The main objective of this study is a graphical display of the results of the high (as well as the low) dimensional multi-class support vector machine classification. Additionally, we will visually be able to detect the outliers and misclassified observations by using this graphical tool. The “outlier map” as a successful graphical outlier detection tool of robust statistics is extended in this paper. In fact, this is a bilateral extension concerning the misclassified and outlying observations recognition. The most important feature of this extension is creating two types of discriminative boundaries to segregate the data and detect the outlying observations. For this purpose, we employed the simple but efficient concept of the “confidence interval”, which is computed for the mean of decision function of support vector machine and then, “thresholding” technique. After that, the efficiency of the outlier map in terms of the preciseness of the correct outlier identification has been tested by the classification accuracy. Moreover, we deployed the margin width “before” and “after” outlier detection as the other criterion to assess the preciseness of the correct outlier identification. We conducted an empirical study based on the proposed method on the simulated and several well-known real datasets. It shows the effectiveness of our proposed method by increasing the “margin width” and gaining a higher classification accuracy.
The Ordinary Least Squares (OLS) method is the most widely used method to estimate the parameters of regression model. One of the critical assumption of the OLS estimation method is that the regression variables are measured without error. However, in many practical situations this assumption is often violated, whereby both dependent and independent variables are measured with errors. In these situations the OLS estimates lead to inconsistent and biased estimates. Consequently, the parameter estimates do not come closer to the true values, even in very large sample. To remedy this problem, instrumental variables (IV) estimation technique is utilized. In this article we examine some interesting numerical examples which are related to measurement errors. The results show that the IV estimates is more appropriate than the OLS estimates in such situations.
The leakage of hazardous compounds in chemical industries has always been one of the factors threatening workers, plants, and the environment. Among them, butyl acrylate is one of the most harmful materials that are widely used in chemical plants. In the present study, a butyl acrylate tank located in a real tank farm in Kocaeli-Turkey was analyzed for the examination of emissions and trinitrotoluene (TNT) equivalent explosion model of the vapor cloud. Areal Locations of Hazardous Atmospheres (ALOHA) program was used to define threat zones of butyl acrylate leakage based on different scenarios, such as a leakage from the tank without fire, burning as a jet fire, and also burning as a fireball during Boiling Liquid Expanding Vapor Explosion (BLEVE). In addition, since the most important parameters that enhance the effects of explosion and the spread of volatile organic compounds (VOCs) are wind speed, filling ratio of the tanks, and temperature, the interaction of these parameters on the threat zones and the highest threat zones of explosions were investigated using the Box-Behnken experimental design and one-way Analysis of Variance (ANOVA), respectively. As butyl acrylate, one of the most dangerous chemicals for industrial facilities, and its explosion effects have not been studied so far, it can be safely mentioned that this paper representing the first study in the literature is highly original and novel.
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