The Comparison Between Different Approaches to Overcome the Multicollinearity Problem in Linear Regression Models

In the presence of multi-collinearity problem, the parameter estimation method based on the ordinary least squares procedure is unsatisfactory. In 1970, Hoerl and Kennard insert analternative method labeled as estimator of ridge regression. In such estimator, ridge parameter plays an important role in estimation. Various methods were proposed by many statisticians to select the biasing constant (ridge parameter). Another popular method that is used to deal with the multi-collinearity problem is the principal component method. In this paper,we employ the simulation technique to compare the performance of principal component estimator with some types of ordinary ridge regression estimators based on the value of the biasing constant (ridge parameter). The mean square error (MSE) is used as a criterion to assess the performance of such estimators.

Soft-Sensor Modeling of PVC Polymerizing Process Based on F-GMDH-Type Neural Network Algorithm

For predicting the conversion velocity of the vinyl chloride monomer (VCM) in the polymerization process of polyvinylchloride (PVC), an improved Group Method of Data Handling- (GMDH-) type neural network soft-sensor model is proposed. After analyzing the technique of PVC manufacturing process, the auxiliary variables for setting up the soft-sensor model are selected and the experimental data are normalized. Because the internal standard of the original GMDH-type neural cannot solve the problem of multiple-collinearity problem and the useful variables tend to be prematurely eliminated in the modeling process, a hybrid method combining the regression analysis method and the least squares method is proposed to solve the multiple-collinearity problem. On the same time, by adopting some optimization experiences in genetic algorithm (GA), the generational crossover combination variables method is proposed to solve the shortcoming of useful variable being eliminated prematurely. The simulation results show that the proposed soft-sensor model can significantly improve the prediction accuracy of economic and technical indicators in the PVC polymerization process and can meet the real time control requirements of polymerization reactor production process.

Incremental Localization Algorithm Based on Regularized Iteratively Reweighted Least Square

Incremental localization algorithm is a distributed localization method with excellent characteristics for wireless network. However, its estimated result is generally influenced by the heteroscedasticity arising from cumulative errors and the collineation among anchor nodes. We have proposed a novel incremental localization algorithm with consideration to cumulative errors and collinearity among anchors. Using iteratively reweighted and regularized method, the algorithm reduces the influences of errors accumulation and avoids collinearity problem between anchors. Simulation experiment results show that compared with the previous incremental localization algorithms, the proposed algorithm obtains a localization solution which not only has high accuracy but also high stability. Therefore, the proposed algorithm is suitable for different deployment environments and has high adaptability.

RESIDENTIAL PROPERTY PRICE INDICES FOR TOKYO

This paper uses hedonic regression techniques to decompose the price of a house into land and structure components using real estate sales data for Tokyo. To get sensible results, a nonlinear regression model using data that covered multiple time periods was used. Collinearity between the amounts of land and structure in each residential property leads to inaccurate estimates for the land and structure value of a property. This collinearity problem was solved by using exogenous information on the rate of growth of construction costs in Tokyo in order to get useful constant-quality subindices for the price of land and structures separately.

Toward Collinearity-Avoidable Localization for Wireless Sensor Network

In accordance with the collinearity problem during computation caused by the beacon nodes used for location estimation which are close to be in the same line or same plane, two solutions are proposed in this paper: the geometric analytical localization algorithm based on positioning units and the localization algorithm based on the multivariate analysis method. The geometric analytical localization algorithm based on positioning units analyzes the topology quality of positioning units used to estimate location and provides quantitative criteria based on that; the localization algorithm based on the multivariate analysis method uses the multivariate analysis method to filter and integrate the beacon nodes coordinate matrixes during the process of location estimation. Both methods can avoid low estimation accuracy and instability caused by multicollinearity.

Odor Recorder

An odor recorder is a gadget to record smells as well as reproduce them. The odor recorder to record the recipe of multiple-component odor, the dynamical change of the odor recipe even under the environmental change, such as humidity and temperature, has been so far studied. The methods to solve the mixture quantification problem, such as multiple linear regression, partial least squares, neural network, etc., are described. Furthermore, the active odor sensing system, which explores the recipe of the blended odor with its output pattern’s similarity to that of the target odor, is described. Then, an example of the actual implementation of the odor recorder based upon a QCM sensor array is shown. Based upon that odor recorder, the experimental result of the fruit flavors made up of 4-8 odor components is described. Then a mass spectrometer without GC for determining the recipe of a few dozen odor components is explained. The mass spectrometry is useful to overcome the collinearity problem. However, the accuracy of the recipe estimation is insufficient when the number of odor-component candidates is more than a few hundred. The selection methods of odor components among the huge number of candidates and its application to the fruit flavors are explained. Finally, the method to find an appropriate set of odor components and the simulation result using mass spectrum database are described.