Information granulation: A search for data structures

… Information Processing and Management, Vol 29 …, 2004

Software: Practice and Experience, 1981

While the control structures in recent programming languages are structured, the data structures are still primitive. This paper examines data structures and operations on them, and proposes some new features in programming languages. These new features are principally in the areas of data description and data usage. In data description, the emphasis is on a global view of dynamic data structures; in data usage, semantic relationships between data items are innate in the operations on these data structures. Finally, example data descriptions and algorithms using some of the new features are contrasted with those using conventional features. K E~ %OHD\ Receieed 8 November 1979 N. H. ~l A D H ; \ V J I AND I . R . WILSON

Knowledge-Based Systems, 2016

Designing information granules used intensively in Granular Computing is of paramount relevance to the fundamentals of the discipline. Information granules are key functional components in granular models, granular classifiers, and granular decision-making models. The design of information granules is central to the discipline of Granular Computing. In this study, we introduce a way of designing information granules by combining the mechanisms of unsupervised and supervised learning and subsequently using the principle of justifiable granularity. An overall design process consists of two phases. First, the granulation process involves hierarchical clustering or K-Means clustering. It is followed by a parametric refinement of information granules realized by the principle of justifiable granularity. The characterization of information granules is offered in terms of measures of coverage, specificity, and entropy. Experimental results including synthetic data and publicly available data are covered to demonstrate the performance of the proposed approach.

Mining association rules is a common data mining technique to find knowledge about the universe [3]. Due to the lack of sufficient information about the universe we can not uniquely identify each element of the universe. To characterize the elements of the universe and to extract knowledge about the universe we classify the elements of the universe based on indiscernibility relation. The classification results in a set of classes called granules which are basic building blocks of the knowledge about the universe [3, 4]. Granular computing processes these granules and produces possible patterns and associations. In this paper we study the concept of indiscernibility and knowledge granulation. We study the association rules using conventional method and granular computing method. We process the granules produced as the result of classification and produce association rules using granular computing. Finally, we compare both the methods in terms of finding association rules.

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2009

Our views are the same, but I adopted an incremental approach: By mapping Neighborhood System(NS) to Zadeh's intuitive definition , I took NS as the GrM, and regarded it as the first GrC model , , . What is Neighborhood Systems(NS)? Totally from different context, namely, approximate retrieval, in 1988-89, I generalized the notion of topological neighborhood systems (TNS) to that of Neighborhood Systems(NS) by simply dropping the axioms of topology , . In this view, each neighborhood is a unit of uncertainty; see Section 10. But in later part of the same year (1989), when I considered the Chinese wall computer security policy model (CWSP), a neighborhood was regarded as a unit of information (known knowledge) . In other words, in early GrC period, a granule is a unit of knowledge or lack of knowledge (uncertainty) Since then 9 working models have been built, and it seems that we have reached the steady state. So one of them (8th GrC MNodel) is selected to be the "final" model. This paper "defines" the concept of granulation in three ways: 1. "Inducitve" Definition: Granulation is defined by a set of examples 2. Zadeh's Informal Definition. This "final" model is a category theory based model (8th GrC model) that fits Zadeh's intuition, and can be specified to those 9 models and classical examples. The paper is roughly organized as follows: After the introduction, we present a soft introduction to the delicate nature of GrC. Then a set of "classical" examples is presented as "inductive definition" of GrC. The main part, which is the formal "final" definition of GrC, is then presented. In this section, we have include Zadeh's intuitive definitiion. Rest of the paper is devoted to relate this final model to 9 models and "classical" examples. In common practices, very often, we loosely regard any collection of objects as a set. Strictly speaking, this loose view needs some qualification. It actually implicitly implies that the interactions among objects are formally ignored. Recall that in set theory, all points are discrete, namely, there are no interactions among elements. However in GrC, these interactions are the main concerns. So the collection of granules, called granular structure (GrS), should never be regarded as a set of granules unless granules are mutually disjoint. In fact, there are three states for GrS: A granule can be considered 1. in isolation, called Isolated State; or Internal State because in this case only the internal structure is relevant, 2. as a subobject of the universe, called Embedded State; or Conceptual State because the full concept of granule is under consideration, and

Knowledge-Based Systems, 2020

Granule description is an important problem in knowledge granularity and representation. In the theoretical study of granule description, two basic sub-problems need to be solved: (1) check whether a target granule is definable, and try to offer an exact description for the target granule if definable; (2) an appropriate approximate description should also be provided to the target granule if indefinable. Up to now, there have been some preliminary studies on these two sub-problems. However, the existing findings are not enough or incomplete since sufficient and necessary conditions of definable granules have not been explored, and there have not been effective ways to find better approximate descriptions of indefinable granules. Motivated by these discussions, this paper puts forward granule description methods for definable and indefinable granules. First of all, we propose the notions of covering elements and inserting elements of a target granule by which sufficient and necessary conditions of ∧-definable and (∧, ¬)-definable granules are constructed. And then, the smallest definable granule containing the target indefinable granule and the largest definable granule included in the target indefinable granule are investigated, which are used to solve the problem of finding better approximate descriptions for indefinable granules. Finally, a comparison is made to show that the existing work on complete sets should be improved for providing feasible solutions to the granule description problem.

Zenodo (CERN European Organization for Nuclear Research), 2021

International Conference on Intelligent User Interfaces, 2019

This paper demonstrates how to explore and visualize different types of structure in data, including clusters, anomalies, causal relations, and higher order relations. The methods are developed with the goal of being as automatic as possible and applicable to massive, streaming, and distributed data. Finally, a decentralized learning scheme is discussed, enabling finding structure in the data without collecting the data centrally. CCS CONCEPTS • Human-centered computing → Visualization; Graphical user interfaces; • Mathematics of computing → Causal networks; • Theory of computation → Unsupervised learning and clustering; • Computing methodologies → Anomaly detection.

Lecture Notes in Computer Science

The premise of this paper is that the acquisition, aggregation, merging and use of information requires some new ideas, tools and techniques which can simplify the construction, analysis and use of what we call ephemeral knowledge structures. Ephemeral knowledge structures are used and constructed by granular agents. Each agent contains its own granular information structure and granular information structures of agents can be combined together. The main concept considered in this paper is an information granule. An information granule is a concise conceptual unit that can be integrated into a larger information infrastructure consisting of other information granules and dependencies between them. The novelty of this paper is that it provides a concise and formal definition of a particular view of information granule and its associated operators, as required in advanced knowledge representation applications.

Computers & Mathematics With Applications, 1992

Many artificial intelligence systems implicitly use notions of granularity in reasoning, but there is very little research into granularity itself. An exception is the work of Hobbs, who outlines several characteristics of granularity. In this paper, we describe an approach to representing granularity which formalizes in computational terms most of Hobbs' notions, often refining and extending them. In particular, two types of granularity have been delineated: aggregation and abstractin. Objects can be described at various grain sizes and connected together into a granularity hierarchy which allows focus shifts along either aggregation or abstractiondimension.Granularity hierarchies can be used in recognition. An especially good domain for granularity-based recognition is educational diagnosis. In an intelligent tutoring system, the ability to recognize student behaviour at varying grain sizes is important both for pedagogical reasons (in order to respond to the student at various levels of detail) and for reasons of robustness in diagnosis (obscure student behaviour can be recognized at least at a coarse grain size). We briefly discuss how we have used granularity hierarchies in the recognition of novice LISP programming strategies, and show how this enhances recognition and leads toward planning appropriate feedback for the student.