Can I use K-means algorithm on a string?

One problem you would face if using scipy.cluster.vq.kmeans is that that function uses Euclidean distance to measure closeness. To shoe-horn your problem into one solveable by k-means clustering, you'd have to find a way to convert your strings into numerical vectors and be able to justify using Euclidean distance as a reasonable measure of closeness.

That seems... difficult. Perhaps you are looking for Levenshtein distance instead?

Note there are variants of the K-means algorithm that can work with non-Euclideance distance metrics (such as Levenshtein distance). K-medoids (aka PAM), for instance, can be applied to data with an arbitrary distance metric.

For example, using Pycluster's implementation of k-medoids, and nltk's implementation of Levenshtein distance,

import nltk.metrics.distance as distance
import Pycluster as PC

words = ['apple', 'Doppler', 'applaud', 'append', 'barker', 
         'baker', 'bismark', 'park', 'stake', 'steak', 'teak', 'sleek']

dist = [distance.edit_distance(words[i], words[j]) 
        for i in range(1, len(words))
        for j in range(0, i)]

labels, error, nfound = PC.kmedoids(dist, nclusters=3)
cluster = dict()
for word, label in zip(words, labels):
    cluster.setdefault(label, []).append(word)
for label, grp in cluster.items():
    print(grp)

yields a result like

['apple', 'Doppler', 'applaud', 'append']
['stake', 'steak', 'teak', 'sleek']
['barker', 'baker', 'bismark', 'park']

K-means doesn't really care about the type of the data involved. All you need to do a K-means is some way to measure a "distance" from one item to another. It'll do its thing based on the distances, regardless of how that happens to be computed from the underlying data.

That said, I haven't used scipy.cluster.vq, so I'm not sure exactly how you tell it the relationship between items, or how to compute a distance from item A to item B.

K-means only works with euclidean distance. Edit distances such as Levenshtein don't even obey the triangle inequality may obey the triangle inequality, but are not euclidian. For the sorts of metrics you're interested in, you're better off using a different sort of algorithm, such as Hierarchical clustering: http://en.wikipedia.org/wiki/Hierarchical_clustering

Alternately, just convert your list of RNA into a weighted graph, with Levenshtein weights at the edges, and then decompose it into a minimum spanning tree. The most connected nodes of that tree will be, in a sense, the "most representative".