5925833
Mixed Monte Carlo Parallel Algorithms for Matrix Computation
In this paper we consider mixed (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. In this paper we show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D - C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D-1C; of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Experimental results with dense and sparse matrices are presented.
507578
Numerical Experiments with Monte Carlo Methods and SPAI Preconditioner for Solving System of Linear Equations
In this paper we present the results of experiments comparing the performance of the mixed Monte Carlo algorithms and SPAI preconditener with BICGSTAB. The experiments are carried out on a Silicon Graphics ONYX2 machine. Based on our experiments, we conclude that these techniques are comparable from the point of view of robustness and rates of convergence, with the Monte Carlo approach performing better for some general cases and SPAI approach performing better in case of very sparse matrices.
46055050
Hybrid Monte Carlo Methods for Matrix Computation
In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D - C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D-1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Experimental results with dense and sparse matrices are presented.
159216
A weight based compact genetic algorithm
In order to improve the performance of the compact Genetic Algorithm (cGA) to solve difficult optimization problems, an improved cGA which named as the weight based compact Genetic Algorithm (wcGA) is proposed. In the wcGA, S individuals are generated from the probability vector in each generation, when the winner competing with the other S-1 individuals to update the probability vector, different weights are multiplied to each solution according to the sequence of the solution ranked in the S-1 individuals. Experimental results on three kinds of Benchmark functions show that the proposed algorithm has higher optimal precision than that of the standard cGA and the cGA simulating higher selection pressures.
11368789
Discovering Interesting Holes in Data
Current machine learning and discovery techniques focus on discovering rules or regularities that exist in data. An important aspect of the research that has been ignored in the past is the learning or discovering of interesting holes in the database. If we view each case in the database as a point in a it-dimensional space, then a hole is simply a region in the space that contains no data point. Clearly, not every hole is interesting. Some holes are obvious because it is known that certain value combinations are not possible. Some holes exist because there are insufficient cases in the database. However, in some situations, empty regions do carry important information. For instance, they could warn us about some missing value combinations that are either not known before or are unexpected. Knowing these missing value combinations may lead to significant discoveries. In this paper, we propose an algorithm to discover holes in databases.
17698779
Neural Network Identification Method Applied to the Nonlinear System
A kind of neural network solution method has been proposed in the paper aiming at a class of non-linear process control system with the characteristic of time delay. In this scheme, a new-type associative memory neural network is used to model the controlled system, and the fuzzy neural network with inverse identification structure is adopted to control the nonlinear process system. This fuzzy neural network control method adopts the structure of three layers combine neural network identifier with inverse structure. Computer simulation and lab application show that it is effective to adopt this scheme to control on-linear process system with time delay.
8341217
Multi-Space-Mapped SVMs for Multi-class Classification
In SVMs-based multiple classification, it is not always possible to find an appropriate kernel function to map all the classes from different distribution functions into a feature space where they are linearly separable from each other. This is even worse if the number of classes is very large. As a result, the classification accuracy is not as good as expected. In order to improve the performance of SVMs-based multi-classifiers, this paper proposes a method, named multi-space-mapped SVMs, to map the classes into different feature spaces and then classify them. The proposed method reduces the requirements for the kernel function. Substantial experiments have been conducted on one-against-all, one-against-one, FSVM, DDAG algorithms and our algorithm using six UCI data sets. The statistical results show that the proposed method has a higher probability of finding appropriate kernel functions than traditional methods and outperforms others.
10102687
Mining interesting knowledge using DM-II
Data mining aims to develop a new generation of tools to intelligently assist humans in analyzing mountains of data. Over the past few years, great progress has been made in both research and applications of data mining. Data mining systems have helped many businesses by exposing previously unknown patterns in their databases, which were used to improve profits, enhance customer services, and ultimately achieve a competitive advantage. In this paper, we present our unique data mining system DM-II (Data Mining Integration and Interestingness). DM-II is a PC-based system working in Windows 95/98/NT environment. Apart from the normal components of a data mining system, DM-II has a number of unique and advanced sub-systems. These sub-systems have been applied in many real-life applications, including education applications, insurance application, accident application, disease application, drug screening application, image classification, etc. Here, we focus on discussing the following sub-systems: CBA: CBA originally stands for Classification-Based on Associations [lo]. It has now been extended with a number of other advanced features. In all, CBA has the following capabilities: Building classifiers using association rules: Traditionally, association rule mining and classifier building are regarded as two different data mining tasks. CBA unifies the two tasks. It is able to ,generate association rules and builds a classifier using a special subset of the association rules. What is significant is that CBA, in general, produces more accurate classifiers compared to the state-ofthe-art classification system C4.5 [ 161. It also helps to solve some outstanding problems with the existing classification systems. Pruning and summarizing the discovered associations: One major problem with association