Joseph P. Herbert

Game-Theoretic Rough Sets

This article investigates the Game-theoretic Rough Set (GTRS) model and its capability of analyzing a major decision problem evident in existing probabilistic rough set models. A major challenge in the application of probabilistic rough set models is their inability to formulate a method of decreasing the size of the boundary region through further explorations of the data. To decrease the size of this region, objects must be moved to either the positive or negative regions. Game theory allows a solution to this decision problem by having the regions compete or cooperate with each other in order to find which is best fit to be selected for the move. There are two approaches discussed in this article. First, the region parameters that define the minimum conditional probabilities for region inclusion can either compete or cooperate in order to increase their size. The second approach is formulated by having classification approximation measures compete against each other. We formulate a learning method using the GTRS model that repeatedly analyzes payoff tables created from approximation measures and modified conditional risk strategies to calculate parameter values.

Criteria for choosing a rough set model

One of the challenges a decision maker faces in using rough sets is to choose a suitable rough set model for data analysis. We investigate how two rough set models, the Pawlak model and the probabilistic model, influence the decision goals of a user. Two approaches use probabilities to define regions in the probabilistic model. These approaches use either user-defined parameters or derive the probability thresholds from the cost associated with making a classification. By determining the implications of the results obtained from these models and approaches, we observe that the availability of information regarding the analysis data is crucial for selecting a suitable rough set approach. We present a list of decision types corresponding to the available information and user needs. These results may help a user match their decision requirements and expectations to the model which fulfills these needs.

Financial time-series analysis with rough sets

We investigate the use of the rough set model for financial time-series data analysis and forecasting. The rough set model is an emerging technique for dealing with vagueness and uncertainty in data. It has many advantages over other techniques, such as fuzzy sets and neural networks, including attribute reduction and variable partitioning of data. These characteristics can be very useful for improving the quality of results from data analysis. We demonstrate a rough set data analysis model for the discovery of decision rules from time series data for example, the New Zealand stock exchanges. Rules are generated through reducts and can be used for future prediction. A unique ranking system for the decision rules based both on strength of the rule and stability of the rule is used in this study. The ranking system gives the user confidence regarding their market decisions. Our experiment results indicate that the forecasting of future stock index values using rough sets obtains decision ruleswith high accuracy and coverage.

Web-Based Support Systems with Rough Set Analysis

Rough sets have been applied to many areas where multi-attribute data is needed to be analyzed to acquire knowledge for decision making. Web-based Support Systems (WSS) are a new research area that aims to support human activities and extend human physical limitations of information processing with Web technologies. The applications of rough set analysis for WSS is looked at in this article. In particular, our focus will be on Web-Based Medical Support Systems (WMSS). A WMSS is a support system that integrates medicine practices (diagnosis and surveillance) with computer science and Web technologies. We will explore some of the challenges of using rough sets in a WMSS and detail some of the applications of rough sets in analyzing medical data.

Game-theoretic risk analysis in decision-theoretic rough sets

Determining the correct threshold values for probabilistic rough set models has been a heated issue among the community. This article will formulate a game-theoretic approach to calculating these thresholds to ensure correct approximation region size. By finding equilibrium within payoff tables created from approximation measures and modified conditional risk strategies, we provide the user with tolerance levels for their loss functions. Using the tolerance values, new thresholds are calculated to provide correct classification regions. Better informed decisions can be made when utilizing these tolerance values.

Learning Optimal Parameters in Decision-Theoretic Rough Sets

A game-theoretic approach for learning optimal parameter values for probabilistic rough set regions is presented. The parameters can be used to define approximation regions in a probabilistic decision space. New values for loss functions are learned from a sequence of risk modifications derived from game-theoretic analysis of the relationship between two classification measures. Using game theory to maximize these measures results in a learning method to reformulate the loss functions. The decision-theoretic rough set model acquires initial values for these parameters through a combination of loss functions provided by the user. The new game-theoretic learning method modifies these loss functions according to an acceptable threshold.

A granular computing framework for self-organizing maps

When using granular computing for problem solving, one can focus on a specific level of understanding without looking at unwanted details of subsequent (more precise) levels. We present a granular computing framework for growing hierarchical self-organizing maps. This approach is ideal since the maps are arranged in a hierarchical manner and each is a complete abstraction of a pattern within data. The framework allows us to precisely define the connections between map levels. Formulating a neuron as a granule, the actions of granule construction and decomposition correspond to the growth and absorption of neurons in the previous model. In addition, we investigate the effects of updating granules with new information on both coarser and finer granules that have a derived relationship. Called bidirectional update propagation, the method ensures pattern consistency among data abstractions. An algorithm for the construction, decomposition, and updating of the granule-based self-organizing map is introduced. With examples, we demonstrate the effectiveness of this framework for abstracting patterns on many levels.

Rough Set Model Selection for Practical Decision Making

One of the challenges a decision maker faces is choosing a suitable rough set model to use for data analysis. The traditional algebraic rough set model classifies objects into three regions, namely, the positive, negative, and boundary regions. Two different probabilistic models, variable- precision and decision-theoretic, modify these regions via l,u user-defined thresholds and alpha, beta values from loss functions respectively. A decision maker whom uses these models must know what type of decisions can be made within these regions. This will allow him or her to conclude which model is best for their decision needs. We present an outline that can be used to select a model and better analyze the consequences and outcomes of those decisions.

A game-theoretic approach to competitive learning in self-organizing maps

Self-Organizing Maps (SOM) is a powerful tool for clustering and discovering patterns in data. Competitive learning in the SOM training process focuses on finding a neuron that is most similar to that of an input vector. Since an update of a neuron only benefits part of the feature map, it can be thought of as a local optimization problem. The ability to move away from a local optimization model into a global optimization model requires the use of game theory techniques to analyze overall quality of the SOM. A new algorithm GTSOM is introduced to take into account cluster quality measurements and dynamically modify learning rates to ensure improved quality through successive iterations.

Supporting online learning with games

This paper presents a study on Web-based learning support systems that is enhanced with two major subsystems: a Web-based learning game and a learning-oriented Web search. The Internet and theWeb may be considered as a first resource for students seeking for information and help. However, much of the information available online is not related to the course contents or is wrong in the worse case. The search subsystem aims to provide students with precise, relative and adaptable documents about certain courses or classes. Therefore, students do not have to spend time to verify the relationship of documents to the class. The learning game subsystem stimulates students to study, enables students to review their studies and to perform self-evaluation through a Web-based learning game such as a treasure hunt game. During the challenge and entertaining learning and evaluation process, it is hoped that students will eventually understand and master the course concepts easily. The goal of developing such a system is to provide students with an efficient and effective learning environment.