数学进化中的知识发现方法

从数学历史发展过程中去发现数学的进化规律,从创造数学符号和包容对立的概念中获得了最早的数学知识.将数学符号组合而成的表达式和方程,使问题变换成了形式化表示,当表达式和方程通过推演和求证,判断其正确性时,就形成了公式和定理,它们是数学中的基础理论.推演和求证过程是采用了等价变换.数学进化中更重要的知识发现方法是利用进化变换(对变量、函数、方程、方法等的变换)来拓展数学的新概念和解决不能求解的问题(可拓变换),从而建立了数学的理论体系.创造、包容、形式化变换、等价变换和进化变换都是数学进化中的知识发现方法.     

一种以领域知识为中心的知识发现过程模型

针对知识发现在实际应用中的问题,提出了一种以领域知识为中心的知识发现过程模型,并将其形式化,描述了其动态语义。与已有的知识发现过程模型相比,此过程模型更能体现知识发现过程的本质特性,同时具有严格的形式化基础,为知识发现系统的设计和实际的知识发现应用提供了一个新的参考。     

The impact of a technology-based mathematics after-school program using ALEKS on student's knowledge and behaviors

The effectiveness of using the Assessment and LEarning in Knowledge Spaces (ALEKS) system, an Intelligent Tutoring System for mathematics, as a method of strategic intervention in after-school settings to improve the mathematical skills of struggling students was examined using a randomized experimental design with two groups. As part of a 25-week program, student volunteers were randomly assigned to either a teacher-led classroom or a classroom in which students interacted with ALEKS while teachers were present. Student's math performance, conduct, involvement, and assistance was needed to complete tasks were investigated to determine overall impact of the two programs. Students assigned to the ALEKS classrooms performed at the same level as students taught by expert teachers on the Tennessee Comprehensive Assessment Program (TCAP), which is given annually to all Tennessee students. Furthermore, student's conduct and involvement remained at the same levels in both conditions. However, students in the ALEKS after-school classrooms required significantly less assistance in mathematics from teachers to complete their daily work.     

Inductive logic programming for relational knowledge discovery

Inductive logic programming (ILP) is concerned with the induction of logic programs from examples and background knowledge. In ILP, the shift of attention from program synthesis to knowledge discovery resulted in advanced techniques that are practically applicable for discovering knowledge in relational databases. This paper gives a brief introduction to ILP, presents selected ILP techniques for relational knowledge discovery and reviews selected ILP applications. Nada Lavrač, Ph.D.: She is a senior research associate at the Department of Intelligent Systems, J. Stefan Institute, Ljubljana, Slovenia (since 1978) and a visiting professor at the Klagenfurt University, Austria (since 1987). Her main research interest is in machine learning, in particular inductive logic programming and intelligent data analysis in medicine. She received a BSc in Technical Mathematics and MSc in Computer Science from Ljubljana University, and a PhD in Technical Sciences from Maribor University, Slovenia. She is coauthor of KARDIO: A Study in Deep and Qualitative Knowledge for Expert Systems, The MIT Press 1989, and Inductive Logic Programming: Techniques and Applications, Ellis Horwood 1994, and coeditor of Intelligent Data Analysis in Medicine and Pharmacology, Kluwer 1997. She was the coordinator of the European Scientific Network in Inductive Logic Programming ILPNET (1993–1996) and program cochair of the 8th European Machine Learning Conference ECML’95, and 7th International Workshop on Inductive Logic Programming ILP’97. Sašo Džeroski, Ph.D.: He is a research associate at the Department of Intelligent Systems, J. Stefan Institute, Ljubljana, Slovenia (since 1989). He has held visiting researcher positions at the Turing Institute, Glasgow (UK), Katholieke Universiteit Leuven (Belgium), German National Research Center for Computer Science (GMD), Sankt Augustin (Germany) and the Foundation for Research and Technology-Hellas (FORTH), Heraklion (Greece). His research interest is in machine learning and knowledge discovery in databases, in particular inductive logic programming and its applications and knowledge discovery in environmental databases. He is co-author of Inductive Logic Programming: Techniques and Applications, Ellis Horwood 1994. He is the scientific coordinator of ILPnet2, The Network of Excellence in Inductive Logic Programming. He was program co-chair of the 7th International Workshop on Inductive Logic Programming ILP’97 and will be program co-chair of the 16th International Conference on Machine Learning ICML’99. Masayuki Numao, Ph.D.: He is an associate professor at the Department of Computer Science, Tokyo Institute of Technology. He received a bachelor of engineering in electrical and electronics engineering in 1982 and his Ph.D. in computer science in 1987 from Tokyo Institute of Technology. He was a visiting scholar at CSLI, Stanford University from 1989 to 1990. His research interests include Artificial Intelligence, Global Intelligence and Machine Learning. Numao is a member of Information Processing Society of Japan, Japanese Society for Artificial Intelligence, Japanese Cognitive Science Society, Japan Society for Software Science and Technology and AAAI.     

知识发现在古代壁画展示中的应用

将面向属性的归纳方法（attribute-oriented induction）用于壁画的展示,提出一种基于知识发现的壁画展示方法。对壁画按内容、位置、时间等强相关维属性,引入本体的层次化描述方式用于对比展示,可帮助研究者更好地获取对象的隐性知识,启发新的类描述和关联规则的发现。结合基于绘画构图学特征的相关度评价方法,可有效地选取研究者关注的内容进行比较和展示。实验以真实的敦煌壁画研究课题为例,验证了本文方法在辅助壁画研究中的有效性。     

Logic of knowledge and discovery via interacting agents - Decision algorithm for true and satisfiable statements

In this paper we study logical properties of the operation chance discovery (CD) via structures based on special Kripke/Hintikka models. These models use as bases partially ordered sets of indexes (indexes of steps in a computation, or ones indicating time points in a time flow), and clusters of states associated to each index. The language chosen to build the logical formulas includes modal/temporal operations, operations for the agents’ knowledge, local and global operations for CD, operation of local common knowledge, and an operation for chance of discovery via agents’ interactions. We introduce and study a logic (of knowledge and discovery via interaction of agents), LDK_a, which is defined by semantics, as the set of all formulas that are valid in all suggested models. The paper provides an algorithm to recognize logical laws (and satisfiable formulas) of LDK_a. The algorithm replaces a formula with a rule in a special, so-called reduced normal form, and, then it verifies the validity of this rule in specific models of exponential size in the size of the rule. We show that the problem of computing the true logical laws of LDK_a is decidable.     

Interpretation and knowledge discovery from the multilayer perceptron network: Opening the black box

This paper interprets the outputs from the multilayer perceptron (MLP) network by finding the input data features at the input layer of the network which activate the hidden layer feature detectors. This leads directly to the deduction of the significant data inputs, the inputs that the network actually uses to perform the input/output mapping for a classification task, and the discovery of the most significant of these data inputs. The analysis presents a method for providing explanations for the network outputs and for representing the knowledge learned by the network in the form of significant input data relationships. During network development the explanation facilities and data relationships can be used for network validation and verification, and after development, for rule induction and data mining where this method provides a potential tool for knowledge discovery in databases (KDD).     

Automated fuzzy knowledge acquisition with connectionist adaptation

This paper presents an automated knowledge acquisition architecture for the truck docking problem. The architecture consists of a neural network block, a fuzzy rule generation block and a genetic optimisation block. The neural network block is used to quickly and adaptively learn from trials the driving knowledge. The fuzzy rule generation block then extracts the driving knowledge to form a knowledge rule base. The driving knowledge rule base is further optimised in the genetic optimisation block using a genetic algorithm. Computer simulations are presented to show the effectiveness of the architecture.     

Architecture for knowledge discovery and knowledge management

In this paper, we propose I-MIN model for knowledge discovery and knowledge management in evolving databases. The model splits the KDD process into three phases. The schema designed during the first phase, abstracts the generic mining requirements of the KDD process and provides a mapping between the generic KDD process and (user) specific KDD subprocesses. The generic process is executed periodically during the second phase and windows of condensed knowledge called knowledge concentrates are created. During the third phase, which corresponds to actual mining by the end users, specific KDD subprocesses are invoked to mine knowledge concentrates. The model provides a set of mining operators for the development of mining applications to discover and renew, preserve and reuse, and share knowledge for effective knowledge management. These operators can be invoked by either using a declarative query language or by writing applications.The architectural proposal emulates a DBMS like environment for the managers, administrators and end users in the organization. Knowledge management functions, like sharing and reuse of the discovered knowledge among the users and periodic updating of the discovered knowledge are supported. Complete documentation and control of all the KDD endeavors in an organization are facilitated by the I-MIN model. This helps in structuring and streamlining the KDD operations in an organization.     

Linguistic database summaries and their protoforms: towards natural language based knowledge discovery tools

We consider linguistic data(base) summaries in the sense of Yager [Information Sciences 28 (1982) 69-86], exemplified by “most employees are young and well paid” (with some degree of truth added), for a personnel database, as an intuitive, human consistent and natural language based knowledge discovery tool. We present first an extension of the classic Yager’s approach to involve more sophisticated criteria of goodness, search methods, etc. We advocate the use of the concept of a protoform (prototypical form), that is recently vividly advocated by Zadeh [A prototype-centered approach to adding deduction capabilities to search engines—the concept of a protoform. BISC Seminar, University of California, Berkeley, 2002], as a general form of a linguistic data summary. We present an extension of our interactive approach, based on fuzzy logic and fuzzy database queries, which makes it possible to implement such linguistic data summaries. We show how fuzzy queries are related to linguistic summaries, and show that one can introduce a hierarchy of protoforms, or abstract summaries in the sense of latest Zadeh’s [A prototype-centered approach to adding deduction capabilities to search engines—the concept of a protoform. BISC Seminar, University of California, Berkeley, 2002] ideas meant mainly for increasing deduction capabilities of search engines. For illustration we show an implementation for a sales database in a computer retailer, employing some type of a protoform of a linguistic summary.     

Cortical hierarchies, sleep, and the extraction of knowledge from memory

Odin the Allfather had in his service two great ravens. These ravens' names were Hugin (Thought) and Munin (Memory) and every morning at dawn they would fly off over Midgard (the world) in search of news and information to learn more about humans and their activities. At sundown, they would return to Odin where they would perch one on each of Odin's shoulders, and whisper into his ears all that they had seen and heard.Experience, stored in the brain as memory, is the raw material for intelligence and thought. It has been suggested that at sundown (i.e., during sleep) the brain adjusts its own synaptic matrix to enable adaptive responses to future events by a process of gradient descent optimization, involving repeated reactivations of recent and older memories and gradual adjustment of the synaptic weights. Memory retrieval, thought, and the generation of adaptive behavioral responses involve globally coordinated trajectories through the neuronal state-space, mediated by appropriate synaptic linkages. Artificial neural networks designed to implement even the most rudimentary forms of memory and knowledge extraction and adaptive behavior incorporate massively and symmetrically interconnected nodes; yet, in the cerebral cortex, the probability of a synaptic connection between any two arbitrarily chosen cells is on the order of 10⁻⁶, i.e., so close to zero that a naive modeler might neglect this parameter altogether. The probability of a symmetric connection is even smaller (10⁻¹²). How then, are thought and memory even possible? The solution appears to have been in the evolution of a modular, hierarchical cortical architecture, in which the modules are internally highly connected but only weakly interconnected with other modules. Appropriate inter-modular linkages are mediated indirectly via common linkages with higher level modules collectively known as association cortex. The hippocampal formation in the temporal lobe is the highest level of association cortex. It generates sequentially coupled patterns unique to the location and content of experience, but which do not contain the actual stored data. Rather, the patterns serve as pointers or ‘links’ to the data. Spontaneous reactivation of these linking patterns during sleep may enable the retrieval of recent sequences of experience stored in the lower levels of the cortex and the gradual extraction of knowledge from them. In this essay I explore these ideas, their implications, and the neuroscientific evidence for them.     

Perception-based hidden Markov models: a theoretical framework for data mining and knowledge discovery

 The combination of objective measurements and human perceptions using hidden Markov models with particular reference to sequential data mining and knowledge discovery is presented in this paper. Both human preferences and statistical analysis are utilized for verification and identification of hypotheses as well as detection of hidden patterns. As another theoretical view, this work attempts to formalize the complementarity of the computational theories of hidden Markov models and perceptions for providing solutions associated with the manipulation of the internet.     

集值信息下的粗集与知识获取

在复杂的决策环境中,集值信息是不可避免的。在此情况下,专家往往也能给出满意的决策。从集值信息系统中提取有用的规则,用于增强智能系统的知识库,具有实际意义。粗集是处理不确定信息的有效方法,但它通常适用于完全决策表。本文对粗集理论在集值信息下进行了初步的拓展,为从集值决策表中挖掘知识提供一定的理论基础。     

Assessing effectiveness of learning units under the teaching unit model in an undergraduate mathematics course

This paper reports on the findings of the evaluation of Learning Units (LU), a special type of Learning Object designed to help overcome the difficulties associated with learning Calculus concepts at undergraduate level. An Interactive Platform for Learning Calculus (PIAC) that serves as a container for the LU was created following a specific instructional design, namely, the Teaching Unit Model (TUM), which in turn, rules the platform's design, development and implementation. A general perspective on the development of the platform and its LU is presented, including the results of usability and functionality evaluations, which indicate that the platform and the LU comply with different functionality and usability criteria which are fundamental for their introduction into formal university courses. The platform was utilized in a higher education Calculus course, and its effects on different aspects of the learning process were studied. Two experimental groups and two control groups for a total of 102 students taking the Calculus course participated in the study. Results indicated an overall acceptance of using PIAC in class. Important evidence was obtained on the positive effects of using PIAC, not only influencing academic performance of students, but also in motivational aspects of the learning process. The grades obtained in all of academic activities by the groups using PIAC, compared with the control groups, provide solid evidence to the positive influence of the intervention of the technology under the TUM.     

Interpretation and knowledge discovery from a multilayer perceptron network that performs whole life assurance risk assessment

This paper interprets the outputs from a Multilayer Perceptron (MLP) network that performs a whole life assurance risk assessment task. Using a new method published by the first author, the paper finds the significant, or key, inputs that the network uses to classify applicants for whole life assurance into standard and non-standard risk. The ranking of the significant inputs enables the knowledge learned by the network during training to be presented in the form of data relationships and induced rules which show that the network learns sensibly and effectively when compared with the training data set. This study demonstrates the potential value of the knowledge discovery method for MLP network validation and case-by-case interpretation both during network learning and network use. This has important implications for safety critical systems.