Industrial Data Analytics for Diagnosis and Prognosis. Yong Chen

Industrial Data Analytics for Diagnosis and Prognosis - Yong Chen


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categorical variable. The idea is to use a box plot to represent the distribution of the numerical variable at each value of the categorical variable. In Figure 2.5, we draw two side-by-side box plots for the auto_spec data set using the following R codes:

      Relationship Between Two Categorical Variables – Mosaic Plot

      Figure 2.6 Mosaic plot for fuel type and aspiration.

      mosaicplot(fuel.type ~ aspiration, data = auto.spec.df,

       xlab = "Fuel Type", ylab = "Aspiration",

       color = c("green", "blue"),

       main = "Mosaic Plot")

      In a mosaic plot, the height of a bar represents the percentage for each value of the variable in the vertical axis given a fixed value of the variable in the horizontal axis. For example, in Figure 2.6 the height of the bar corresponding to turbo aspiration is much higher when the fuel type is diesel than when it is gas, which means a higher percentage of diesel cars use turbo aspiration, while a lower percentage of gasoline cars use turbo aspiration. The width of a bar in a mosaic plot corresponds to the frequency, or the number of observations, for each value of the variable in the horizontal axis. For example, from Figure 2.6, the bars for gas fuel type is much wider than those for diesel fuel type, indicating that a much larger number of cars are gasoline cars in the data set.

      2.1.3 Plots for More than Two Variables

      It is very difficult to plot more than two variables in a two dimensional plot. This section introduces commonly used plots that show some aspects of how multiple variables are related to each other. In Chapter 4, we will study another technique called principal component analysis, which can also serve as a useful tool to visualize high dimensional data in a low dimensional space.

      Color Coded Scatter Plot

      oldpar <- par(xpd = TRUE) plot(auto.spec.df$peak.rpm ~ auto.spec.df$horsepower,

       xlab = "Horsepower", ylab = "Peak RPM",

       col = ifelse(auto.spec.df$fuel.type == "gas",

       "black", "gray")) legend("topleft", inset = c(0, -0.2),

       legend = c("gas", "diesel"),

       col = c(“black”, "gray"), pch = 1, cex = 0.8) par(oldpar)

      Although there is no clear relationship between the peak RPM and horsepower of a car from the scatter plot in Figure 2.7, it is obvious from the color coded plot that diesel cars tend to have low peak RPM and low horsepower.

      Scatter Plot Matrix and Heatmap

      The pairwise relationship of multiple numerical variables can be visualized simultaneously by using a matrix of scatter plots. The following R codes plot the scatter plot matrix for five of the numerical variables in the auto_spec data set: wheel.base, height, curb.weight, city.mpg, and highway.mpg. The column indices of the five variables are 8, 11, 12, 22, and 23, respectively.

      var.idx <- c(8, 11, 12, 22, 23) plot(auto.spec.df[, var.idx])

      For a large number of numerical variables, it is difficult to visualize all pairwise scatter plots as in the scatter plot matrix. In this case, we can use a heatmap for pairwise correlations of the variables to quickly show the strength of the relationship. The heatmap uses different shades of colors to represent the values of the correlations so that the spots or regions of strong positive or negative relationship can be quickly detected. Detailed discussion of correlation is provided in Section 2.2. We draw the heatmap of correlations for all numerical variables in the auto_spec data set using the following R codes.

      library(gplots) var.idx <-c(8:12, 15, 17:23) data.nomiss <- na.omit(auto.spec.df[, var.idx]) heatmap.2(cor(data.nomiss), Rowv = FALSE, Colv = FALSE, dendrogram = “none”, cellnote = round(cor(data.nomiss),2), notecol = “black”, key = FALSE, trace = ’none’, margins=c(10,10))


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