AMS-SFE: Towards an Alignment of Manifold Structures via Semantic Feature Expansion for Zero-shot Learning

Zero-shot learning (ZSL) aims at recognizing unseen classes with knowledge transferred from seen classes. This is typically achieved by exploiting a semantic feature space (FS) shared by both seen and unseen classes, i.e., attributes or word vectors, as the bridge. However, due to the mutually disjoint of training (seen) and testing (unseen) data, existing ZSL methods easily and commonly suffer from the domain shift problem. To address this issue, we propose a novel model called AMS-SFE. It considers the Alignment of Manifold Structures by Semantic Feature Expansion. Specifically, we build up an autoencoder based model to expand the semantic features and joint with an alignment to an embedded manifold extracted from the visual FS of data. It is the first attempt to align these two FSs by way of expanding semantic features. Extensive experiments show the remarkable performance improvement of our model compared with other existing methods

Rota-Baxter operators on the polynomial algebras, integration and averaging operators

The concept of a Rota–Baxter operator is an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota–Baxter operators and integrals in the case of the polynomial algebra k[x] k[x] . We consider two classes of Rota–Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota–Baxter operators. For the second class, we make use of the double product on Rota–Baxter algebras