R help - Oct 2024 - Help in Recursive Function for steps reconstruction in Clusters Analysis - HCA: Single Link

Hello everybody,

I'm trying to build a function to illustrate, in 2D, the sequence of the 
"Single Link" algorithm (the purpose is merely didactic).

The idea is to have the scatter of points on a graph.
Iteratively, build the segments (with the "segments()" function, for 
each step).

I simulated a data set "d", and created an object "r" using
the command:

r <- hclust( dist( d ), met='single' )

My problem:

I created a recursive function, "f()", to find the shortest distances.
It is defined below.
But the return has only one column, while I thought there would be two 
columns.


What I get:
###############
# Testing f()
f( c(2, 3) )?? #### is the fourth step of hclust

 ???? [,1]
xmd1?? -6
xmd2? -10
xmd1?? -3
xmd1?? -4
xmd2?? -5

What I expected:
##################

# xmd1?? xmd2
# -6???? -10
# -3????? -5
# -4????? -5


If anyone can help me with this recursive function, I would appreciate 
it in advance.
I've never used recursion before, so I don't have a good grasp of how it
works.

Thank you very much in advance,

Cleber.



All details are below:
########################


d <- scan()
 ?0.986? 0.900
-1.331? 1.503
-0.220 -0.752
 ?0.102 -0.071
-0.171? 0.018
-0.782? 0.490
 ?1.154 -0.074
-0.768 -1.529
 ?1.761 -1.396
-0.730? 0.910

d <- matrix( d, 10, byrow=T )

r <- hclust( dist( d ), met='single' )
r$merge
#????? [,1] [,2]
# [1,]?? -4?? -5
# [2,]?? -6? -10
# [3,]?? -3??? 1
# [4,]??? 2??? 3
# [5,]?? -2??? 4
# [6,]?? -8??? 5
# [7,]?? -1?? -7
# [8,]??? 6??? 7
# [9,]?? -9??? 8


f <- function(xmd) {

 ??? rs <- NULL
 ??? xmd1 <- 999999999
 ??? xmd2 <- 999999999

 ??? if (xmd[1] > 0) {
 ??????? xmd1 <- f(r$merge[ xmd[1], ])
 ??? } else {
 ??????? xmd1 <- xmd[1]
 ??? }

 ??? if (xmd[2] > 0) {
 ??????? xmd2 <- f(r$merge[ xmd[2], ])
 ??? } else {
 ??????? xmd2 <- xmd[2]
 ??? }

 ??? return( rbind( rs, rbind( xmd1, xmd2 ) ) )
}



# Testing f()
f( c(2, 3) )

# result of f()
#????? [,1]
# xmd1?? -6
# xmd2? -10
# xmd1?? -3
# xmd1?? -4
# xmd2?? -5

# My expectative:
# xmd1?? xmd2
# -6???? -10
# -3????? -5
# -4????? -5


# Testing f()
 ?f( c( 6, 7) )

# result of f()
#????? [,1]
# xmd1?? -8
# xmd1?? -2
# xmd1?? -6
# xmd2? -10
# xmd1?? -3
# xmd1?? -4
# xmd2?? -5
# xmd1?? -1
# xmd2?? -7


# My expectative:
# xmd1?? xmd2
# -8???? -10
# -2???? -10
# -6???? -10
# -3????? -5
# -4????? -5
# -1????? -7

On 2024-10-26 3:14 p.m., Cleber Borges via R-help wrote:
> Hello everybody,
> 
> I'm trying to build a function to illustrate, in 2D, the sequence of
the
> "Single Link" algorithm (the purpose is merely didactic).
> 
> The idea is to have the scatter of points on a graph.
> Iteratively, build the segments (with the "segments()" function,
for
> each step).
> 
> I simulated a data set "d", and created an object "r"
using the command:
> 
> r <- hclust( dist( d ), met='single' )
> 
> My problem:
> 
> I created a recursive function, "f()", to find the shortest
distances.
> It is defined below.
> But the return has only one column, while I thought there would be two
> columns.
> 
I suspect you used rbind() where you should have used cbind() in your f, 
here:
>   ??? return( rbind( rs, rbind( xmd1, xmd2 ) ) )
which should have been


   return( rbind( rs, cbind( xmd1, xmd2 ) ) )

There may be other places where this change is needed; I haven't tried 
running your code.

Duncan Murdoch

For now, I've been able to think of a temporary solution... until I can 
think of a better teaching solution:

The same function f():

#####
f <- function(xmd) {
 ??? rs <- NULL
 ??? xmd1 <- 999999999
 ??? xmd2 <- 999999999

 ??? if (xmd[1] > 0) {
 ??????? xmd1 <- f(r$merge[ xmd[1], ])
 ??? } else {
 ??????? xmd1 <- xmd[1]
 ??? }

 ??? if (xmd[2] > 0) {
 ??????? xmd2 <- f(r$merge[ xmd[2], ])
 ??? } else {
 ??????? xmd2 <- xmd[2]
 ??? }

 ??? return( rbind( rs, rbind( xmd1, xmd2 ) ) )
}

####

Didactic example to illustrate the chain behavior of the "Single Link"
Algorithm


n <- 100

d <- matrix( runif( n * 2 ), n, 2 )

r <- hclust( dist( d ), met='single' )

plot( d, cex=1, col=1 )

for( i in 1:( nrow( d ) - 1 ) ){

 ??? p <- as.numeric( abs( f( r$merge[ i, ] ) ) )

 ??? points( d[ p,], col=i, cex=2, pch=19 )

 ??? cat(' Step: ', i, '\n' )

 ??? flush.console()

 ??? Sys.sleep( .2 )

}






Em 26/10/2024 16:14, Cleber Borges escreveu:
> Hello everybody,
>
> I'm trying to build a function to illustrate, in 2D, the sequence of 
> the "Single Link" algorithm (the purpose is merely didactic).
>
> The idea is to have the scatter of points on a graph.
> Iteratively, build the segments (with the "segments()" function,
for
> each step).
>
> I simulated a data set "d", and created an object "r"
using the command:
>
> r <- hclust( dist( d ), met='single' )
>
> My problem:
>
> I created a recursive function, "f()", to find the shortest
distances.
> It is defined below.
> But the return has only one column, while I thought there would be two 
> columns.
>
>
> What I get:
> ###############
> # Testing f()
> f( c(2, 3) )?? #### is the fourth step of hclust
>
> ???? [,1]
> xmd1?? -6
> xmd2? -10
> xmd1?? -3
> xmd1?? -4
> xmd2?? -5
>
> What I expected:
> ##################
>
> # xmd1?? xmd2
> # -6???? -10
> # -3????? -5
> # -4????? -5
>
>
> If anyone can help me with this recursive function, I would appreciate 
> it in advance.
> I've never used recursion before, so I don't have a good grasp of
how
> it works.
>
> Thank you very much in advance,
>
> Cleber.
>
>
>
> All details are below:
> ########################
>
>
> d <- scan()
> ?0.986? 0.900
> -1.331? 1.503
> -0.220 -0.752
> ?0.102 -0.071
> -0.171? 0.018
> -0.782? 0.490
> ?1.154 -0.074
> -0.768 -1.529
> ?1.761 -1.396
> -0.730? 0.910
>
> d <- matrix( d, 10, byrow=T )
>
> r <- hclust( dist( d ), met='single' )
> r$merge
> #????? [,1] [,2]
> # [1,]?? -4?? -5
> # [2,]?? -6? -10
> # [3,]?? -3??? 1
> # [4,]??? 2??? 3
> # [5,]?? -2??? 4
> # [6,]?? -8??? 5
> # [7,]?? -1?? -7
> # [8,]??? 6??? 7
> # [9,]?? -9??? 8
>
>
> f <- function(xmd) {
>
> ??? rs <- NULL
> ??? xmd1 <- 999999999
> ??? xmd2 <- 999999999
>
> ??? if (xmd[1] > 0) {
> ??????? xmd1 <- f(r$merge[ xmd[1], ])
> ??? } else {
> ??????? xmd1 <- xmd[1]
> ??? }
>
> ??? if (xmd[2] > 0) {
> ??????? xmd2 <- f(r$merge[ xmd[2], ])
> ??? } else {
> ??????? xmd2 <- xmd[2]
> ??? }
>
> ??? return( rbind( rs, rbind( xmd1, xmd2 ) ) )
> }
>
>
>
> # Testing f()
> f( c(2, 3) )
>
> # result of f()
> #????? [,1]
> # xmd1?? -6
> # xmd2? -10
> # xmd1?? -3
> # xmd1?? -4
> # xmd2?? -5
>
> # My expectative:
> # xmd1?? xmd2
> # -6???? -10
> # -3????? -5
> # -4????? -5
>
>
> # Testing f()
> ?f( c( 6, 7) )
>
> # result of f()
> #????? [,1]
> # xmd1?? -8
> # xmd1?? -2
> # xmd1?? -6
> # xmd2? -10
> # xmd1?? -3
> # xmd1?? -4
> # xmd2?? -5
> # xmd1?? -1
> # xmd2?? -7
>
>
> # My expectative:
> # xmd1?? xmd2
> # -8???? -10
> # -2???? -10
> # -6???? -10
> # -3????? -5
> # -4????? -5
> # -1????? -7
>