Regularized tree partitioning and its application to unsupervised image segmentation.

In this paper, we propose regularized tree partitioning approaches. We study normalized cut (NCut) and average cut (ACut) criteria over a tree, forming two approaches: 1) normalized tree partitioning (NTP) and 2) average tree partitioning (ATP). We give the properties that result in an efficient algorithm for NTP and ATP.

Trace ratio problem revisited.

Dimensionality reduction is an important issue in many machine learning and pattern recognition applications, and the trace ratio (TR) problem is an optimization problem involved in many dimensionality reduction algorithms. Conventionally, the solution is approximated via generalized eigenvalue decomposition due to the difficulty of the original problem. However, prior works have indicated that it is more reasonable to solve it directly than via the conventional way.