Yulan Zhang

Baihong Lin, Zengrong Lin, Yulan Guo et al.

RGB-T semantic segmentation has been widely adopted to handle hard scenes with poor lighting conditions by fusing different modality features of RGB and thermal images. Existing methods try to find an optimal fusion feature for segmentation, resulting in sensitivity to modality noise, class-imbalance, and modality bias. To overcome the problems, this paper proposes a novel Variational Probabilistic Fusion Network (VPFNet), which regards fusion features as random variables and obtains robust segmentation by averaging segmentation results under multiple samples of fusion features. The random samples generation of fusion features in VPFNet is realized by a novel Variational Feature Fusion Module (VFFM) designed based on variation attention. To further avoid class-imbalance and modality bias, we employ the weighted cross-entropy loss and introduce prior information of illumination and category to control the proposed VFFM. Experimental results on MFNet and PST900 datasets demonstrate that the proposed VPFNet can achieve state-of-the-art segmentation performance.

Yulan Zhang, Anna C. Gilbert, Stefan Steinerberger

Modern methods in dimensionality reduction are dominated by nonlinear attraction-repulsion force-based methods (this includes t-SNE, UMAP, ForceAtlas2, LargeVis, and many more). The purpose of this paper is to demonstrate that all such methods, by design, come with an additional feature that is being automatically computed along the way, namely the vector field associated with these forces. We show how this vector field gives additional high-quality information and propose a general refinement strategy based on ideas from Morse theory. The efficiency of these ideas is illustrated specifically using t-SNE on synthetic and real-life data sets.

Yulan Zhang, Stefan Steinerberger

t-SNE is one of the most commonly used force-based nonlinear dimensionality reduction methods. This paper has two contributions: the first is forceful colorings, an idea that is also applicable to other force-based methods (UMAP, ForceAtlas2,...). In every equilibrium, the attractive and repulsive forces acting on a particle cancel out: however, both the size and the direction of the attractive (or repulsive) forces acting on a particle are related to its properties: the force vector can serve as an additional feature. Secondly, we analyze the case of t-SNE acting on a single homogeneous cluster (modeled by affinities coming from the adjacency matrix of a random k-regular graph); we derive a mean-field model that leads to interesting questions in classical calculus of variations. The model predicts that, in the limit, the t-SNE embedding of a single perfectly homogeneous cluster is not a point but a thin annulus of diameter $\sim k^{-1/4} n^{-1/4}$. This is supported by numerical results. The mean field ansatz extends to other force-based dimensionality reduction methods.