Can anyone please let me know once I have a distance matrix at hand can any clustering method be used on it regardless of the type of distance measure used to get the matrix. Can the distance matrix be thought of as a new dataset and do the clustering? Is it going to give different results?
Many, if not most, clustering methods can be implemented using a distance matrix as input. In skleaen and R, most functions will accept a distance matrix, or can be configured to do so.
The main reason to not use distance matrixes is scalability: a distance maid needs O(n²) memory and O(n²) time to build. So at around 30.000 to 60.000 instances you usually run into problems.
There are some obvious exceptions: k-means for example needs to compute the mean, which requires the original data. It also never uses the distance inbetween of two data points, only point to center.
If you falsely pass a distance matrix to k-means you will likely still get a possible result. Just the mean will no longer be in your input data, and you get some very hard to grasp semantic - the presence of absence of some big cluster in one region affects the clustering result in a complete different region. So statistically the result is not desirable, even if it at first sight appears to be okay.