View source: R/compute_elastic_shape_mean.R

compute_elastic_shape_mean | R Documentation |

Computes an elastic full Procrustes mean for curves stored in `data_curves`

.
Constructor function for class `elastic_shape_mean`

.

```
compute_elastic_shape_mean(
data_curves,
knots = seq(0, 1, len = 13),
type = c("smooth", "polygon"),
penalty = 2,
var_type = c("smooth", "constant", "zero"),
pfit_method = c("smooth", "polygon"),
smooth_warp = function(i) 0,
eps = 0.05,
max_iter = 50,
verbose = FALSE,
cluster = NULL
)
```

`data_curves` |
list of |

`knots` |
set of knots for the mean spline curve |

`type` |
if "smooth" linear srv-splines are used which results in a differentiable mean curve if "polygon" the mean will be piecewise linear. |

`penalty` |
the penalty to use in the covariance smoothing step. use '-1' for no penalty. |

`var_type` |
(experimental) assume "smooth", "constant" or "zero" measurement-error variance along t |

`pfit_method` |
(experimental) "smooth" or "polygon" |

`smooth_warp` |
(experimental) controls the weighting of original and smoothed observations over the iterations, if pfit_method == "smooth". |

`eps` |
the algorithm stops if L2 norm of coefficients changes by less than |

`max_iter` |
maximal number of iterations |

`verbose` |
print iterations |

`cluster` |
(experimental) use the parallel package for faster computation |

an object of class `elastic_shape_mean`

, which is a `list`

with entries

`type` |
"smooth" if mean was modeled using linear srv-splines, "polygon" if constant srv-splines |

`coefs` |
spline coefficients |

`knots` |
spline knots |

`variance` |
sample elastic shape variance |

`data_curves` |
list of |

`fit` |
see |

```
curve <- function(t){
rbind(t*cos(13*t), t*sin(13*t))
}
set.seed(18)
data_curves <- lapply(1:4, function(i){
m <- sample(10:15, 1)
delta <- abs(rnorm(m, mean = 1, sd = 0.05))
t <- cumsum(delta)/sum(delta)
data.frame(t(curve(t)) + 0.07*t*matrix(cumsum(rnorm(2*length(delta))),
ncol = 2))
})
#randomly rotate and scale curves
rand_scale <- function(curve){ ( 0.5 + runif(1) ) * curve }
rand_rotate <- function(curve){
names <- colnames(curve)
theta <- 2*pi*runif(1)
mat <- matrix(c(cos(theta), sin(theta), -sin(theta), cos(theta)), nrow = 2, ncol = 2)
curve.rot <- as.matrix(curve) %*% t(mat)
curve.rot <- as.data.frame(curve.rot)
colnames(curve.rot) <- names
return(curve.rot)
}
data_curves <- lapply(data_curves, rand_scale)
data_curves <- lapply(data_curves, rand_rotate)
#compute smooth procrustes mean with 2 order penalty
knots <- seq(0,1, length = 11)
elastic_shape_mean <- compute_elastic_shape_mean(
data_curves,
knots = knots,
type = "smooth",
penalty = 2
)
plot(elastic_shape_mean)
```

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