An effective framework for supervised dimension reduction

We consider supervised dimension reduction (SDR) for problems with discrete inputs. Existing methods are computationally expensive, and often do not take the local structure of data into consideration when searching for a low-dimensional space. In this paper, we propose a novel framework for SDR with the aims that it can inherit scalability of existing unsupervised methods, and that it can exploit well label information and local structure of data when searching for a new space. The way we encode local information in this framework ensures three effects: preserving inner-class local structure, widening inter-class margin, and reducing possible overlap between classes. These effects are vital for the success in practice. The framework is general and flexible so that it can be easily adapted to various unsupervised topic models. We then adapt our framework to three unsupervised topic models which results in three methods for SDR. Extensive experiments on 10 practical domains demonstrate that our framework can yield scalable and qualitative methods for SDR. In particular, one of the adapted methods can perform consistently better than the state-of-the-art method for SDR while enjoying 30-450 times faster speed.