In a classical topic model such as LDA, the learned topic can be uninterpretable. We need to eyeball the top words to interpret the semantic of the learned topic. Labeled LDA (L-LDA) is a model that assigns each topic to a supervisor signal. Many documents contain tags and labels, these data can be treated as target topics. If we can group similar words based on the corresponding labels, then each topic will be readable.
The trick is to constrain the available topics that each document can learn. In LDA, a document draws a topic distribution from a K-simplex ( a Dirichlet distribution ). But L-LDA draws a topic distribution from L-simplex where L is the number of tags for the given document. This implies that each document will draw a topic distribution from a different shape of simplex. L-LDA calculates the parameter of dirichlet distribution based on the tags.
For example, if there are K possible tags, , a document with L tags (k=2, k=5) will have an alpha . Then the topic assignment will be constraint to only topic 2 and 5.
Due to this model assumption, L-LDA assumes that all words appear in the same document are definitely drawn from a small set of topics. For a single-label dataset, this means that all words in the same document are from the same topic. Is this a good idea?
It turns out that this is a valid assumption. When a document is assigned a label, it is because the combination of words in the document contributes a very specific theme or ideas. Another view of this constraint is that the documents that share the same labels will share the same set of words that likely to appear.
When L-LDA is applied on a multi-labeled dataset, then the learned topic will become more interesting because the way each document share the same set of words become more complicated.