Autoweighted multi-view smooth representation preserve projection for dimensionality reduction

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Over the past few decades, we have witnessed a large family of algorithms that has been designed to provide different solutions to the problem of dimensionality reduction (DR). DR is an essential tool to excavate important information from the high-dimensional data by mapping the data to a low-dimensional subspace. Even though most DR algorithms can achieve satisfactory performance for many practical applications, they fail to fully consider the information from multiple views. Therefore, how to learn the subspace for high-dimensional features by utilizing the consistency and complementary properties of multi-view features is important and challenging in the present. To tackle this problem, we propose an effective multi-view DR algorithm named multi-view smooth representation preserve projection (MvSMRP2). MvSMRP2 seeks to find a set of linear transformations to project each view features into one common low-dimensional subspace where the multi-view smooth reconstructive weights are preserved as much as possible. A pair-wise-consistent scheme is designed by fully exploiting the Hilbert–Schmidt independence criterion to maximize the dependence among different views, which can obtain one common subspace and force multiple views to learn from each other jointly. Moreover, MvSMRP2 can allocate ideal weight for each view automatically according to view importance without explicit weight definition. Finally, an iterative alternating strategy is proposed to obtain the optimal solution of MvSMRP2. Plenty of experiments on various datasets show the excellent performances of the proposed method.