Zero-shot learning (ZSL) aims to build models to recognize novel visual categories that have no associated labelled training samples. The basic framework is to transfer knowledge from seen classes to unseen classes by learning the visual-semantic embedding. However, most of approaches do not preserve the underlying sub-manifold of samples in the embedding space. In addition, whether the mapping can precisely reconstruct the original visual feature is not investigated in-depth. In order to solve these problems, we formulate a novel framework named Graph and Autoencoder Based Feature Extraction (GAFE) to seek a low-rank mapping to preserve the sub-manifold of samples. Taking the encoder-decoder paradigm, the encoder part learns a mapping from the visual feature to the semantic space, while decoder part reconstructs the original features with the learned mapping. In addition, a graph is constructed to guarantee the learned mapping can preserve the local intrinsic structure of the data. To this end, an L21 norm sparsity constraint is imposed on the mapping to identify features relevant to the target domain. Extensive experiments on five attribute datasets demonstrate the effectiveness of the proposed model.

Sparse representation based classification (SRC) has gained great success in image recognition. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which may help improve the separability and margin between nearby data points, we propose Euler SRC for image classification, which is essentially the SRC with Euler sparse representation. To be specific, it first maps the images into the complex space by Euler representation, which has a negligible effect for outliers and illumination, and then performs complex SRC with Euler representation. The major advantage of our method is that Euler representation is explicit with no increase of the image space dimensionality, thereby enabling this technique to be easily deployed in real applications. To solve Euler SRC, we present an efficient algorithm, which is fast and has good convergence. Extensive experimental results illustrate that Euler SRC outperforms traditional SRC and achieves better performance for image classification.

Due to the importance and efficiency of learning complex structures hidden in data, graph-based methods have been widely studied and get successful in unsupervised learning. Generally, most existing graph-based clustering methods require post-processing on the original data graph to extract the clustering indicators. However, there are two drawbacks with these methods: (1) the cluster structures are not explicit in the clustering results; (2) the final clustering performance is sensitive to the construction of the original data graph. To solve these problems, in this paper, a novel learning model is proposed to learn a graph based on the given data graph such that the new obtained optimal graph is more suitable for the clustering task. We also propose an efficient algorithm to solve the model. Extensive experimental results illustrate that the proposed model outperforms other state-of-the-art clustering algorithms.

Locality preserving projection (LPP) is one of the most representative linear manifold learning methods and well exploits intrinsic structure of data. However, the performance of LPP remarkably degenerate in the presence of outliers. To alleviate this problem, the authors propose a robust LPP, namely LPP‐L21. LPP‐L21 employs L2‐norm as the distance metric in spatial dimension of data and L1‐norm as the distance metric over different data points. Moreover, the authors employ L1‐norm to construct similarity graph, this helps to improve robustness of algorithm. Accordingly, the authors present an efficient iterative algorithm to solve LPP‐L21. The authors’ proposed method not only well suppresses outliers but also retains LPP's some nice properties. Experimental results on several image data sets show its advantages.

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