to tackle this problem. The proposed methodology, which imitates the human ability to process information, acquires knowledge from Information Granules rather then from numerical data. This method also introduces a Latent Semantic Indexing based feature extraction tool by using Singular Value Decomposition, to dramatically reduce the data dimensions. In addition, several data sets from the UCI Machine Learning Repository are employed to demonstrate the effectiveness of our method. Experimental results show that our method can significantly increase the ability of classifying imbalanced data.     

A variational approach to intensity approximation for remote sensing images using dynamic neural networks

Abstract: In remote sensing image processing, image approximation, or obtaining a high‐resolution image from a corresponding low‐resolution image, is an ill‐posed inverse problem. In this paper, the regularization method is used to convert the image approximation problem into a solvable variational problem. In regularization, the constraints on smoothness and discontinuity are considered, and the original ill‐posed problem is thereby converted to a well‐posed optimization problem. In order to solve the variational problem, a Hopfield‐type dynamic neural network is developed. This neural network possesses two states that describe the discrepancy between a pixel and adjacent pixels, the intensity evolution of a pixel and two kinds of corresponding weights. Based on the experiment in this study with a Landsat TM image free of added noise and a noisy image, the proposed approach provides better results than other methods. The comparison shows the feasibility of the proposed approach.     

Financial ratings with scarce information: A neural network approach

On a wake of Basel II Accord in 2004, banks and financial institutions can build an internal rating system. This work focuses on Italian small firms that are more hard to judge because quite often financial data are not simply available. The aim of this paper is to propose a simulation model for assigning rating judgements to these firms, using poor financial information.The proposed model produces a simulated counterpart of Bureau van Dijk-K Finance (BvD) rating judgements. It is clear that there are problems when small firms must be judged because it is difficult to obtain financial data; indeed in Italy these enterprises must deposit the balance-sheet in reduced form. Suggested methodology is a three-layer process where each of them is formed by, respectively, one, two and four feed-forward artificial neural networks with back-propagation algorithm. The proposed model is a good solution for evaluating small firms with poor financial information but not only: the research underlines and supports the ability of artificial neural networks of learning and reproducing some aspects or some features or behaviours of reality.     

Granular neural networks for land use classification

Granulation of information is a new way to describe the increased complexity of natural phenomena. The lack of clear borders in nature calls for a more efficient way to process such data. Land use both in general but also as perceived in satellite images is a typical example of data that are inherently not clearly delimited. A granular neural network (GNN) approach is used here to facilitate land use classification. The GNN model used combines membership functions of spectral as well as non-spectral spatial information to produce land use categories. Spectral information refers to IRS satellite image bands and non-spectral data are here of topographic nature, namely slope, aspect and elevation. The processing is done through a standard neural network trained by back-propagation learning algorithm. A thorough presentation of the results is given in order to evaluate the merits of this method.     

The granular extension of Sugeno-type fuzzy models based on optimal allocation of information granularity and its application to forecasting of time series

The Sugeno-type fuzzy models are used frequently in system modeling. The idea of information granulation inherently arises in the design process of Sugeno-type fuzzy model, whereas information granulation is closely related with the developed information granules. In this paper, the design method of Sugeno-type granular model is proposed on a basis of an optimal allocation of information granularity. The overall design process initiates with a well-established Sugeno-type numeric fuzzy model (the original Sugeno-type model). Through assigning soundly information granularity to the related parameters of the antecedents and the conclusions of fuzzy rules of the original Sugeno-type model (i.e. granulate these parameters in the way of optimal allocation of information granularity becomes realized), the original Sugeno-type model is extended to its granular counterpart (granular model). Several protocols of optimal allocation of information granularity are also discussed. The obtained granular model is applied to forecast three real-world time series. The experimental results show that the method of designing Sugeno-type granular model offers some advantages yielding models of good prediction capabilities. Furthermore, those also show merits of the Sugeno-type granular model: (1) the output of the model is an information granule (interval granule) rather than the specific numeric entity, which facilitates further interpretation; (2) the model can provide much more flexibility than the original Sugeno-type model; (3) the constructing approach of the model is of general nature as it could be applied to various fuzzy models and realized by invoking different formalisms of information granules.     

模糊神经网络在移动机器人信息融合中的应用

针对移动机器人所用的传感器,提出了一种用于多传感器信息融合的方法,将模糊逻辑和神经网络结合起来,构建了模糊神经网络,并建立了网络的计算模型.通过建立的模糊神经网络对移动机器人的多传感器信息进行融合,实现了移动机器人对动态环境中障碍和环境类型的实时识别以及无冲突运动.网络的训练和试验表明该方法在移动机器人躲避运动物体中是可行的.     

过程神经元网络及其在时变信息处理中的应用

针对时变信息处理和动态系统建模等类问题,建立了输入输出均为时变函数的过程神经元网络和有理式过程神经元网络2种网络模型.在输入输出为时变函数的过程神经元网络中,过程神经元的时间累积算子取为对时间的积分或其他代数运算,它的时空聚合机制和激励能同时反映外部时变输入信号对输出结果的空间聚合作用和时间累积效应,可实现非线性系统输入、输出之间的复杂映射关系.在有理式过程神经元网络中,其基本信息处理单元为由2个成对偶出现的过程神经元组成,逻辑上分为分子和分母2部分,通过有理式整合后输出,可有效提高过程神经元网络对带有奇异值过程函数的柔韧逼近性和在奇异值点附近反应的灵敏性.分析了2种过程神经元网络模型的性质,给出了具体学习算法,并以油田开发过程模拟和旋转机械故障诊断问题为例,验证了这2种网络模型在时变信息处理中的有效性.     

From content delivery today to information centric networking

Today, content delivery is a heterogeneous ecosystem composed by various independent infrastructures. The ever increasing growth of Internet traffic has encouraged the proliferation of different architectures to serve content provider needs and user demand. Despite the differences among the technology, their low level implementation can be characterized in a few fundamental building blocks: network storage, request routing, and data transfer. Existing solutions are inefficient because they try to build an information centric service model over a network infrastructure which was designed to support host-to-host communications. The Information-Centric Networking (ICN) paradigm has been proposed as a possible solution to this mismatch. ICN integrates content delivery as a native network feature. The rationale is to architect a network that automatically interprets, processes, and delivers content (information) independently of its location. This paper makes the following contributions: (1) it identifies a set of building blocks for content delivery, (2) it surveys the most popular approaches to realize the above building blocks, (3) it compares content delivery solutions relying on the current Internet infrastructure with novel ICN approaches.