how to find similarity based on only one column value

Question

I am not sure if it is possible and that is why I am asking the question here.

I have a data looks like below

Column A     Column B
  A           0.098
  B           0.076
  C           0.871
  D           0.837
  E           1.981
  F           0.736
  G           0.983
  H           0.019
  I           0.836
  J           0.936
  K           0.197
  L           0.986
  M           0.084
  N           0.048
  O           0.471

The values in column B are linked to the letters in column A. I want to know if it is possible to make a decision on which letters are similar and which letters are not similar based on the value in column B? Is this possible ? if so, how ?

Answer 1

This tool is JMP, but there are many others too.

Here is how to do it in JMP:

This dialog shows several families of how to make a 1d clustering.

Choosing the defaults, and coloring by value of "Column B", then selecting only the constellation plot gives the following:

This is only about the 2-norm between all pairs of points. There are other norms. There are other transformations.

When the distribution is plotted, the "clusters" (vertical groupings) are also somewhat visible.

To my untrained eye there are at least 3 general groups, and one of those has what looks like 3 sub-groups.

HERE is how to do similar (not same) in R:

Here is the code:
#load data mydata <- read.csv("data.csv")

#compute distance matrix
d <- dist(as.matrix(mydata$Column.B),  #the data
          method = "euclidean")        #the distance measure

#compute cluster membership
hc_0 <- hclust(d,                      #the distance matrix
               method = "ward.D2"       #the cluster method
               ) 

#plot of dendrogram
plot(hc_0)

Here is the result:

It is not a constellation plot, but a dendrogram. Other functions to look at include "rect.hclust" and the "rpuHclust". The "rpuHclust" comes from the "rpuHclust" package.

There are at least 3 other things to consider.

1. The "method" in "dist" can be lots of things including absolute distance, squared distance, or some other measure.
2. The "method" in "hclust" can be lots of other things including "ward.D", "average", "centroid", "median" and others. Each has strengths and weaknesses.
3. The "hclust" is one type of clustering but there are others. K-means or Gaussian mixture models come to mind.

All of these approaches can be appropriate for some cases and not appropriate for others. What question are you trying to answer with the cluster membership? If you want robust classification then you need a lot more samples. If true physics says your data is multivariate and you are trying to defy it using statistics, then your correct binning might be a problem. If you are just looking to get a sense of how many buckets might be a good value to start with for the data give what you have then this might not be a bad way to start in on that.