Zheng Wu

Zhaodan Kong, Kayhan Özcimder, Nathan Fuller et al.

The movements of birds, bats, and other flying species are governed by complex sensorimotor systems that allow the animals to react to stationary environmental features as well as to wind disturbances, other animals in nearby airspace, and a wide variety of unexpected challenges. The paper and talk will describe research that analyzes the three-dimensional trajectories of bats flying in a habitat in Texas. The trajectories are computed with stereoscopic methods using data from synchronous thermal videos that were recorded with high temporal and spatial resolution from three viewpoints. Following our previously reported work, we examine the possibility that bat trajectories in this habitat are governed by optical flow sensing that interpolates periodic distance measurements from echolocation. Using an idealized geometry of bat eyes, we introduce the concept of time-to-transit, and recall some research that suggests that this quantity is computed by the animals' visual cortex. Several steering control laws based on time-to-transit are proposed for an idealized flight model, and it is shown that these can be used to replicate the observed flight of what we identify as typical bats. Although the vision-based motion control laws we propose and the protocols for switching between them are quite simple, some of the trajectories that have been synthesized are qualitatively bat-like. Examination of the control protocols that generate these trajectories suggests that bat motions are governed both by their reactions to a subset of key feature points as well by their memories of where these feature points are located.

Qinxun Bai, Steven Rosenberg, Zheng Wu et al.

We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust estimator of the class probability $P(y|\pmb{x})$. The regularization term measures the volume of this submanifold, based on the intuition that overfitting produces rapid local oscillations and hence large volume of the estimator. This technique can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. In experiments, we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification.