19552464
Attribute reduction and optimal decision rules acquisition for continuous valued information systems
For continuous valued information systems, the attribute values of objects for the same attribute represent not only their ordinal relationship but also their relative distances. Therefore, the classical rough set model is not suitable for deducing attribute reductions and optimal decision rules for continuous valued information systems. Though some discretization methods are proposed to transform the continuous valued information systems into discrete ones, but those methods are too categorical and may lead to loss of information in some cases. To solve such information loss problem, we propose a tolerance rough set model in this paper. With a given level, the proposed model can divide a universe into some maximal tolerance classes. Also two types of lower and upper approximations are defined accordingly. Then the reductions of the maximal tolerance class and optimal decision rules based on the proposed attribute descriptors are defined, and the approximate discernibility function for the maximal tolerance class is constructed and used to compute all the corresponding optimal decision rules via using Boolean reasoning techniques. Finally, the general reductions and consistent reductions for continuous valued information systems are discussed.
452800
Rough Derivatives in Rough Function Model and Their Application
On the theory and application of rough derivatives in rough function model, the notion of generalized rough functions is defined to improve the definition of higher order rough derivatives Pawlak proposed, and analyze the functional features of roughly derived functions and higher order roughly derived functions. The rough extremum definition of discrete functions is given, Fermat theorem and Rolle theorem of roughly smooth discrete functions are proposed and proved, which complete and perfect the theoretical foundation of rough derivatives application in rough function model. The concepts that are rough monotone and rough convexity of discrete functions are defined. By comparing with the derivative application of real continuous function, a series of theorems are put forward which are the relation theorem of rough derivatives and rough monotone, the two sufficient conditions of rough extrema, the two relation theorems of rough derivatives and rough convexity. Moreover, some new results are achieved such as the sufficient condition of rough smoothing of discrete functions, etc.
5078035
Order-Based Decision Rules Acquisition in Continuous-Valued Decision Information Systems
In a continuous-valued information system, attribute values of objects represent not only the relative distances, but also the ordinal relation of objects. By considering the relative distances of objects, some discretization approaches and other approaches were proposed in previous literature, to discuss the attribute reduces of the system. This paper considers ordinal relations of objects, and utilizes dominance relation rough set model to discuss decision rules acquisition problems. Firstly, concepts of order-based decision rules and generalized order-based decision rules are introduced. Then the concept of optimal order-based decision rule is defined. In order to compute optimal order-based decision rules, the concept of reduct of the object is proposed. Lastly, discernibility functions of objects are constructed, and used to compute optimal order-based decision rules by Boolean reasoning techniques.
21906808
The Theory and Application of Rough Integration in Rough Function Model
The definition of the rough integral Pawlak proposed is improved. New notions are proposed, which are respectively the rough integral on a constant interval and the roughly integral upper limit function, and so on. By comparing with the definite integral of real functions, the properties of rough integrals are analyzed. Giving the concept of mean value of discrete functions, the mean value method for rough integration is derived. At the same time, the intermediate value theorem of rough integration is proposed and its geometric significance is analyzed, which provides a dependable theoretical tool for rough integral operation, etc.. Conclusions including the existence theorem of rough primitives and the fundamental formula of rough calculus are proposed. By the representative of discrete functions, the method of computing a primitive is given, by which basic formulas for rough integration in common use are derived, and the method of rough direct integration is obtained. There is also the method of rough integration by parts for rough integrals which is like that of definite integrals. Thus the recurrence formula for rough integration is deduced, in which the integrand of the rough integral is in the shape of the product of a rough power function and a rough exponential function. It is pointed out that integration by substitution is not applicable for rough integral operation.
13987121
A Unified Framework for Segmentation-Assisted Image Registration
This paper presents a unified variational framework for seamlessly integrating prior segmentation information into non-rigid registration procedures. Under this framework, in addition to the forces arise from the similarity measure in seeking for detailed correspondence, another set of forces generated by the prior segmentation contours can provide an extra guidance in assisting the alignment process towards a more meaningful, stable and noise-tolerant procedure. Local correlation (LC) is being used as the underlying similarity measures to handle intensity variations. We present several 2D/3D examples on synthetic and real data.
63568794
Plenary lecture 1: an information flow based model of representation for developing informatics as an academic discipline
In informatics and information systems, a fundamental notion is representation. And yet, it would seem that in the literature of information systems this notion has been taken as self-evident and therefore treated largely intuitively, and in particular, how a possible representational relationship between two systems may be systematically identified and formalized has not been fully addressed. We believe that a mathematical model of representation helps develop informatics as a proper academic discipline. We observe that the notion of representation is formalizable. This is because it is information flow channels that underpin representational relationships between systems. We propose an information flow based model whereby to capture, formalize, analyze and reason about representation for distributed systems. We draw on semantic information theories, which not only lay solid philosophical foundations, but also contribute to forming a mathematical foundation for the model. Regularities is taken as a fundamental principle based upon which an information flow channel is constructed in which both tokens and types of a classification are taken into consideration. We introduce the notion of representation link, which connects classifications (contexts in FCA) through type level constraints and token level connections. Our model enables an analysis of information flow within a distributed system both qualitatively and quantitatively. The channel hierarchy and link hierarchy take into account background information, which enhances inference on representation links. The model allows agents to choose a channel that is the most appropriate for their purposes without violating the objectivity of information flow. 
 
This model is then applied to the problem of semantic interoperability. A semantic integration model is thus built. The process of semantic integration is examined by using the mathematical mechanism of the model. The validity of the model is verified by analyzing results of semantic integration from both content and quantity perspectives, and also by showing that the notion of channel and representation link hierarchy involved in our model helps reason over different but relevant integrations.
117639554
Multidimensional two-scale dilation equations
Abstract . This work involves the study of multidimensional scaling functions. These functions satisfy a two-scale dilation equation, just as the 1-D scaling functions which are used to construct 1-D wavelets. Two frameworks are presented for studying these dilation equations. Fourier methods are used to analyze existence, uniqueness and regularity of solutions. Expansions with infinite matrix products are used to derive an iterated function system (IFS) algorithm for generating the scaling function. Application to subdivision schemes for surface generation is presented, as a genuine multidimensional example where scaling functions arise and the IFS algorithm can be applied.
17540624
Asymptotic White noise Hypothesis for PCM quantization
For a signal distributed in Rd with an arbitrary density we find the limit distribution as the cell size goes to zero of the quantization noise in the case of a redundant system and the pulse-code modulation scheme. The dimension the support of the limiting distribution equals the largest number of non-comeasurable vectors in the frame and the limit distribution is uniform over its support. This gives the necessary and sufficient conditions for the asymptotic form of the white noise hypothesis.
6225988
A global optimal algorithm for class-dependent discretization of continuous data
This paper presents a new method to convert continuous variables into discrete variables for inductive machine learning. The method can be applied to pattern classification problems in machine learning and data mining. The discretization process is formulated as an optimization problem. We first use the normalized mutual information that measures the interdependence between the class labels and the variable to be discretized as the objective function, and then use fractional programming (iterative dynamic programming) to find its optimum. Unlike the majority of class-dependent discretization methods in the literature which only find the local optimum of the objective functions, the proposed method, OCDD, or Optimal Class-Dependent Discretization, finds the global optimum. The experimental results demonstrate that this algorithm is very effective in classification when coupled with popular learning systems such as C4.5 decision trees and Naive-Bayes classifier. It can be used to discretize continuous variables for many existing inductive learning systems.