# Equally sized topics in Latent Dirichlet allocation

I'm using the topicmodels package for R to cluster a big set of short texts (between 10-75 words) into topics. After manually reviewing a few models it seems like there are 20 realtivly stable topics. However, what I find really weird is that they are all roughly the same size! Each topic catches around 5% of tokens and 5% of texts. In terms of the tokens, the smallest topic is 4.5% the largest 5.5%.

Can anybody suggest if this a 'normal' behaviour? This is the code I'm using:

ldafitted <- LDA(sentences.tm, k = K, method = "Gibbs",
control = list(alpha = 0.1, # default is 50/k which would be 2.5.  a lower alpha value places more weight on having each document composed of only a few dominant topics
delta = 0.1, # default 0.1 is suggested in Griffiths and Steyvers (2004).
estimate.beta = TRUE,
verbose = 50, # print every 50th draw to screen
seed = 5926696,
save = 0,    # can save model every xth iteration
iter = 5000,
burnin = 500,
thin = 5000, #  every thin iteration is returned for iter iterations. Standard is same as iter
best = TRUE)) #only the best draw is returned


In short: My question is if there are circumstances under which it is reasonable that Latent Dirichlet allocation will cluster text in topics of equal size? Or is it something I should be worried if it happens?

It is normal, the best explantation I found for it, is from physics. Since Gibbs Sampling was known in physics long before LDA and LDA can simply be seen as a kind of matrix factorization. There is a system which has particles (words) and the particles can be in different states (topics). States with lower energy have a higher probability of being occupied than states with higher energy. Or simply: Since LDA is a dimensity reduction method that just compresses a words x documents matrix into a topics x documents and a words x topics matrix, the most effective way to do it is by maximizing the entropy which is done if the clusters get equal size. 