Creates a data frame with the discrete Fréchet distance between two trajectories

Description

Creates a data frame with the discrete Fréchet distance between two trajectories

Usage

FD_data(data, i, j)

Arguments

Value

A data frame with the subjects and trips identifiers and the discrete Fréchet distance

Computes extended Hausdorff distance between two trajectories.

Description

Computes extended Hausdorff distance between two trajectories.

Usage

HD(pp1, pp2, q = 1)

Arguments

Value

A numerical value with the distance.

References

Magdy, N., Sakr, M., Abdelkader, T., Elbahnasy, K. (2015). Review on trajectory similarity measures. 10.1109/IntelCIS.2015.7397286.

Min, D., Zhilin, L., Xiaoyong, C. (2007) Extended Hausdorff distance for spatial objects in GIS. International Journal of Geographical Information Science, 21:4, 459–475

Examples

# Take two trajectories
library(dplyr)
library(sp)
sample_data<-gull_data %>% filter(ID %in% c(5107912,5107913), trip %in% c("V02","V01"))
tr1<-gull_data %>% filter((ID == 5107912) & (trip=="V02"))
tr2<-gull_data %>% filter((ID == 5107913) & (trip=="V01"))
pts1 = SpatialPoints(tr1[c("LONG","LAT")], proj4string=CRS("+proj=longlat"))
pts2 = SpatialPoints(tr2[c("LONG","LAT")], proj4string=CRS("+proj=longlat"))
# Hausdorff distance
HD(pts1,pts2,q=1)
# Median Hausdorff distance
HD(pts1,pts2,q=0.5)

Creates a data frame with the Hausdorff distance between two trajectories

Description

Creates a data frame with the Hausdorff distance between two trajectories

Usage

HD_data(data, i, j, q)

Arguments

Value

A data frame with the subjects and trips identifiers and the extended Hausdorff distance

Computes the intraclass correlation coefficient (ICC) using a matrix of distances.

Description

Computes the intraclass correlation coefficient (ICC) using a matrix of distances.

Usage

ICC(X, nt)

Arguments

Details

The intraclass correlation coefficient is estimated using the distance matrix among trajectories.

Value

Data frame with the estimates of the ICC (r), the subjects' mean sum-of-squares (MSA), the between-subjects variance (sb), the total variance (st), and the within-subjects variance (se).

Generates a bootstrap sample and estimates the ICC

Description

Generates a bootstrap sample and estimates the ICC

Usage

boot_ICC(X, nt, Bmat, indB)

Arguments

Value

Data frame with the estimates of the ICC (r), the subjects' mean sum-of-squares (MSA), the between-subjects variance (sb), the total variance (st), and the within-subjects variance (se).

Creates a matrix with the pairwise distances

Description

Creates a matrix with the pairwise distances

Usage

dist_mat(dataD, nt)

Arguments

Value

A list with two components:

• *D*. A matrix with the pairwise distances

• *data*. A data frame with the pairwise distances

Generates a data frame with the pairwise distances between trajectories

Description

Generates a data frame with the pairwise distances between trajectories

Usage

genHD(
  data_list,
  parallel = TRUE,
  distance = c("H", "F"),
  q = 0.5,
  future_seed = 123
)

Arguments

Value

A data frame with the subjects and trips identifiers and their distances

Preprocessing of data

Description

Preprocessing of data

Usage

get_data(data, ID, trip, LON, LAT, time)

Arguments

Value

A data frame

Gull data

Description

A data frame with sample of 90 gull trajectories.

Usage

gull_data

Format

A data frame containing 90 trajectories

ID

Subject identifier

trip

Trip identifier

LONG

Longitude

LAT

Latitude

triptime

Time in seconds when the locations were obtained

Estimates the intraclass correlation coefficient (ICC) for trajectory data

Description

Estimates the intraclass correlation coefficient (ICC) for trajectory data

Usage

iccTraj(
  data,
  ID,
  trip,
  LON,
  LAT,
  time,
  projection = CRS("+proj=longlat"),
  origin = "1970-01-01 UTC",
  parallel = TRUE,
  individual = TRUE,
  distance = c("H", "F"),
  bootCI = TRUE,
  nBoot = 100,
  q = 0.5,
  future_seed = 123
)

Arguments

Details

The intraclass correlation coefficient is estimated using the distance matrix among trajectories.

Bootstrap resamples are obtained using balanced randomized cluster bootstrap approach (Davison and Hinkley, 1997; Field and Welsh, 2007)

Value

An object of class iccTraj.The output is a list with the following components:

• est. Data frame with the following estimates: the ICC (r), the subjects' mean sum-of-squares (MSA), the between-subjects variance (sb), the total variance (st), and the within-subjects variance (se).

• boot. If bootCI argument is set to TRUE, data frame with the bootstrap estimates.

• D. Data frame with the pairwise distances among trajectories.

• indW. Data frame with the following columns: the subject's identifier (ID), the individual within-subjects variances (w), the individual ICC (r), and the number of trips (n).

References

Davison A.C., Hinkley D.V. (1997). Bootstrap Methods and Their Application. Cambridge: Cambridge University Press.

Field, C.A., Welsh, A.H. (2007). Bootstrapping Clustered Data. Journal of the Royal Statistical Society. Series B (Statistical Methodology). 69(3), 369-390.

Examples

# Using median Hausdorff distance.
 Hd<-iccTraj(gull_data,"ID","trip","LONG","LAT","triptime")
 Hd$est
# Using discrete Fréchet distance.
Fd<-iccTraj(gull_data,"ID","trip","LONG","LAT","triptime", distance="F")
Fd$est

Computes the confidence interval for the ICC

Description

Computes the confidence interval for the ICC

Usage

interval(x, conf = 0.95, method = c("BCa", "Perc", "EB", "AN", "ZT"))

Arguments

Details

Let \hat{\theta} denote the ICC sample estimate and \theta_i^{B} denote the ICC bootstrap estimates with i=1,\ldots,B. Let \delta_{\alpha/2}^{B} and \delta_{1-\alpha/2}^{B} be the \frac{\alpha}{2} and 1-\frac{\alpha}{2} percentiles of \delta_{i}^{B}=\theta_i^{B}-\hat{\theta}.

The percentile bootstrap confidence interval is computed as \hat{\theta}+\delta_{\alpha/2}^{B},\hat{\theta}+\delta_{1-\alpha/2}^{B}.

The empirical bootstrap confidence interval is estimated as \hat{\theta}-\delta_{1-\alpha/2}^{B},\hat{\theta}-\delta_{\alpha/2}^{B}

Asymptotic Normal (AN) interval is obtained as \hat{\theta} \pm Z_{1-\alpha/2}*SE_B where SE_B denotes the standard deviation of \theta_i^{B}, and Z_{1-\alpha/2} stands for the 1-\alpha/2 quantile of the standard Normal distribution.

In the ZT approach, the ICC is transformed using Fisher's Z-transformation. Then, the AN approach is applied to the transformed ICC.

Value

A vector with the two boundaries of the confidence interval.

Examples

# Using median Hausdorff distance
Hd<-iccTraj(gull_data,"ID","trip","LONG","LAT","triptime", parallel=FALSE, distance="H")
Hd$est
interval(Hd)

Computes the number of trips by subject

Description

Computes the number of trips by subject

Usage

ntrips(data)

Arguments

Value

A data frame with the number of trips by subject.

Prints the ICC

Description

Prints the ICC

Usage

## S3 method for class 'iccTraj'
print(x, ...)

Arguments

Value

The ICC estimate.

Creates a list containing the trajectories information.

Description

Creates a list containing the trajectories information.

Usage

tr_gen(data, projection = CRS("+proj=longlat"), origin = "1970-01-01 UTC")

Arguments

Value

Every component of the list has the following subcomponents: #'

• An object of class Track.

• An object of class SpatialPoints.

• Subject identifier

• Trip identifier.