Validation of clustering results I have a data which  contains several columns which I later reduced using a PCA algorithms to two different components. I then applied the k-means algorithms to the data.
Now, how can I verify that my data  clustered  well into each group? Or how do I determine misclassification rate?
For instance, using R, if I check the cluster vector say k$cluster against the labels of the data I had previously before clustering  can I just draw a confusion matrix from that and assume that 1 in the clustered vector is equivalent to 1 in my labels?
col3    col2     Col1   lables                                           
123     2.32      2.50    0           
124    2.81      3.10     1     
125    2.72      3.09     2     
126    2.92      3.03     3     
127    2.32      2.95     4     

Please note this is a hypothetical data; my data is way bigger than this.
 A: If you have an a priori classification into groups, you should not rely on labels being identical between the a priori classification and the one you obtained. I would start  by computing the distances between the two clusterings (treating the classification  as a clustering) using a metric distance between clusterings. All such metrics can typically be derived from the confusion matrix only, and hence do not depend on labels beyond their indicating commonality of grouping within a single clustering. I usually recommend Comparing clusterings by the variation of information by Marina Meila. It discusses three metrics: the main contribution of the paper, the variation of information (which is very good), the Mirkin distance (related to the Jaccard index, well known, but not so good as it is affected in a quadratical manner by cluster sizes), and the split/join distance (Meila calls it 'van Dongen' distance). Disclaimer: the last one was developed by me. It has the advantage that it is interpretable as the number of nodes that need reallocation to change one clustering or classification into the other. There are many other clustering (dis)similarity measures, but I would only recommend these three, and although popular, I would not recommend the Jaccard/Mirkin measures.
A: One classic approach is the adjusted Rand index, which is a chance-corrected measure of similarity between two partitions (a clustering is, after all, a partition).  This is already implemented in R, in the mclust package (see here).  This value of the adjusted Rand index always lies between -1 and 1, and the index is not a metric (e.g., it doesn't satisfy the triangle inequality).  It has the nice property of being able to compare partitions of different sizes (i.e., clusterings containing different numbers of clusters).
