总体思路是独立预测 x 和 y,假设它们实际上是独立的:
library(splines)
path <- data.frame(
x = c(3, 3.5, 4.6875, 9.625, 5.5625, 19.62109375, 33.6796875, 40.546875, 36.59375, 34.5, 33.5, 33),
y = c(0, 1, 4, 5, 6, 8, 7, 6, 5, 2, 1, 0)
)
# add the time variable
path$time <- seq(nrow(path))
# fit the models
df <- 5
lm_x <- lm(x~bs(time,df),path)
lm_y <- lm(y~bs(time,df),path)
# predict the positions and plot them
pred_df <- data.frame(x=0,y=0,time=seq(0,nrow(path),length.out=100) )
plot(predict(lm_x,newdata = pred_df),
predict(lm_y,newdata = pred_df),
type='l')
您确实需要小心定义时间变量,因为路径并不独立于时间的选择(即使它们是连续的),因为样条曲线在预测变量空间中的点间距上不是不变的。例如:
plotpath <- function(...){
# add the time variable with random spacing
path$time <- sort(runif(nrow(path)))
# fit the models
df <- 5
lm_x <- lm(x~bs(time,df),path)
lm_y <- lm(y~bs(time,df),path)
# predict the positions and plot them
pred_df <- data.frame(x=0,y=0,time=seq(min(path$time),max(path$time),length.out=100) )
plot(predict(lm_x,newdata = pred_df),
predict(lm_y,newdata = pred_df),
type='l',...)
}
par(ask=TRUE); # wait until you click on the figure or hit enter to show the next figure
for(i in 1:5)
plotpath(col='red')