凸面，二维数据的最佳二进制分类

问题

我有一个非常复杂的数据集，我想尽可能地分开：

我想找到一个简单的凸形，例如可以捕捉90％的红色点，同时减少绿色的点

  mydata = cbind(
    "Temperature" = c( -3.62, -3.45, -3.47, -8.84, -6.47, -11, -6, -5.3, -4.24, -3.45, -2.91, -5.27, -9.9, -4.06, -8.71, -7.26, -7.67, -5.1, -3.19, -3.98, -6.9, -8.27, -8.37, -8.8, -2.68, -2.43, -6.99, -3.44, -3.49, -6.45, -4.24, -7.3, -2.22, -3.88, -9.57, -6.38, -3.86, -11.6, -5.45, -7.52, -4.05, -5.07, -6.55, -12, -9.41, -4.11, -7.3, -6.08, -3.71, -3.12, -8.17, -7.4, -3.26, -4.12, -2.74, -2.42, -7.02, -9.44, -6.62, -3.76, -4.12, -9.84, -3.78, -2.86, -4.3, -6.3, -5.29, -2.89, -3.94, -6.56, -6.58, -10.9, -3.16, -2.5, -5.33, -4.1, -3.22, -4.24, -6.19, -3.1, -5.48, -7.48, -9.56, -7.08, -3.59, -8.24, -8.44, -6.2, -3.41, -7.9, -7.66, -2.86, -8.39, -7.16, -9.42, -10.9, -3.47, -6.2, -3.57, -3.09, -7.29, -3.3, -5.8, -9.75, -4.82, -3.91, -3.34, -3.07, -9.39, -6.51, -6.6, -7.57, -11, -5.9, -4.42, -10.2, -2.02, -8.06, -3.82, -2.84, -3.27, -3.37, -2.93, -5.18, -9.29, -8.72, -3.17, -7.47, -8.85, -5.27, -3.15, -5.07, -5.4, -3.38, -4.07, -8.92, -2.54, -7.87, -8.7, -4.88, -9.35, -8.57, -10.3, -4.08, -3.06, -6.02, -4.43, -8.24, -3.46, -8.15, -9.9, -6.37, -2.65, -3.2, -4.23, -4.29, -8.06, -8.3, -9.36, -5.82, -11.3, -5.87, -3.1, -8.48, -4.47, -3.44, -6.34, -3.39, -5.29, -9.76, -7.29, -4.2, -3.84, -4.12, -10.6, -3.34, -9.75, -7.41, -11.4, -3.7, -7.57, -4.29, -4.18, -4.87, -3.85, -10, -3.94, -4.55, -3.57, -5.29, -9.29, -6.17, -4.58, -3.92, -3.08, -4.51, -8.21, -2.7, -3.56, -7.92, -4.38, -3.3, -6.94, -6.92, -7.5, -9.1, -6.72, -7.66, -7.76, -6.84, -4.23, -6.11, -12.6, -5.95, -9.34, -3.81, -9.35, -7.37, -6.66, -3.89, -7.64, -7.8, -10.3, -5.06, -3.62, -2.15, -7.66, -2.74, -6.9, -4.36, -2.21, -6.5, -2.95, -4.19, -9.96, -6.81, -10, -6.59, -9.19, -4.27, -7.64, -6.13, -4.01, -4.98, -7.11, -4.72, -11.2, -3.88, -3.03, -3.88, -2.39, -6.83, -5.94, -6.92, -3.54, -11, -7.74, -10.3, -9.04, -4.93, -8.96, -2.74, -4.15, -5.06, -10.8, -5.94, -7.96, -4.32, -4.23, -4.68, -4.8, -2.86, -2.31, -3.37, -6.06, -2.4, -2.57, -4.54, -3.11, -3.1, -5.2, -4.23, -4.22, -3.6, -3.16, -3.45, -3.65, -3.28, -3.6, -3.13, -3.08, -3.74, -2.61, -4.42, -2.82, -2.52, -3.05, -3.56, -5.58, -4.53, -2.82, -4.73, -3.17, -4.37, -3.39, -4.74, -4.06, -2.49, -4.35, -2.57, -3.88, -3.53, -3.11, -2.9, -2.76, -4.2, -3.28, -4.07, -3.1, -2.96, -3.5, -2.5, -6.26, -3.5, -3.16, -3.05, -1.95, -2.19, -4.1, -5.71, -3.53, -3.77, -1.95, -4.18, -3.96, -3.45, -3.86, -3.1, -3.54, -3.96, -3.23, -2.32, -2.7, -3.73, -2.77, -3.04, -3.17, -2.35, -3.46, -4.01, -3.05, -2.64, -5.51, -2.44, -2.6, -5.34, -2.83, -2.84, -6.01, -4.64, -2.69, -4.28, -4.28, -2.82, -3.18, -2.89, -3.12, -2.93, -3.36, -4.86, -4.92, -4.5, -3.69, -3.72, -4.67, -3.19, -3.74, -3.94, -2.81, -3.66, -2.98, -4.46, -2.46, -3.85, -3.66, -2.88, -4.19, -3.03, -3.46, -3.96, -2.4, -3.09, -4.08, -4.18, -2.56, -2.06, -3.14, -3.44, -3.51, -4.99, -2.9, -3.41, -3.36, -4.53, -2.76, -3.74, -3.33, -2.75, -2.39, -3.1, -6.21, -4.45, -2.81, -2.5, -4.14, -3.56, -3.06, -3.36, -2.86, -3.22, -3.33, -3.88, -5.38, -2.88, -2.25, -2.97, -5.22, -4.49, -4.76, -2.73, -2.98, -4.85, -4.03, -3.48, -2.54, -2.02, -2.86, -2.7, -3.63, -3.46, -2.71, -2.9, -2.96, -8.07, -2.83, -2.87, -2.87, -3.98, -4.34, -4.84, -4.06, -3.03, -3.1, -3.2, -3.86, -3.72, -2.82, -5.83, -3.1, -4.24, -3.33, -3.2, -2.92, -2.1, -3.61, -2.78, -3.37, -4.26, -2.38, -3.65, -5.05, -5.54, -3.77, -5.37, -3.51, -3.2, -3.67, -4.36, -2.21, -2.78, -2.85, -3.53, -2.04, -4.97, -2.94, -5.7, -4.14, -3.8, -2.69, -4, -3.18, -3.58, -2.14),
    "Loss" = c( -74.6, -77.6, -77.3, -74.1, -73, -72.9, -83.3, -73.3, -73.5, -73.9, -77.7, -76.9, -74.7, -75.4, -80.9, -74.9, -77.6, -75.8, -78.9, -74.7, -73.2, -72.7, -83.8, -73.4, -75.1, -75.8, -77.2, -76.5, -72.3, -73.4, -72.4, -74.6, -74.3, -73.9, -73.7, -78.8, -78.9, -83.1, -71.7, -82.1, -72.8, -73.7, -82.6, -74.9, -79.7, -74, -75.2, -73.4, -75.2, -72.8, -79, -76.9, -74.1, -74, -76.7, -73.9, -85.5, -79, -78.5, -72.5, -73.1, -76, -73.1, -77.2, -73.5, -78.8, -76.9, -76.8, -76.5, -77, -77.9, -73.2, -77.1, -75.8, -73.2, -76.5, -76.2, -72.8, -71.5, -74, -74.4, -85.8, -79.6, -82.3, -75.7, -72, -75.3, -81.5, -72.8, -74.3, -78.9, -73.7, -75.6, -73.9, -74.1, -78.3, -74.8, -80.8, -79.7, -74.8, -80.7, -76, -75.9, -78.3, -79.8, -78.9, -76.2, -74.1, -75.4, -75.6, -80.4, -77.8, -72.4, -72.3, -73.4, -78.4, -75.7, -80.7, -74.9, -75.8, -73.1, -74.4, -73, -72.9, -79.4, -74.2, -82.4, -75.5, -73.1, -75.8, -82.5, -76, -73.7, -78.4, -72.1, -82.2, -73, -72.9, -76.1, -74.1, -73.2, -74.7, -74.3, -71.6, -75.1, -75.4, -81, -74.6, -72.8, -76.9, -78.3, -73.8, -74.2, -73.9, -73.5, -75.2, -76.4, -79.6, -76.1, -76.3, -75.4, -78, -73.1, -80.7, -74.3, -72.9, -78.2, -81.5, -77.3, -73.5, -74, -73.7, -74.4, -74, -76, -73.9, -75.8, -74.5, -77.5, -73.2, -82.7, -73.1, -75, -79.8, -72.6, -85.1, -72.3, -72.5, -75.3, -72.6, -75.8, -74.2, -74.1, -73.2, -75.7, -72.3, -74.3, -75.2, -72, -77.8, -76.5, -75.9, -82.3, -73.7, -74.5, -75.1, -77.2, -76.6, -76.2, -75.6, -75.7, -74.8, -72.8, -72, -72.7, -72, -74.7, -72.8, -77.8, -74.5, -74.4, -75.2, -73, -76.4, -76.2, -73.3, -84.3, -73.2, -72.9, -76.2, -79.7, -82.6, -75.3, -73.6, -72.6, -77.8, -75.9, -76.7, -77.8, -76.8, -76.1, -73.9, -83.1, -75.1, -72.6, -74.7, -80.9, -76.7, -76.1, -74.6, -72.3, -74.4, -82.2, -74, -74.1, -75.3, -78.8, -75.4, -73.9, -72.6, -84.7, -71.8, -73.2, -73.6, -73.2, -75, -79, -71.7, -75.1, -75.5, -77.5, -78.7, -73.3, -72, -76.4, -75, -73.7, -81.7, -76.2, -78.4, -80, -79.8, -75.6, -70.5, -80.2, -69.9, -76.5, -74.4, -77.1, -71.6, -72.9, -74, -82.5, -74.5, -76.4, -73.5, -75.9, -77.6, -74.5, -80.9, -78.8, -77.7, -71.1, -80.2, -75.1, -83.7, -76.8, -81.8, -77.3, -77.9, -80.4, -77.3, -74.2, -77.2, -70, -74.2, -83, -75.8, -73, -75.1, -73.1, -71, -72.9, -76.8, -82.6, -76.5, -73.9, -75.9, -74.7, -76.3, -76.6, -77.7, -72.9, -73, -73.9, -75.2, -78.4, -73.6, -75.3, -73.3, -73.5, -79.9, -76.9, -74.5, -75.9, -76.4, -76.4, -73.4, -73, -73.2, -74.2, -75.1, -78.5, -72.8, -77.5, -79.5, -72.3, -76.6, -73, -83.8, -75.9, -70, -77.8, -73.9, -72.2, -76.6, -74, -70.9, -73, -79.3, -78.1, -81, -84.1, -71, -80, -73.1, -74, -71.7, -73.5, -73.2, -80.2, -77.7, -76, -78.5, -76.7, -72.6, -74.8, -73.1, -69.9, -74.7, -74.9, -82.9, -75.4, -78.4, -76.8, -75.9, -77.8, -80.5, -76.9, -78.7, -74.4, -80.3, -72.3, -73.9, -72.3, -73.8, -75.2, -74.4, -76.6, -79.1, -74.3, -76.2, -76.6, -71.7, -79, -74.8, -73.8, -73, -73.7, -74, -74.2, -79, -76.3, -78.4, -74.8, -81, -76.7, -77, -75.4, -73.8, -74.2, -78.4, -74.6, -72.7, -81.5, -78.4, -74.3, -74.1, -71.2, -76.7, -77.5, -76.2, -75.1, -72.4, -75.4, -74.4, -73.3, -86, -71.6, -80.4, -73.5, -72.5, -77.8, -74.5, -79.9, -76.3, -73.9, -76.5, -83.8, -77.2, -74.5, -80.4, -75.4, -72.8, -77.3, -78.7, -74, -73.6, -73, -72.8, -82.8, -71.6, -78.9, -74.9, -73.1, -82.4, -77.1, -74.5, -71.8, -72.9, -85.3, -73.9, -84.4, -79, -78.1, -74.5, -75.7, -75.6, -75, -71.8, -74.6, -73.4, -73.3),
    "Class" = c( 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0))

plot(mydata[,1:2], pch=2+mydata[,3], col=2+mydata[,3])

• 现在让我们忽略过度拟合

目标

• 绘制最佳矩形（内部最小绿色）
• 画出N <= 6面的最佳（内部最小绿色）多边形（或画一个圆）

我想得到：

• 方程/多边形点最佳分离，并且
• 内/外百分比/计数。

我想

• 固定内部所需的百分比，并优化污染的不希望有的数量，或者
• fix the % purity and maximize the number of desired points falling inside the polygon

Tried

I tried SVM packages e1071 and kernlab, but I did not get useful results.

• Either SVM not designed for so overlapping data, or just I did not get how it works.

Googling it was otherwise pretty unsuccesful, I am probaly just missing the right phrases to search for this problem, this simple problem must have been solved decades ago.

Any help appreciated. Thanks in advance.