How to find out which graph is most similar to another graph? [closed]

I have this list of matrices in R:

 my_list =  structure(list(
        matrix(c(2,2,2,2,3, 1,2,2,2,3, 1,2,3,3,3, 1,2,1,3,3, 1,1,1,3,3), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,2,2, 1,1,1,2,2, 1,1,1,3,3, 1,1,3,3,3, 1,1,3,3,3), nrow=5, byrow=TRUE),
        matrix(c(2,2,2,3,3, 2,2,2,3,3, 1,1,3,3,3, 1,1,3,3,3, 1,1,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,3, 2,2,3,3,3, 2,2,2,3,3, 2,2,2,1,1, 1,1,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,3, 1,1,1,2,2, 1,1,1,2,2, 1,1,1,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,3,3, 1,1,1,3,3, 1,1,1,2,2, 1,1,2,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,3,3,2,2, 1,3,3,2,2, 1,1,3,3,2, 1,1,1,3,2, 1,1,1,1,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,2,2, 1,1,1,2,2, 1,1,1,2,3, 1,1,1,2,3, 1,1,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(2,2,2,2,2, 3,3,3,3,3, 3,3,3,3,3, 1,1,3,3,3, 1,1,3,3,3), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,1,1,1,2, 3,1,1,1,2, 3,3,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,1,1,1,1, 3,3,1,1,1, 3,3,2,2,1, 2,2,2,1,1, 2,2,2,1,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,3, 3,3,1,3,1, 2,2,1,1,1, 2,2,1,1,1, 2,2,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,1,1,1, 3,1,1,1,1, 3,2,2,1,1, 3,2,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,1,1,1,2, 1,1,1,1,2, 3,3,3,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,2, 1,1,1,3,2, 1,3,1,3,2, 1,3,3,3,2, 1,1,3,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,3, 3,3,2,2,2, 3,3,2,2,2, 1,1,2,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,3,3, 1,1,1,3,3, 1,1,2,2,3, 1,1,1,2,3, 1,1,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,3, 1,1,2,3,3, 1,1,2,3,3, 1,1,2,2,2, 1,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,2,2,1,1, 1,1,2,2,1, 3,3,2,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,1,1, 1,1,1,1,2, 1,1,1,1,2, 1,2,1,2,2, 1,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(2,3,3,3,3, 2,3,3,3,3, 2,3,3,3,3, 2,2,2,1,1, 1,1,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(2,2,2,2,2, 2,2,2,2,2, 2,2,2,2,2, 2,3,1,1,2, 3,3,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,1,1,1,1, 3,1,1,1,1, 2,2,1,1,1, 2,2,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,3,3, 2,1,1,3,3, 2,2,1,1,3, 2,2,2,1,1, 2,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,1,1,1,1, 3,3,3,3,1, 2,2,2,2,1, 2,2,2,2,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,1, 3,3,2,1,1, 3,3,2,1,1, 3,3,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,1,1, 3,3,3,1,1, 3,2,2,1,1, 2,2,2,1,1, 2,2,2,1,1), nrow=5, byrow=TRUE),
        matrix(c(2,2,2,1,1, 2,2,2,1,1, 2,2,1,1,1, 3,2,2,1,1, 3,3,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,1,1, 1,2,1,1,1, 1,2,2,1,1, 1,1,2,3,3, 1,1,2,3,3), nrow=5, byrow=TRUE),
        matrix(c(1,1,3,3,3, 1,2,2,2,3, 1,2,2,3,3, 1,2,2,3,3, 1,1,1,3,3), nrow=5, byrow=TRUE),
        matrix(c(3,1,1,1,1, 3,1,1,1,1, 3,3,1,1,2, 3,1,1,2,2, 3,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(1,1,1,3,3, 1,1,1,3,3, 2,3,3,3,3, 2,3,3,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,2,2,2,2, 3,2,2,2,2, 3,1,2,1,1, 3,1,1,1,1, 3,3,3,3,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,3, 3,3,3,1,1, 2,1,1,1,1, 2,2,2,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
        matrix(c(3,3,3,3,2, 3,3,3,3,2, 3,1,1,1,2, 3,1,1,1,1, 3,1,1,1,1), nrow=5, byrow=TRUE),
        matrix(c(3,3,2,2,2, 3,1,1,2,2, 3,1,1,2,2, 1,1,1,2,2, 1,1,1,2,2), nrow=5, byrow=TRUE)
    ), class = "list")

I then plotted all of them using the following code:

library(ggplot2)
library(gridExtra)
library(reshape2)
library(dplyr)

plot_matrix <- function(mat, plot_number) {
    df <- melt(mat)
    names(df) <- c("row", "col", "value")
    
    df$index <- (df$row - 1) * 5 + df$col
    
    colors <- c(
        "1" = "#FFB3B3",
        "2" = "#B3D9FF",
        "3" = "#B3FFB3"
    )
    
    p <- ggplot(df, aes(x = col, y = -row, fill = factor(value))) +
        geom_tile(color = "black", linewidth = 0.5) +
        geom_text(aes(label = index), size = 3) +
        scale_fill_manual(values = colors) +
        labs(title = paste("Object", plot_number)) +
        coord_equal() +
        theme_minimal() +
        theme(
            legend.position = "none",
            plot.title = element_text(hjust = 0.5, margin = margin(b = 10)),
            axis.text = element_blank(),
            axis.title = element_blank(),
            panel.grid = element_blank(),
            plot.margin = margin(5, 5, 5, 5)
        )
    
    return(p)
}

plot_list <- lapply(seq_along(my_list), function(i) {
    plot_matrix(my_list[[i]], i)
})

n_plots <- length(plot_list)
n_cols <- 6
n_rows <- ceiling(n_plots / n_cols)

grid.arrange(
    grobs = plot_list,
    ncol = n_cols,
    nrow = n_rows,
    padding = unit(2, "mm")
)

I have the following question: If we take object 1 – is there something we can do to find out which of the remaining objects is “most similar” to object 1 based on : A) distribution of colors AND B) shape of color boundaries AND C) placement of color boundaries?

My current approach is to answer each one of these questions separately and average them. For example:

A) Find out the color distribution of each object as a vector and take the euclidean distance between object 1 and all other objects.
B) and C) Use something like Jaccard Distance or Hausdorf Distance between object 1 and all other objects
take the average of all differences to get an idea of general similarity. The pair (object1, object_i) with the lowest average is most similar

I am not sure how correct this approach is and I was wondering if there is something easier.

An idea for A)

library(plotly)

color_counts <- data.frame(
    object = 1:length(my_list),
    red = sapply(my_list, function(mat) sum(mat == 1)),
    blue = sapply(my_list, function(mat) sum(mat == 2)),
    green = sapply(my_list, function(mat) sum(mat == 3))
)

point_colors <- ifelse(color_counts$object == 1, "orange", "black")

plot_ly(color_counts, 
        x = ~red, 
        y = ~blue, 
        z = ~green,
        text = ~paste("Object", object),
        type = "scatter3d",
        mode = "markers",
        marker = list(
            color = point_colors,
            size = 6  # Making points slightly larger for better visibility
        )) %>%
    layout(scene = list(
        xaxis = list(title = "Red (1s)"),
        yaxis = list(title = "Blue (2s)"),
        zaxis = list(title = "Green (3s)")
    ))

This question is hard to answer, but Part A and Part B should be relatively straightforward, hclust() and a some sort of jaccard distance can be calculated (although not the traditional jaccard ‘how many things in common’, as all Objects have the same values (1, 2, and 3) but in they’re in different positions).

The part that I’m struggling with is:

B) shape of color boundaries AND C) placement of color boundaries?

This is way outside my area of expertise, but perhaps the clustering-type approaches might help you get started.

E.g.

library(tidyverse)
my_list =  structure(list(
  matrix(c(2,2,2,2,3, 1,2,2,2,3, 1,2,3,3,3, 1,2,1,3,3, 1,1,1,3,3), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,2,2, 1,1,1,2,2, 1,1,1,3,3, 1,1,3,3,3, 1,1,3,3,3), nrow=5, byrow=TRUE),
  matrix(c(2,2,2,3,3, 2,2,2,3,3, 1,1,3,3,3, 1,1,3,3,3, 1,1,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,3, 2,2,3,3,3, 2,2,2,3,3, 2,2,2,1,1, 1,1,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,3, 1,1,1,2,2, 1,1,1,2,2, 1,1,1,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,3,3, 1,1,1,3,3, 1,1,1,2,2, 1,1,2,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,3,3,2,2, 1,3,3,2,2, 1,1,3,3,2, 1,1,1,3,2, 1,1,1,1,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,2,2, 1,1,1,2,2, 1,1,1,2,3, 1,1,1,2,3, 1,1,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(2,2,2,2,2, 3,3,3,3,3, 3,3,3,3,3, 1,1,3,3,3, 1,1,3,3,3), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,1,1,1,2, 3,1,1,1,2, 3,3,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,1,1,1,1, 3,3,1,1,1, 3,3,2,2,1, 2,2,2,1,1, 2,2,2,1,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,3, 3,3,1,3,1, 2,2,1,1,1, 2,2,1,1,1, 2,2,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,1,1,1, 3,1,1,1,1, 3,2,2,1,1, 3,2,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,1,1,1,2, 1,1,1,1,2, 3,3,3,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,2, 1,1,1,3,2, 1,3,1,3,2, 1,3,3,3,2, 1,1,3,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,3, 3,3,2,2,2, 3,3,2,2,2, 1,1,2,2,2, 1,1,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,3,3, 1,1,1,3,3, 1,1,2,2,3, 1,1,1,2,3, 1,1,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,3, 1,1,2,3,3, 1,1,2,3,3, 1,1,2,2,2, 1,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,2,2,1,1, 1,1,2,2,1, 3,3,2,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,1,1, 1,1,1,1,2, 1,1,1,1,2, 1,2,1,2,2, 1,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(2,3,3,3,3, 2,3,3,3,3, 2,3,3,3,3, 2,2,2,1,1, 1,1,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(2,2,2,2,2, 2,2,2,2,2, 2,2,2,2,2, 2,3,1,1,2, 3,3,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,1,1,1,1, 3,1,1,1,1, 2,2,1,1,1, 2,2,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,3,3, 2,1,1,3,3, 2,2,1,1,3, 2,2,2,1,1, 2,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,1,1,1,1, 3,3,3,3,1, 2,2,2,2,1, 2,2,2,2,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,1, 3,3,2,1,1, 3,3,2,1,1, 3,3,2,2,2, 3,3,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,1,1, 3,3,3,1,1, 3,2,2,1,1, 2,2,2,1,1, 2,2,2,1,1), nrow=5, byrow=TRUE),
  matrix(c(2,2,2,1,1, 2,2,2,1,1, 2,2,1,1,1, 3,2,2,1,1, 3,3,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,1,1, 1,2,1,1,1, 1,2,2,1,1, 1,1,2,3,3, 1,1,2,3,3), nrow=5, byrow=TRUE),
  matrix(c(1,1,3,3,3, 1,2,2,2,3, 1,2,2,3,3, 1,2,2,3,3, 1,1,1,3,3), nrow=5, byrow=TRUE),
  matrix(c(3,1,1,1,1, 3,1,1,1,1, 3,3,1,1,2, 3,1,1,2,2, 3,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(1,1,1,3,3, 1,1,1,3,3, 2,3,3,3,3, 2,3,3,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,2,2,2,2, 3,2,2,2,2, 3,1,2,1,1, 3,1,1,1,1, 3,3,3,3,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,3, 3,3,3,1,1, 2,1,1,1,1, 2,2,2,2,2, 2,2,2,2,2), nrow=5, byrow=TRUE),
  matrix(c(3,3,3,3,2, 3,3,3,3,2, 3,1,1,1,2, 3,1,1,1,1, 3,1,1,1,1), nrow=5, byrow=TRUE),
  matrix(c(3,3,2,2,2, 3,1,1,2,2, 3,1,1,2,2, 1,1,1,2,2, 1,1,1,2,2), nrow=5, byrow=TRUE)
), class = "list")

library(ggplot2)
library(gridExtra)
#> 
#> Attaching package: 'gridExtra'
#> The following object is masked from 'package:dplyr':
#> 
#>     combine
library(reshape2)
#> 
#> Attaching package: 'reshape2'
#> The following object is masked from 'package:tidyr':
#> 
#>     smiths
library(dplyr)

plot_matrix <- function(mat, plot_number) {
  df <- melt(mat)
  names(df) <- c("row", "col", "value")
  
  df$index <- (df$row - 1) * 5 + df$col
  
  colors <- c(
    "1" = "#FFB3B3",
    "2" = "#B3D9FF",
    "3" = "#B3FFB3"
  )
  
  p <- ggplot(df, aes(x = col, y = -row, fill = factor(value))) +
    geom_tile(color = "black", linewidth = 0.5) +
    geom_text(aes(label = index), size = 3) +
    scale_fill_manual(values = colors) +
    labs(title = paste("Object", plot_number)) +
    coord_equal() +
    theme_minimal() +
    theme(
      legend.position = "none",
      plot.title = element_text(hjust = 0.5, margin = margin(b = 10)),
      axis.text = element_blank(),
      axis.title = element_blank(),
      panel.grid = element_blank(),
      plot.margin = margin(5, 5, 5, 5)
    )
  
  return(p)
}

plot_list <- lapply(seq_along(my_list), function(i) {
  plot_matrix(my_list[[i]], i)
})

n_plots <- length(plot_list)
n_cols <- 6
n_rows <- ceiling(n_plots / n_cols)

grid.arrange(
  grobs = plot_list,
  ncol = n_cols,
  nrow = n_rows,
  padding = unit(2, "mm")
)

my_list
#> [[1]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    2    2    2    2    3
#> [2,]    1    2    2    2    3
#> [3,]    1    2    3    3    3
#> [4,]    1    2    1    3    3
#> [5,]    1    1    1    3    3
#> 
#> [[2]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    1    1    2    2
#> [2,]    1    1    1    2    2
#> [3,]    1    1    1    3    3
#> [4,]    1    1    3    3    3
#> [5,]    1    1    3    3    3
#> 
#> ...
#> 
#> [[36]]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    3    3    2    2    2
#> [2,]    3    1    1    2    2
#> [3,]    3    1    1    2    2
#> [4,]    1    1    1    2    2
#> [5,]    1    1    1    2    2
#> 
#> attr(,"class")
#> [1] "list"

# combine all of the melted matrices into a single dataframe
list_of_dfs <- map(seq_along(my_list), ~melt(my_list[[.x]]) %>%
                     mutate(id = .x) %>%
                     pivot_wider(id_cols = id,
                                 names_from = c(Var1, Var2),
                                 values_from = value)) %>%
  bind_rows()

# get all of the combinations, e.g. Object 1 vs 1, 1 vs 2, etc
combinations <- expand.grid(1:nrow(list_of_dfs), 1:nrow(list_of_dfs)) %>%
  filter(Var1 != Var2)
output <- map2(combinations$Var2, combinations$Var1, ~sum(list_of_dfs[.x,] == list_of_dfs[.y,]))
combinations$total_matches <- unlist(output)

# check the top matches i.e. how many values are in the same place
head(combinations[order(combinations$total_matches, decreasing = TRUE),], 15)
#>     Var1 Var2 total_matches
#> 328   14   10            23
#> 465   10   14            23
#> 125   21    4            21
#> 191   17    6            21
#> 566    6   17            21
#> 704    4   21            21
#> 261   17    8            20
#> 376   27   11            20
#> 568    8   17            20
#> 921   11   27            20
#> 29    30    1            19
#> 42     8    2            19
#> 145    6    5            19
#> 159   20    5            19
#> 175   36    5            19

Looks like Object 30 is the closest match to Object 1 (i.e. it has 19 values in the same position in the matrices). Using hclust you get the same answer:


list_of_dfs <- map(seq_along(my_list), ~melt(my_list[[.x]]) %>%
                     mutate(id = .x) %>%
                     pivot_wider(id_cols = id,
                                 names_from = c(Var1, Var2),
                                 values_from = value)) %>%
  bind_rows() %>%
  dplyr::mutate(across(-id, ~scale(.x)))

hc <- hclust(dist(list_of_dfs[-1]), method = "complete")
plot(hc)

^{Created on 2024-12-16 with reprex v2.1.0}

Hope this helps; good luck!

Trang chủ Giới thiệu Sinh nhật bé trai Sinh nhật bé gái Tổ chức sự kiện Biểu diễn giải trí Dịch vụ khác Trang trí tiệc cưới Tổ chức khai trương Tư vấn dịch vụ Thư viện ảnh Tin tức - sự kiện Liên hệ Chú hề sinh nhật Trang trí YEAR END PARTY công ty Trang trí tất niên cuối năm Trang trí tất niên xu hướng mới nhất Trang trí sinh nhật bé trai Hải Đăng Trang trí sinh nhật bé Khánh Vân Trang trí sinh nhật Bích Ngân Trang trí sinh nhật bé Thanh Trang Thuê ông già Noel phát quà Biểu diễn xiếc khỉ Xiếc quay đĩa Dịch vụ tổ chức sự kiện 5 sao Thông tin về chúng tôi Dịch vụ sinh nhật bé trai Dịch vụ sinh nhật bé gái Sự kiện trọn gói Các tiết mục giải trí Dịch vụ bổ trợ Tiệc cưới sang trọng Dịch vụ khai trương Tư vấn tổ chức sự kiện Hình ảnh sự kiện Cập nhật tin tức Liên hệ ngay Thuê chú hề chuyên nghiệp Tiệc tất niên cho công ty Trang trí tiệc cuối năm Tiệc tất niên độc đáo Sinh nhật bé Hải Đăng Sinh nhật đáng yêu bé Khánh Vân Sinh nhật sang trọng Bích Ngân Tiệc sinh nhật bé Thanh Trang Dịch vụ ông già Noel Xiếc thú vui nhộn Biểu diễn xiếc quay đĩa Dịch vụ tổ chức tiệc uy tín Khám phá dịch vụ của chúng tôi Tiệc sinh nhật cho bé trai Trang trí tiệc cho bé gái Gói sự kiện chuyên nghiệp Chương trình giải trí hấp dẫn Dịch vụ hỗ trợ sự kiện Trang trí tiệc cưới đẹp Khởi đầu thành công với khai trương Chuyên gia tư vấn sự kiện Xem ảnh các sự kiện đẹp Tin mới về sự kiện Kết nối với đội ngũ chuyên gia Chú hề vui nhộn cho tiệc sinh nhật Ý tưởng tiệc cuối năm Tất niên độc đáo Trang trí tiệc hiện đại Tổ chức sinh nhật cho Hải Đăng Sinh nhật độc quyền Khánh Vân Phong cách tiệc Bích Ngân Trang trí tiệc bé Thanh Trang Thuê dịch vụ ông già Noel chuyên nghiệp Xem xiếc khỉ đặc sắc Xiếc quay đĩa thú vị

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