Exercise_B_Similarity

Author

Céline Spitzli

Exercise B: Similarity

Task 1: Similarity measures

We will now calculate similarties between trajectories using a new dataset pedestrian.csv (available on moodle). Download an import this dataset as a data.frame or tibble. It it a set of six different but similar trajectories from pedestrians walking on a path.

For this task, explore the trajectories first and get an idea on how the pedestrians moved.

Loading libraries

library(readr)
library(dplyr)
library(sf)

library(ggplot2)

Read Data

pedestrians <- read_delim("Daten/pedestrian.csv")

pedestrians <- st_as_sf(pedestrians, coords = c("E", "N"), crs = 2056, remove = FALSE)

# EDA
pedestrians |> 
  ggplot(aes(E,N)) +
  geom_point(colour = pedestrians$TrajID) +
  geom_line(colour = pedestrians$TrajID) +
  facet_wrap(~TrajID) +
  theme_minimal()

Task 2: Calculate similarity

Install the package SimilarityMeasures (install.packages(“SimilarityMeasures”)). Familiarize yourself with this package by skimming through the function descriptions help(package = “SimilarityMeasures”). Now compare trajectory 1 to trajectories 2-6 using different similarity measures from the package. Your options are. DTW, EditDist, Frechet and LCSS.

Before visualizing your results think about the following: Which two trajectories to you percieve to be most similar, which are most dissimilar? Now visualize the results from the computed similarity measures. Which measure reflects your own intuition the closest?

Note: All functions in the package need matrices as input, with one trajectory per matrix.

1 and 6 look really similar, but 2 and 3 also have a lot in common 4 and 3 look very dissimlar

library("SimilarityMeasures")
library(SimilarityMeasures)

# Convert trajectories to dataframes
p1 <- pedestrians |> 
  filter(TrajID == 1) |> 
  select(E,N)

p2 <- pedestrians |> 
  filter(TrajID == 2) |> 
  select(E,N)

p3 <- pedestrians |> 
  filter(TrajID == 3) |> 
  select(E,N)

p4 <- pedestrians |> 
  filter(TrajID == 4) |> 
  select(E,N)

p5 <- pedestrians |> 
  filter(TrajID == 5) |> 
  select(E,N)

p6 <- pedestrians |> 
  filter(TrajID == 6) |> 
  select(E,N)

# Convert into matrix (extra conversion because there is an issue I do not understand. ChatGPT helped me solve this problem with the second code to create a matrix)
path1 <- as.matrix(p1)
path1 <- matrix(unlist(path1), ncol = 2, byrow = FALSE)

path2 <- as.matrix(p2)
path2 <- matrix(unlist(path2), ncol = 2, byrow = FALSE)

path3 <- as.matrix(p3)
path3 <- matrix(unlist(path3), ncol = 2, byrow = FALSE)

path4 <- as.matrix(p4)
path4 <- matrix(unlist(path4), ncol = 2, byrow = FALSE)

path5 <- as.matrix(p5)
path5 <- matrix(unlist(path5), ncol = 2, byrow = FALSE)

path6 <- as.matrix(p6)
path6 <- matrix(unlist(path6), ncol = 2, byrow = FALSE)

# help(package = "SimilarityMeasures")

Calculating Similarities

# DTW
DTW12 <- DTW(path1, path2, pointSpacing = -1)

# EditDist
EditDist(path1, path2, pointDistance = 20)

[1] 93

# Frechet
Frechet(path1, path2, testLeash = -1)

[1] 964525.3

# LCSS
LCSS(path1, path2, pointSpacing = -1, pointDistance = 20, errorMarg = 100, returnTrans = FALSE)

[1] 5

# or even easier with one big dataframe and all the results added

# function needed for LCSS
My_LCSS <- function(path1, path2) {
  LCSS(path1, path2, errorMarg = 100.0)
}

# creating a empty data.frame
results <- data.frame(Name = character(), Comparator = numeric(), Result = double(), stringsAsFactors = FALSE)
results <- rbind(results, data.frame(Name = "EditDist", Comparator = 2, Result = EditDist(path1, path2)))
results <- rbind(results, data.frame(Name = "EditDist", Comparator = 3, Result = EditDist(path1, path3)))
results <- rbind(results, data.frame(Name = "EditDist", Comparator = 4, Result = EditDist(path1, path4)))
results <- rbind(results, data.frame(Name = "EditDist", Comparator = 5, Result = EditDist(path1, path5)))
results <- rbind(results, data.frame(Name = "EditDist", Comparator = 6, Result = EditDist(path1, path6)))
results <- rbind(results, data.frame(Name = "DTW", Comparator = 2, Result = DTW(path1, path2)))
results <- rbind(results, data.frame(Name = "DTW", Comparator = 3, Result = DTW(path1, path3)))
results <- rbind(results, data.frame(Name = "DTW", Comparator = 4, Result = DTW(path1, path4)))
results <- rbind(results, data.frame(Name = "DTW", Comparator = 5, Result = DTW(path1, path5)))
results <- rbind(results, data.frame(Name = "DTW", Comparator = 6, Result = DTW(path1, path6)))
results <- rbind(results, data.frame(Name = "Frechet", Comparator = 2, Result = Frechet(path1, path2, testLeash = -1)))
results <- rbind(results, data.frame(Name = "Frechet", Comparator = 3, Result = Frechet(path1, path3)))
results <- rbind(results, data.frame(Name = "Frechet", Comparator = 4, Result = Frechet(path1, path4)))
results <- rbind(results, data.frame(Name = "Frechet", Comparator = 5, Result = Frechet(path1, path5)))
results <- rbind(results, data.frame(Name = "Frechet", Comparator = 6, Result = Frechet(path1, path6)))
results <- rbind(results, data.frame(Name = "LCSS", Comparator = 2, Result = My_LCSS(path1, path2)))
results <- rbind(results, data.frame(Name = "LCSS", Comparator = 3, Result = My_LCSS(path1, path3)))
results <- rbind(results, data.frame(Name = "LCSS", Comparator = 4, Result = My_LCSS(path1, path4)))
results <- rbind(results, data.frame(Name = "LCSS", Comparator = 5, Result = My_LCSS(path1, path5)))
results <- rbind(results, data.frame(Name = "LCSS", Comparator = 6, Result = My_LCSS(path1, path6)))

Visualize results

ggplot(results, aes(Comparator, Result, fill = Comparator)) +
  geom_bar(stat = "identity") +
  facet_wrap(~Name, scales = "free_y")

For me it is unclear why I have other values than the github page shows. but i do not find the error.

Which measure reflects your own intuition the closest? LCSS shows the same assumption, that 1 and 6 look very similar.