Semantic Graph for Zero-Shot Learning

Zero-shot learning aims to classify visual objects without any training data via knowledge transfer between seen and unseen classes. This is typically achieved by exploring a semantic embedding space where the seen and unseen classes can be related. Previous works differ in what embedding space is used and how different classes and a test image can be related. In this paper, we utilize the annotation-free semantic word space for the former and focus on solving the latter issue of modeling relatedness. Specifically, in contrast to previous work which ignores the semantic relationships between seen classes and focus merely on those between seen and unseen classes, in this paper a novel approach based on a semantic graph is proposed to represent the relationships between all the seen and unseen class in a semantic word space. Based on this semantic graph, we design a special absorbing Markov chain process, in which each unseen class is viewed as an absorbing state. After incorporating one test image into the semantic graph, the absorbing probabilities from the test data to each unseen class can be effectively computed; and zero-shot classification can be achieved by finding the class label with the highest absorbing probability. The proposed model has a closed-form solution which is linear with respect to the number of test images. We demonstrate the effectiveness and computational efficiency of the proposed method over the state-of-the-arts on the AwA (animals with attributes) dataset.Comment: 9 pages, 5 figure

Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\chi$ is a $k$-valued character for $G$ with $\chi(a)\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over $H'$ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over $H$ and $H'$, and classify them. Finally, when $\chi(a)$ is a primitive $n$-th root of unity for some $n>2$, we determine all finite dimensional indecomposable projective objects in the category of weight modules over $H'$.Comment: arXiv admin note: substantial text overlap with arXiv:1206.394