Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

error rate Related Abstracts

2 The Classification Performance in Parametric and Nonparametric Discriminant Analysis for a Class- Unbalanced Data of Diabetes Risk Groups

Authors: Lily Ingsrisawang, Tasanee Nacharoen

Abstract:

Introduction: The problems of unbalanced data sets generally appear in real world applications. Due to unequal class distribution, many research papers found that the performance of existing classifier tends to be biased towards the majority class. The k -nearest neighbors’ nonparametric discriminant analysis is one method that was proposed for classifying unbalanced classes with good performance. Hence, the methods of discriminant analysis are of interest to us in investigating misclassification error rates for class-imbalanced data of three diabetes risk groups. Objective: The purpose of this study was to compare the classification performance between parametric discriminant analysis and nonparametric discriminant analysis in a three-class classification application of class-imbalanced data of diabetes risk groups. Methods: Data from a healthy project for 599 staffs in a government hospital in Bangkok were obtained for the classification problem. The staffs were diagnosed into one of three diabetes risk groups: non-risk (90%), risk (5%), and diabetic (5%). The original data along with the variables; diabetes risk group, age, gender, cholesterol, and BMI was analyzed and bootstrapped up to 50 and 100 samples, 599 observations per sample, for additional estimation of misclassification error rate. Each data set was explored for the departure of multivariate normality and the equality of covariance matrices of the three risk groups. Both the original data and the bootstrap samples show non-normality and unequal covariance matrices. The parametric linear discriminant function, quadratic discriminant function, and the nonparametric k-nearest neighbors’ discriminant function were performed over 50 and 100 bootstrap samples and applied to the original data. In finding the optimal classification rule, the choices of prior probabilities were set up for both equal proportions (0.33: 0.33: 0.33) and unequal proportions with three choices of (0.90:0.05:0.05), (0.80: 0.10: 0.10) or (0.70, 0.15, 0.15). Results: The results from 50 and 100 bootstrap samples indicated that the k-nearest neighbors approach when k = 3 or k = 4 and the prior probabilities of {non-risk:risk:diabetic} as {0.90:0.05:0.05} or {0.80:0.10:0.10} gave the smallest error rate of misclassification. Conclusion: The k-nearest neighbors approach would be suggested for classifying a three-class-imbalanced data of diabetes risk groups.

Keywords: bootstrap, error rate, diabetes risk groups, k-nearest neighbors

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1 An Efficient Process Analysis and Control Method for Tire Mixing Operation

Authors: Hwang Ho Kim, Do Gyun Kim, Jin Young Choi, Sang Chul Park

Abstract:

Since tire production process is very complicated, company-wide management of it is very difficult, necessitating considerable amounts of capital and labors. Thus, productivity should be enhanced and maintained competitive by developing and applying effective production plans. Among major processes for tire manufacturing, consisting of mixing component preparation, building and curing, the mixing process is an essential and important step because the main component of tire, called compound, is formed at this step. Compound as a rubber synthesis with various characteristics plays its own role required for a tire as a finished product. Meanwhile, scheduling tire mixing process is similar to flexible job shop scheduling problem (FJSSP) because various kinds of compounds have their unique orders of operations, and a set of alternative machines can be used to process each operation. In addition, setup time required for different operations may differ due to alteration of additives. In other words, each operation of mixing processes requires different setup time depending on the previous one, and this kind of feature, called sequence dependent setup time (SDST), is a very important issue in traditional scheduling problems such as flexible job shop scheduling problems. However, despite of its importance, there exist few research works dealing with the tire mixing process. Thus, in this paper, we consider the scheduling problem for tire mixing process and suggest an efficient particle swarm optimization (PSO) algorithm to minimize the makespan for completing all the required jobs belonging to the process. Specifically, we design a particle encoding scheme for the considered scheduling problem, including a processing sequence for compounds and machine allocation information for each job operation, and a method for generating a tire mixing schedule from a given particle. At each iteration, the coordination and velocity of particles are updated, and the current solution is compared with new solution. This procedure is repeated until a stopping condition is satisfied. The performance of the proposed algorithm is validated through a numerical experiment by using some small-sized problem instances expressing the tire mixing process. Furthermore, we compare the solution of the proposed algorithm with it obtained by solving a mixed integer linear programming (MILP) model developed in previous research work. As for performance measure, we define an error rate which can evaluate the difference between two solutions. As a result, we show that PSO algorithm proposed in this paper outperforms MILP model with respect to the effectiveness and efficiency. As the direction for future work, we plan to consider scheduling problems in other processes such as building, curing. We can also extend our current work by considering other performance measures such as weighted makespan or processing times affected by aging or learning effects.

Keywords: Compound, Particle Swarm Optimization, makespan, error rate, flexible job shop scheduling problem, particle encoding scheme, sequence dependent setup time, tire mixing process

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