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.

中文翻译：

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自动加权的多视图平滑表示可保留投影以减少维数

在过去的几十年中，我们目睹了一大批算法，这些算法旨在为降维（DR）问题提供不同的解决方案。DR是通过将数据映射到低维子空间来从高维数据中挖掘重要信息的重要工具。即使大多数DR算法可以在许多实际应用中获得令人满意的性能，但它们仍无法从多个角度充分考虑信息。因此，目前如何利用多视图特征的一致性和互补性来学习高维特征的子空间是重要且具有挑战性的。为了解决这个问题，我们提出了一种有效的多视图DR算法，称为多视图平滑表示保留投影（MvSMRP2）。MvSMRP2试图找到一组线性变换，以将每个视图特征投影到一个公共的低维子空间中，在该空间中尽可能多地保留多视图平滑重构权重。通过充分利用希尔伯特-施密特独立性准则来设计成对一致的方案，以最大化不同视图之间的依赖性，这可以获取一个公共子空间并强制多个视图相互学习。此外，MvSMRP2可以根据视图重要性自动为每个视图分配理想权重，而无需明确定义权重。最后，提出了一种迭代交替策略，以获得MvSMRP2的最优解。在各种数据集上的大量实验表明了该方法的出色性能。