# Topic Discovery through Data Dependent and Random Projections

arXiv: https://arxiv.org/abs/1303.3664 · HTML: https://mlsanity.com/paper/1303.3664/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2013.

## Built on by (most cited first, 1 of 1)

- [Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculations](https://mlsanity.com/paper/2107.05766/) (2021)

## Abstract (arXiv)

We present algorithms for topic modeling based on the geometry of cross-document word-frequency patterns. This perspective gains significance under the so called separability condition. This is a condition on existence of novel-words that are unique to each topic. We present a suite of highly efficient algorithms based on data-dependent and random projections of word-frequency patterns to identify novel words and associated topics. We will also discuss the statistical guarantees of the data-dependent projections method based on two mild assumptions on the prior density of topic document matrix. Our key insight here is that the maximum and minimum values of cross-document frequency patterns projected along any direction are associated with novel words. While our sample complexity bounds for topic recovery are similar to the state-of-art, the computational complexity of our random projection scheme scales linearly with the number of documents and the number of words per document. We present several experiments on synthetic and real-world datasets to demonstrate qualitative and quantitative merits of our scheme.