benchmarks.tex 4.01 KB
 Michael Keller committed Apr 21, 2022 1 2 \chapter{Benchmark Problems}  Michael Keller committed May 14, 2022 3 4 TODO: Add arnold scores  Michael Keller committed Apr 27, 2022 5 6 7 8 9 10 11 12 13 Our goal is to develop methods that work well in many or all cases. However, data that is based on real observations is of particular interest. Agroscope, the Swiss Federal Research center for agriculture, nutrition and the environment, has compiled some real world data. They have kindly supplied us with the relationship matrices so we can see how well our methods work on real data.  Michael Keller committed Apr 21, 2022 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 The first matrix is: \FloatBarrier \begin{figure}[h] \centering \begin{tabular}{ c c c c c c c c c c c c } & $c_1$ & $c_2$ & $c_3$ & $c_4$ & $c_5$ & $c_6$ & $c_7$ & $c_8$ & $c_9$ & $c_{10}$ & $c_{11}$ \\ $c_1$ & $-0.5$ & $1$ & $1$ & $1$ & $1$ & $1$ & $0.5$ & $-1$ & $0.5$ & $0.5$ & $1$ \\ $c_2$ & $1$ & $-0.5$ & $-1$ & $1$ & $1$ & $0.5$ & $0.5$ & $-1$ & $1$ & $1$ & $1$ \\ $c_3$ & $1$ & $-1$ & $-0.5$ & $-1$ & $1$ & $0$ & $0.5$ & $0.5$ & $0$ & $0$ & $0$ \\ $c_4$ & $1$ & $1$ & $-1$ & $-0.5$ & $0$ & $0$ & $0.5$ & $-1$ & $1$ & $-1$ & $0$ \\ $c_5$ & $1$ & $1$ & $1$ & $0$ & $-0.5$ & $0$ & $0.5$ & $1$ & $1$ & $1$ & $1$ \\ $c_6$ & $1$ & $0.5$ & $0$ & $0$ & $0$ & $-0.5$ & $0.5$ & $0$ & $0$ & $0$ & $0$ \\ $c_7$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ & $0.5$ \\ $c_8$ & $-1$ & $-1$ & $0.5$ & $-1$ & $1$ & $0$ & $0.5$ & $-0.5$ & $0$ & $0.5$ & $0$ \\ $c_9$ & $0.5$ & $1$ & $0$ & $1$ & $1$ & $0$ & $0.5$ & $0$ & $-0.5$ & $1$ & $0$ \\ $c_{10}$ & $0.5$ & $1$ & $0$ & $-1$ & $1$ & $0$ & $0.5$ & $0.5$ & $1$ & $-0.5$ & $1$\\ $c_{11}$ & $1$ & $1$ & $0$ & $0$ & $1$ & $0$ & $0.5$ & $0$ & $0$ & $1$ & $-0.5$ \\ \end{tabular} \end{figure} \FloatBarrier where \FloatBarrier \begin{figure}[h] \centering \begin{tabular}{@{}llr@{}} \toprule Crop Id & Crop Name\\ \midrule $c_1$ & Kreuzblütler \\ $c_2$ & Schmetterlingsblütler \\ $c_3$ & Nachtschattengewächse \\ $c_4$ & Kartoffel \\ $c_5$ & Korbblütler \\ $c_6$ & Getreide \\ $c_7$ & Kräuter \\ $c_8$ & Liliengewächse \\ $c_9$ & Süssgräser \\ $c_{10}$ & Kürbisgewächse \\ $c_{11}$ & Gänsefussgewächse \\ \bottomrule \end{tabular} \end{figure} \FloatBarrier and the second matrix is: \FloatBarrier  Michael Keller committed Apr 27, 2022 56 \begin{figure}[h]  Michael Keller committed Apr 21, 2022 57 58  \centering \begin{tabular}{ c c c c c c c c c c c }  Michael Keller committed Apr 27, 2022 59  & $c_1$ & $c_2$ & $c_3$ & $c_4$ & $c_5$ & $c_6$ & $c_7$ & $c_8$ & $c_9$ & $c_{10}$\\  Michael Keller committed Apr 21, 2022 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90  $c_1$ & $-1$ & $0$ & $0.5$ & $-0.5$ & $1$ & $0$ & $0.5$ & $1$ & $0.5$ & $0$\\ $c_2$ & $0$ & $-1$ & $0$ & $1$ & $0$ & $0$ & $0.5$ & $0.5$ & $0.5$ & $0$\\ $c_3$ & $0.5$ & $0$ & $-1$ & $0$ & $0$ & $0$ & $0.5$ & $0.5$ & $0$ & $-0.5$\\ $c_4$ & $-0.5$ & $1$ & $0$ & $-1$ & $0$ & $0$ & $-1$ & $0.5$ & $0.5$ & $0.5$\\ $c_5$ & $0$ & $0$ & $0$ & $0$ & $-1$ & $0$ & $0$ & $0$ & $0$ & $0$\\ $c_6$ & $0$ & $0$ & $0$ & $0$ & $0$ & $-1$ & $1$ & $0.5$ & $0$ & $0$\\ $c_7$ & $0.5$ & $0.5$ & $0.5$ & $-0.5$ & $0$ & $0.5$ & $-1$ & $0.5$ & $0.5$ & $0.5$\\ $c_8$ & $0$ & $0$ & $0$ & $0$ & $0$ & $0$ & $0$ & $0$ & $0$ & $0$ \\ $c_9$ & $0.5$ & $0.5$ & $0$ & $1$ & $0$ & $0$ & $0.5$ & $0.5$ & $-1$ & $0$\\ $c_{10}$ & $0$ & $0$ & $-0.5$ & $0.5$ & $0$ & $0$ & $1$ & $0.5$ & $0.5$ & $-1$\\ \end{tabular} \end{figure} \FloatBarrier where \FloatBarrier \begin{figure}[h] \centering \begin{tabular}{@{}llr@{}} \toprule Crop Id & Crop Name\\ \midrule $c_1$ & Weisskohl \\ $c_2$ & Karotten \\ $c_3$ & Kartoffeln \\ $c_4$ & Zwiebeln \\ $c_5$ & Hanf \\ $c_6$ & Zuckermais \\ $c_7$ & Buschbohnen \\ $c_8$ & Kräutermischung \\ $c_9$ & Kopfsalat \\ $c_{10}$ & Randen \\ \bottomrule \end{tabular} \end{figure}  Michael Keller committed Apr 27, 2022 91 92 93 94 \FloatBarrier Throughout this thesis we will report for the presented methods how well they work on these two matrices. Our standard field size will be $15 \times 15$ pixels.