Statistical inference for exploratory data analysis ... - Hadley Wickham
Statistical inference for exploratory data analysis ... - Hadley Wickham Statistical inference for exploratory data analysis ... - Hadley Wickham
esiduals 20 10 0 −10 −20 20 10 0 −10 −20 20 10 0 −10 −20 20 10 0 −10 −20 20 10 0 −10 −20 1 5 9 13 17 100 200 300 400 500 Statistical inference for graphics 4375 2 6 10 14 18 100 200 300 400 500 100 200 300 400 500 order 3 7 11 15 19 4 8 12 16 20 100 200 300 400 500 Figure 6. Residuals of the Boston Housing Data plotted against order in the data. What does the structure in the real plot indicate? In supervised classification problems, especially when the size of the sample is small in relation to the number of variables, the PDA index is suitable. This index is designed to overcome the variance estimation problems that arise in the LDA index. When the sample size is small and the number of variables is large, the LDA index produces unreliable results, which express themselves as Phil. Trans. R. Soc. A (2009) Downloaded from rsta.royalsocietypublishing.org on January 7, 2010
4376 A. Buja et al. 5 0 5 0 −5 5 0 PP2 −5 −5 5 0 −5 5 0 −5 1 5 9 13 17 −5 0 5 10 2 6 10 14 18 −5 0 5 10 −5 0 5 10 PP1 3 7 11 15 19 4 8 12 16 20 −5 0 5 10 Figure 7. These 20 plots show two-dimensional projection pursuit projections of the best separation of three classes in gene expression data, having 72 samples and 3571 variables. Which plot is most different from the others? Why? Group: pink, AML; green, B-ALL; blue, T-ALL. data piling. To avoid this problem, the PDA index uses a penalization term regulated by a parameter λ. In this example we examine the two-dimensional optimal projection using the PDA index with λ = 0.8. Figure 7 shows the plot of the real data mingling among nineteen plots of data using permuted classes. Which plot shows the real data? Why? Phil. Trans. R. Soc. A (2009) Downloaded from rsta.royalsocietypublishing.org on January 7, 2010
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Figure 7. These 20 plots show two-dimensional projection pursuit projections of the best separation<br />
of three classes in gene expression <strong>data</strong>, having 72 samples and 3571 variables. Which plot is most<br />
different from the others? Why? Group: pink, AML; green, B-ALL; blue, T-ALL.<br />
<strong>data</strong> piling. To avoid this problem, the PDA index uses a penalization term<br />
regulated by a parameter λ. In this example we examine the two-dimensional<br />
optimal projection using the PDA index with λ = 0.8. Figure 7 shows the plot<br />
of the real <strong>data</strong> mingling among nineteen plots of <strong>data</strong> using permuted classes.<br />
Which plot shows the real <strong>data</strong>? Why?<br />
Phil. Trans. R. Soc. A (2009)<br />
Downloaded from<br />
rsta.royalsocietypublishing.org on January 7, 2010
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