The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Linear Segmentation

John Mount

2023-08-19

In this example we fit a piecewise linear function to example data.
Please see here for a discussion of the methodology.

library("RcppDynProg")


set.seed(2018)
g <- 100
d <- data.frame(
  x = 0.05*(1:(3*g))) # ordered in x
d$y_ideal <- sin((0.3*d$x)^2)
d$y_observed <- d$y_ideal + 0.25*rnorm(length(d$y_ideal))


# plot
plot(d$x, d$y_observed,
     xlab = "x", ylab = "y",
     main = "raw data\ncircles: observed values, dashed line: unobserved true values")
lines(d$x, d$y_ideal,
     type = "l",
     lty = "dashed")

x_cuts <- solve_for_partition(d$x, d$y_observed, penalty = 1)
print(x_cuts)
##        x       pred group  what
## 1   0.05 -0.1570880     1  left
## 2   4.65  1.1593754     1 right
## 3   4.70  1.0653666     2  left
## 4   6.95 -0.9770792     2 right
## 5   7.00 -1.2254925     3  left
## 6   9.20  0.8971391     3 right
## 7   9.25  1.3792437     4  left
## 8  11.10 -1.1542021     4 right
## 9  11.15 -1.0418353     5  left
## 10 12.50  1.1519490     5 right
## 11 12.55  1.3964906     6  left
## 12 13.75 -1.2045219     6 right
## 13 13.80 -1.3791405     7  left
## 14 15.00  1.0195679     7 right
d$estimate <- approx(x_cuts$x, x_cuts$pred, xout = d$x, method = "linear", rule = 2)$y
d$group <- as.character(findInterval(d$x, x_cuts[x_cuts$what=="left", "x"]))
print(sum((d$y_observed - d$y_ideal)^2))
## [1] 20.42462
print(sum((d$estimate - d$y_ideal)^2))
## [1] 3.536541
print(sum((d$estimate - d$y_observed)^2))
## [1] 20.53796
# plot
plot(d$x, d$y_observed,
     xlab = "x", ylab = "y",
     main = "RcppDynProg piecewise linear estimate\ndots: observed values, segments: estimated shape")
points(d$x, d$y_ideal,
     type = "l",
     lty = "dashed")
cmap <- c("#a6cee3",
          "#1f78b4",
          "#b2df8a",
          "#33a02c",
          "#fb9a99",
          "#e31a1c",
          "#fdbf6f",
          "#ff7f00",
          "#cab2d6",
          "#6a3d9a",
          "#ffff99",
          "#b15928")
names(cmap) <- as.character(seq_len(length(cmap)))
points(d$x, d$y_observed, col = cmap[d$group], pch=19)
groups <- sort(unique(d$group))
for(gi in groups) {
  di <- d[d$group==gi, , drop = FALSE]
  lines(di$x, di$estimate, col = cmap[di$group[[1]]], lwd=2)
}

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.