In machine learning, the idea of maximizing the margin between two classes is widely used in classifier design. Enlighted by the idea, this paper proposes a novel supervised dimensionality reduction method for tensor data based on local decision margin maximization. The proposed method seeks to preserve and protect the local discriminant information of the original data in the low-dimensional data space. Firstly, we depart the original tensor dataset into overlapped localities with discriminant information. Then, we extract the similarity and anti-similarity coefficients of each high-dimensional locality and preserve these coefficients in the embedding data space via the multilinear projection scheme. Under the combined effect of these coefficients, each dimension-reduced locality tends to be a convex set where strongly correlated intraclass points gather. Simultaneously, the local decision margin, which is defined as the shortest distance from the boundary of each locality to the nearest point of each side, will be maximized. Therefore, the local discriminant structure of the original data could be well maintained in the low-dimensional data space. Moreover, a simple iterative scheme is proposed to solve the final optimization problem. Finally, the experiment results on 6 real-world datasets demonstrate the effectiveness of the proposed method.

中文翻译：

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基于局部决策余量最大化的张量数据降维

在机器学习中，最大化两个类别之间的余量的想法广泛用于分类器设计中。受这一想法的启发，本文提出了一种基于局部决策余量最大化的张量数据监督降维方法。所提出的方法试图在低维数据空间中保存和保护原始数据的局部判别信息。首先，我们将原始张量数据集分为具有判别信息的重叠局部。然后，我们提取每个高维位置的相似度和反相似度系数，并通过多线性投影方案将这些系数保留在嵌入数据空间中。在这些系数的综合作用下，每个减少维数的位置都倾向于是凸集，其中高度相关的类内点会聚集。同时，局部决策余量将最大化，该局部决策余量定义为从每个局部的边界到两边的最近点的最短距离。因此，可以在低维数据空间中很好地维护原始数据的局部判别结构。此外，提出了一种简单的迭代方案来解决最终的优化问题。最后，在6个真实数据集上的实验结果证明了该方法的有效性。原始数据的局部判别结构可以很好地保持在低维数据空间中。此外，提出了一种简单的迭代方案来解决最终的优化问题。最后，在6个真实数据集上的实验结果证明了该方法的有效性。原始数据的局部判别结构可以很好地保持在低维数据空间中。此外，提出了一种简单的迭代方案来解决最终的优化问题。最后，在6个真实数据集上的实验结果证明了该方法的有效性。