Husserl’s philosophy of mathematics: its origin and relevance

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

Manifold embedding for zero-shot recognition

Zero-Shot Recognition (ZSR) has gained its popularity recently owing to its promising characteristic that extends the classifiers to the unseen classes. It is typically addressed by resorting to a class semantic space to transfer the knowledge from the seen classes to unseen ones. Therefore, constructing the effective interactions between the visual space and the class semantic space is the key for ZSR. In this paper, under the assumption that the distribution of the semantic categories in the semantic space has an intrinsic manifold structure, we propose two manifold embedding-based ZSR approaches to capture the intrinsic structures of both the visual space and the class semantic space, i.e., ME-ZSR and MCCA-ZSR. Specifically, ME-ZSR builds embedding from visual space to semantic space, while MCCA-ZSR explores to embed both visual and semantic features into a common space. The linear, closed-form solutions make both methods efficient to optimize. Extensive experiments on three popular datasets AwA, CUB and NAB validate the effectiveness of both methods.