## 3 Results and Discussion
### Classification of Stalk Lodging Resistance  
Some multivariate analytical methods can be used by agricultural scientists to classify corn varieties and to search for those with the best stalk lodging properties. From the measurement results, the eigenvalues calculated using the SVD algorithm are displayed in Figure 2. The eigenvalues of the first three principal components are expectedly much higher than the others. These components explain the variations of the experimental results listed in Table 1. The first component (PC1) explains 40% of the variation, the second component (PC2) and third component (PC3) explains 28% and 17% of the variations, respectively. The first three eigenvalues accounted for 85% of the total eigenvalues. Therefore, in the current experiment, a truncation value \(tr\) = 3 was used and the first three eigenvalues and their corresponding eigenvector coefficients were used in evaluating the corn's stalk lodging properties. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Density** & **Varieties** & \begin{tabular}{c} **Plant** \\ **Height** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Ear** \\ **Height** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Interode** \\ **Length** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Stalk** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Ear** \\ **Diameter** \\ **(mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Lodging** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Maximum** \\ **Coefficient** \\ \end{tabular} \\ \hline
60,000 & DH605 & 2510.00 b & 950.00 e & 71.00 d & 23.59 a & 0.38 c & 42.40 a & 50.76 a \\
60,000 & XD20 & 2640.00 a & 1250.00 a & 98.10 a & 21.49 b & 0.47 a & 38.09 b & 24.79 d \\
60,000 & XY335 & 2360.00 c & 990.00 d & 94.0 b & 20.49 c & 0.42 b & 26.50 c & 37.61 b \\
60,000 & YD606 & 2500.00 b & 1120.00 b & 93.00 b & 20.81 d & 0.45 ab & 41.10 a & 34.50 c \\
60,000 & ZD958 & 2500.00 b & 1000.00 c & 74.20 c & 24.09 a & 0.40 b & 40.50 ab & 38.83 b \\
75,000 & DH605 & 2650.00 d & 995.00 e & 80.00 c & 24.21 a & 0.38 c & 37.90 a & 39.93 a \\
75,000 & XD20 & 3020.00 a & 1340.00 a & 109.30 a & 23.51 b & 0.44 b & 25.60 c & 26.07 d \\
75,000 & XY335 & 2920.00 b & 1180.00 c & 111.00 a & 21.43 c & 0.40 b & 28.90 b & 38.30 a \\
75,000 & YD606 & 2680.00 c & 1250.00 b & 95.10 b & 22.37 c & 0.47 a & 29.50 b & 34.69 c \\
75,000 & ZD958 & 2450.00 e & 1100.00 d & 78.20 d & 24.79 a & 0.45 ab & 26.22 c & 37.50 b \\ \hline \hline \end{tabular} Note: The lowercase letters a, b, c, d and e in Table 1 indicate the significant differences between different corn varieties for each stalk agronomic traits, which were achieved by using the Least Significant Difference (LSD) (the \(p\)-value = 0.05). Here, the plant height is the distance from root surface to tip of tassels. The ear height is the distance from root surface to node of top ear. The internode length is the average internode length of the stalk between the 3 rd node and 4 th node counting from the ground. The stalk diameter at mid-growth stages is measured by using a Vernier caliper. The ear position coefficient is the ratio of the ear height to the plant height.  
\end{table} 
Table 1: The agronomic traits and stalk lodging properties from five corn varieties with two planting densities. A three-dimensional scattering plot of the first three principle components obtained from SVD analysis of the measurement results are shown in Figure 3. The contours of the Gaussian distributions of data are represented by the error ellipses. From the error ellipses, the five corn varieties with two planting densities were evidently identified and segregated. The green ellipse represented corn stalks with high lodging properties such as ZD958 (60,000), DH605 (60,000), and DH605 (75,000).