Granular Computing for Data Analytics:A Manifesto of Human-Centric Computing

In the plethora of conceptual and algorithmic developments supporting data analytics and system modeling,humancentric pursuits assume a particular position owing to ways they emphasize and realize interaction between users and the data.We advocate that the level of abstraction,which can be flexibly adjusted,is conveniently realized through Granular Computing.Granular Computing is concerned with the development and processing information granules–formal entities which facilitate a way of organizing knowledge about the available data and relationships existing there.This study identifies the principles of Granular Computing,shows how information granules are constructed and subsequently used in describing relationships present among the data.

Three Perspectives of Granular Computing

As an emerging field of study, granular computing has received much attention. Many models, frameworks, methods and techniques have been proposed and studied. It is perhaps the time to seek for a general and unified view so that fundamental issues can be examined and clarified.This paper examines granular computing from three perspectives.By viewing granular computing as a way of structured thinking,we focus on its philosophical foundations in modeling human perception of the reality.By viewing granular computing as a method of structured problem solving,we examine its theoretical and methodological foundations in solving a wide range of real-world problems.By viewing granular computing as a paradigm of information processing,we turn our attention to its more concrete techniques. The three perspectives together offer a holistic view of granular computing.

Rough-Granular Computing

Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Computing(GC). We discuss the Rough-Granular Computing(RGC) approach to modeling of computations in complex adaptive systems and multiagent systems as well as for approximate reasoning about the behavior of such systems. The RGC methods have been successfully applied for solving complex problems in areas such as identification of objects or behavioral patterns by autonomous systems, web mining, and sensor fusion.

Granular Computing on Partitions, Coverings and Neighborhood Systems

Granular Computing on partitions(RST),coverings(GrCC) and neighborhood systems(LNS) are examined: (1) The order of generality is RST, GrCC, and then LNS. (2) The quotient structure: In RST, it is called quotient set. In GrCC, it is a simplical complex, called the nerve of the covering in combinatorial topology. For LNS, the structure has no known description. (3) The approximation space of RST is a topological space generated by a partition, called a clopen space. For LNS, it is a generalized/pretopological space which is more general than topological space. For GrCC,there are two possibilities. One is a special case of LNS,which is the topological space generated by the covering. There is another topological space, the topology generated by the finite intersections of the members of a covering The first one treats covering as a base, the second one as a subbase. (4) Knowledge representations in RST are symbol-valued systems. In GrCC, they are expression-valued systems. In LNS, they are multivalued system; reported in 1998 . (5) RST and GRCC representation theories are complete in the sense that granular models can be recaptured fully from the knowledge representations.

Two Classes of Models of Granular Computing

This paper reviews a class of important models of granular computing which are induced by equivalence relations,or by general binary relations,or by neighborhood systems,and propose a class of models of granular computing which are induced by coverings of the given universe.

The rise of granular computing

This paper has two purposes.One is to present a critical examination of the rise of granular computing and the other is to suggest a triarchic theory of granular computing.By examining the reasons,justifications,and motivations for the rise of granular computing,we may be able to fully appreciate its scope,goal and potential values.The results enable us to formulate a triarchic theory in the light of research results from many disciplines.The three components of the theory are labeled as the philosophy,the methodology,and the computation.The integration of the three offers a unified view of granular computing as a way of structured thinking,a method of structured problem solving,and a paradigm of structured information processing,focusing on hierarchical granular structures.The triarchic theory is an important effort in synthesizing the various theories and models of granular computing.

Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing

Dominance-based rough set approach(DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions.DRSA has also some merits within granular computing,as it extends the paradigm of granular computing to ordered data,specifies a syntax and modality of information granules which are appropriate for dealing with ordered data,and enables computing with words and reasoning about ordered data.Granular computing with ordered data is a very general paradigm,because other modalities of information constraints,such as veristic,possibilistic and probabilistic modalities,have also to deal with ordered value sets(with qualifiers relative to grades of truth,possibility and probability),which gives DRSA a large area of applications.

Dynamic Distribution Model with Prime Granularity for Parallel Computing

Dynamic distribution model is one of the best schemes for parallel volume rendering. How- ever, in homogeneous cluster system.since the granularity is traditionally identical, all processors communicate almost simultaneously and computation load may lose balance. Due to problems above, a dynamic distribution model with prime granularity for parallel computing is presented. Granularities of each processor are relatively prime, and related theories are introduced. A high parallel performance can be achieved by minimizing network competition and using a load balancing strategy that ensures all processors finish almost simultaneously. Based on Master-Slave-Gleaner ( MSG) scheme, the parallel Splatting Algorithm for volume rendering is used to test the model on IBM Cluster 1350 system. The experimental results show that the model can bring a considerable improvement in performance, including computation efficiency, total execution time, speed, and load balancing.

Research of optimization to solve nonlinear equation based on granular computing

In this article,a real number is defined as a granulation and the real space is transformed into real granular space[1].In the entironment,solution of nonlinear equation is denoted by granulation in real granular space.Hence,the research of whole optimization to solve nonlinear equation based on granular computing is proposed[2].In classical case,we solve usually accurate solution of problems.If can't get accurate solution,also finding out an approximate solution to close to accurate solution.But in real space,approximate solution to close to accurate solution is very vague concept.In real granular space,all of the approximate solutions to close to accurate solution are constructed a set,it is a granulation in real granular space.Hence,this granulation is an accurate solution to solve problem in some sense,such,we avoid to say vaguely "approximate solution to close to accurate solution".We introduce the concept of granulation in one dimension real space.Any positive real number a together with moving infinite small distance ε will be constructed an interval [a-ε,a+ε],we call it as granulation in real granular space,denoted by ε(a)or [a].We will discuss related properties and operations[3] of the granulations.Let one dimension real space be R,where each real number a will be generated a granulation,hence we get a granular space R based on real space R.Obviously,R∈R.Infinite small number in real space R is only 0,and there are three infinite small granulations in real number granular space R:[0],[ε] and [-ε].As the graph in Fig.1 shows.In Fig.1,[-ε] is a negative infinite small granulation,[ε] is a positive infinite small granulation,[0] is a infinite small granulation.[a] is a granulation of real number a generating,it could be denoted by interval [a-ε,a+ε] in real space [3-5].Fig.1 Real granulations [0] and [a] Let f(x)=0 be a nonlinear equation,its graph in interval [-3,10] is showed in Fig.2.Where-3≤x≤10 Relation ρ(f| |,ε)is defined as follows:(x1,x2)∈ρ(f| |,ε)iff |f(x1)-f(x2)| < ε Where ε is any given small real number.We have five approximate solution sets on the nonlinear equation f(x)=0 by ρ(f| |,ε)∧|f(x)|[a,b]max,to denote by granulations [(xi1+xi2)/2],[(xi3+xi4)/2],[(xi5+xi6)/2],[(xi7+xi8)/2] and [(xi9+xi10)/2] respectively,where |f(x)|[a,b]max denotes local maximum on x∈[a,b].This is whole optimum on nonlinear equation in interval [-3,10].We will get best optimization solution on nonlinear equation via computing f(x)to use the five solutions denoted by granulation in one dimension real granular space[2,5].

Research on the Development Trend and General Applications of the Fuzzy Rough Granularity Computing Theory

In this paper, we conduct research on the development trend and general applications of the fuzzy rough granular computing theory. Granular computing is a new concept of general information processing and computing paradigm which covers all the granularity the study of the theory, methods, techniques and the tools. In many areas are the basic ideas of granular computing, such as the interval analysis, rough set theory, clustering analysis and information retrieval, machine learning, database, etc. With the theory of domain known division of target concept and rule acquisition, in knowledge discovery, data mining and the pattern recognition is widely used. Under this basis, in this paper, we propose the fuzzy rough theory based computing paradigm that gains ideal performance.

A rough-granular computing in discovery of process models from data and domain knowledge

The rapid expansion of the Internet has resulted not only in the ever growing amount of data therein stored,but also in the burgeoning complexity of the concepts and phenomena pertaining to those data.This issue has been vividly compared by the renowned statistician,prof.Friedman of Stanford University,to the advances in human mobility from the period of walking afoot to the era of jet travel.These essential changes in data have brought new challenges to the development of new data mining methods,especially that the treatment of these data increasingly involves complex processes that elude classic modeling paradigms."Hot" datasets like biomedical,financial or net user behavior data are just a few examples.Mining such temporal or stream data is on the agenda of many research centers and companies worldwide.In the data mining community,there is a rapidly growing interest in developing methods for process mining,e.g.,for discovery of structures of temporal processes from data.Works on process mining have recently been undertaken by many renowned centers worldwide.This research is also related to functional data analysis,cognitive networks,and dynamical system modeling,e.g.,in biology.In the lecture,we outline an approach to discovery of processes from data and domain knowledge which is based on the rough-granular computing.

Domain-Oriented Software Defined Computing Architecture

With the introduction of software defined hardware by DARPA Electronics Resurgence Initiative,software definition will be the basic attribute of information system.Benefiting from boundary certainty and algorithm aggregation of domain applications,domain-oriented computing architecture has become the technical direction that considers the high flexibility and efficiency of information system.Aiming at the characteristics of data-intensive computing in different scenarios such as Internet of Things(IoT),big data,artificial intelligence(AI),this paper presents a domain-oriented software defined computing architecture,discusses the hierarchical interconnection structure,hybrid granularity computing element and its computational kernel extraction method,finally proves the flexibility and high efficiency of this architecture by experimental comparison.

Computational multiscale methods for granular materials

The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales,respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed. c 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301101]

Editorial: Computational mechanics of granular materials

Most of granular materials are highly heteroge- neous, composed of voids and particles with different sizes and shapes. Geological matter, soil and clay in nature, geo-structure, concrete, etc. are practical ex- amples among them. From the microscopic view, a lo- cal region in the medium is occupied by particles with small but finite sizes and granular material is naturally modeled as an assembly of discrete particles in contacts On the other hand, the local region is identified with a material point in the overall structure and this discon- tinuous medium can then be represented by an effective continuum on the macroscopic level

Three-dimensional simulation of pore scale fluid flow in granular ore media with realistic geometry

The images of granular ore media were captured by X-ray CT scanner. Combined with digital image processing and finite element techniques, the three-dimensional geometrical model, which represents the realistic pore structure of the media, was constructed. With this model, three dimensional pore scale fluid flow among particles was simulated. Then the distributions of fluid flow velocity and pressure were analyzed and the hydraulic conductivity was calculated. The simulation results indicate the fluid flow behaviors are mainly dominated by the volume and topological structure of pore space. There exist obvious preferential flow and leaching blind zones simultaneously in the medium. The highest velocities generally occur in those narrow pores with high pressure drops. The hydraulic conductivity obtained by simulation is the same order of magnitude as the laboratory test result, which denotes the validity of the model. The pore-scale and macro-scale are combined and the established geometrical model can be used for the simulations of other phenomena during heap leaching process.

基于GrC-NN和DS证据理论的电动汽车故障诊断

文章针对电动汽车故障数据庞杂、非线性的问题,提出了一种基于粒计算神经网络(granular computation-neural network,GrC-NN)和Dempster-Shafer(DS)证据理论的电动汽车故障诊断方法。该方法采用GrC对电动汽车故障信息进行属性约简,使用约简后的样本训练反向传播(back propagation,BP)神经网络与径向基函数(radial basis function,RBF)神经网络,并将测试数据输入到神经网络中分别进行初步诊断,最后利用DS证据理论对初步诊断结果进行决策级融合,得到最终诊断结果。仿真结果表明,该方法能有效简化神经网络结构,提高电动汽车故障诊断的准确度。

基于GrC的信息系统软规则及其度量关系的研究

粒计算(GranularComputing,简称GrC)是一种新的软计算方法。该文利用信息颗粒的位表示(BitRepresenta-tions)来进行信息系统软规则及其度量之间关系的研究。具体地,首先利用软规则对关联规则、决策规则、函数依赖之间的关系进行了分析,然后对关联规则度量、决策规则度量、外延的函数依赖度量的关系进行了研究,并且建立了这些度量的统一模型。

Call for Paper of 2008 IEEE International Conference on Granular Computing Hangzhou,China,Aug.26～28,2008(http://www.cs.sjsu.edu/～grc/)Sponsored By IEEE Computational Intelligence Society

Contact Information:qliu_ncu@yahoo.com.cn,thu@cis.drexel.edu,and cc:grc@cs.sjsu.edu Keynote Speeches:Lotfi A.Zadeh(EE-Nobel Laureate,UC Berkeley,USA) Tsau Young Lin(GrC initiator,SJSU)