Conventional vision algorithms adopt a single type of feature or a simple concatenation of multiple features, which is always represented in a high-dimensional space. In this paper, we propose a novel unsupervised spectral embedding algorithm called Kernelized Multiview Projection (KMP) to better fuse and embed different feature representations. Computing the kernel matrices from different features views, KMP can encode them with the corresponding weights to achieve a low-dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative. More crucially, KMP is linear for the reproducing kernel Hilbert space (RKHS) and solves the out-of-sample problem, which allows it to be competent for various practical applications. Extensive experiments on three popular image datasets demonstrate the effectiveness of our multiview embedding algorithm.
However, both DSE and MSE are based on nonlinear embedding, which leads to a serious computational complexity problem and the problem @cite_10 . In particular, when we apply them to classification or retrieval tasks, the methods have to be re-trained for learning the low-dimensional embedding when new test data are used. Due to their nonlinearity nature, this will cause heavily computational costs and even become impractical for realistic and large-scale scenarios.
@cite_10
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This paper considers the problem of embedding Knowledge Graphs (KGs) consisting of entities and relations into lowdimensional vector spaces. Most of the existing methods perform this task based solely on observed facts. The only requirement is that the learned embeddings should be compatible within each individual fact. In this paper, aiming at further discovering the intrinsic geometric structure of the embedding space, we propose Semantically Smooth Embedding (SSE). The key idea of SSE is to take full advantage of additional semantic information and enforce the embedding space to be semantically smooth, i.e., entities belonging to the same semantic category will lie close to each other in the embedding space. Two manifold learning algorithms Laplacian Eigenmaps and Locally Linear Embedding are used to model the smoothness assumption. Both are formulated as geometrically based regularization terms to constrain the embedding task. We empirically evaluate SSE in two benchmark tasks of link prediction and triple classification, and achieve significant and consistent improvements over state-of-the-art methods. Furthermore, SSE is a general framework. The smoothness assumption can be imposed to a wide variety of embedding models, and it can also be constructed using other information besides entities’ semantic categories.