How to identify and merge connected cases in a list of integer vectors

Identify and Merge Connected Cases in a List of Integer Vectors

In this blog post, we'll explore how to identify and merge connected cases in a list of integer vectors using R. This is a common task in data analysis and can be applied to various scenarios such as clustering, network analysis, and anomaly detection.

The Problem

Given a list of integer vectors, our objective is to identify and merge connected cases. Two cases are considered connected if they share at least one common element. The goal is to obtain a new list where each vector represents a connected cases with unique elements.

Solution 1: Recursive Approach

One approach to solve this problem is to use a recursive function. The idea is to iteratively merge connected cases until no further merging is possible. Here's the R code for such a solution:

create_merged_list <- function(l, check_finished_list = NULL) {
    new_l <- unique(lapply(seq(l), \(i) merge_elements(l, i)))

    if (identical(check_finished_list, new_l)) {
        return(new_l)
    }
    create_merged_list(new_l, l)
}

merge_elements <- function(l, i) {
    l_compare <- l[-i]
    el <- l[[i]]
    match_vals <- which(outer(el, unlist(l_compare), \(x, y) x == y), arr.ind = TRUE)[,
    "col"]

    if (!length(match_vals)) {
        return(el)
    }

    l_breaks <- cumsum(lengths(l_compare))

    l_match_idx <- vapply(match_vals, \(x) min(which(x <= l_breaks)), integer(1))
    new_el <- sort(unique(c(el, unlist(l_compare[l_match_idx]))))
    new_el
}

The create_merged_list function starts the recursive process, and the merge_elements function does the actual merging of connected cases.

Solution 2: Using expand.grid and mapply

Another approach involves using the expand.grid and mapply functions. Here's the R code for this solution:

Merge <- function(List){
  Seq <- seq_along(List)
  ExpSeq <- expand.grid(Seq, Seq)
  rows <- which(upper.tri(matrix(Seq, ncol=max(Seq), nrow=max(Seq))))

  c(list(as.vector(na.omit(unique(unlist(
    mapply(\(x, y) 
      ifelse(any(List[[x]] %in% List[[y]]), list(c(List[[x]], List[[y]])), NA), 
        ExpSeq[rows,1], ExpSeq[rows,2])))))),

    List[Seq[!Seq %in% na.omit(unique(unlist(
    mapply(\(x, y) 
      ifelse(any(List[[x]] %in% List[[y]]), list(c(x, y)), NA), 
        ExpSeq[rows,1], ExpSeq[rows,2]))))]]
  )
}

This approach uses expand.grid to generate all possible pairs of vectors in the list, and then uses mapply to merge connected cases and identify non-matching cases.

Solution 3: Base R Option

A base R solution can be implemented using two for loops to iteratively merge connected cases. Here's the R code for this solution:

f <- function(l) {
    repeat {
        grp <- seq_along(l)
        for (i in 1:(length(l) - 1)) {
            for (j in (i + 1):length(l)) {
                if (any(l[[i]] %in% l[[j]])) {
                    # update the labelling of groups
                    grp[j] <- grp[i]
                }
            }
        }
        # update the list as per the updated group labels
        lst <- tapply(l, grp, \(x) unique(unlist(x)))
        if (length(lst) < length(l)) {
            l <- lst
        } else {
            return(unname(lst))
        }
    }
}

The f function takes a list of vectors as input and iteratively merges connected cases until no further merging is possible.

Solution 4: Using the igraph Package

If you have the igraph package installed, you can use its graph-based approach to solve this problem. Here's the R code for this solution:

int_list %>%
    setNames(paste0("x", seq_along(.))) %>%
    stack() %>%
    graph_from_data_frame() %>%
    set_vertex_attr(name = "type", value = startsWith(names(V(.)), "x")) %>%
    bipartite.projection() %>%
    pluck("proj1") %>%
    decompose() %>%
    lapply(\(x) as.integer(names(V(x))))

This solution represents the list of vectors as a graph, where nodes are the elements and edges represent shared elements between vectors. It then uses the decompose function to identify connected components, which correspond to the merged connected cases.

I hope these solutions provide you with different approaches to identify and merge connected cases in a list of integer vectors in R. The most suitable solution for your specific problem may depend on the size and complexity of your data, as well as your preferences and familiarity with the different approaches presented here.