k-means and LDA for text classification: how to test accuracy?
First of all, you use two terms Clustering and Classification interchangably and I would like to draw your attention to this. Your problem is purely Clustering.
Secondly, you asked for testing accuracy. As your problem is pure Clustering, there is no evaluation for that.
The last but not least is the problem of &quot;Short Text Understanding&quot;. In short texts, LDA of TF-IDF based approaches (like LSA) do not work well as they rely on co-occurrences of words in texts.
Considering these two facts let's discuss the solution. I would recommend that you use a pre-trained model (I recommend S-BERT which is implemented in Sentence-Transformer Python package). Simply follow this semantic similarity search piece of code and you can implement it easily in a few lines.
Probably fine-tuning the model will be tricky according to the nature of your task, so just use a pre-trained model and see how it works.
For evaluation, I recommend to capture some similar tweets manually (more the better) and check the performance on them.
For Topic Modeling approach you can use the pytho implementation of the paper I mentioned above here.
Two above mentioned can also be combined creatively (search similarity with S-BERT and compare to bi-term topic model for example)
Hope it helped.
Good Luck!