Multiview spectral embedding.

In computer vision and multimedia search, it is common to use multiple features from different views to represent an object. For example, to well characterize a natural scene image, it is essential to find a set of visual features to represent its color, texture, and shape information and encode each feature into a vector. Therefore, we have a set of vectors in different spaces to represent the image. Conventional spectral-embedding algorithms cannot deal with such datum directly, so we have to concatenate these vectors together as a new vector. This concatenation is not physically meaningful because each feature has a specific statistical property. Therefore, we develop a new spectral-embedding algorithm, namely, multiview spectral embedding (MSE), which can encode different features in different ways, to achieve a physically meaningful embedding. In particular, MSE finds a low-dimensional embedding wherein the distribution of each view is sufficiently smooth, and MSE explores the complementary property of different views. Because there is no closed-form solution for MSE, we derive an alternating optimization-based iterative algorithm to obtain the low-dimensional embedding. Empirical evaluations based on the applications of image retrieval, video annotation, and document clustering demonstrate the effectiveness of the proposed approach.