title: Clustering data after dimension reduction with PCA
body: <p>Say we have a dataset of a large dimension, which we have reduced to a lower dimension using PCA, would it be wise/accurate to then use a clustering algorithm on said data? Assuming that we do not know how many clusters to expect.</p>
  
  <p>Using PCA on the Iris dataset(with the data in the csv ordered such that all of the first class are listed, then the second, then the third) yields the following plot:-
  <img src="https://i.stack.imgur.com/8ESsZ.jpg" alt="Ordered data run through PCA"></p>
  
  <p>It can be seen that the three classes in the Iris dataset have been retained. However, when the order of the samples is randomised, the following plot is produced:-
  <img src="https://i.stack.imgur.com/40QLE.jpg" alt="Unordered data run thorough PCA"></p>
  
  <p>Above, it is not clear how many clusters/classes are contained in the data set. In this case(the more real world case), how would one identify the number of classes, would a clustering algorithm such as K-Means be effective?</p>
  
  <p>Would there be innacuracies due to the discarding of lower order Principal Components?</p>
  
  <p>EDIT:- To be clear, I am asking if a dataset can be clustered after running PCA, and if so, what the most accurate method would be.</p>