Supervised Distance Preserving Projection (SDPP) is a dimension reduction method in supervised setting proposed recently by Zhu et. al in [43]. The method learns a linear mapping from the input space to the reduced feature space. While the method showed very promising result in regression task, for classification problems the performance is not satisfactory. The preservation of distance relation with neighborhood points forces data to project very close to one another in the projected space irrespective of their classes which ends up with low classification rate. To avoid the crowdedness of SDPP approach we have proposed a modification of SDPP which deals both regression and classification problems and significantly improves the performance of SDPP. We have incorporated the total variance of the projected co-variates to the SDPP problem which is maximized to preserve the global structure. This approach not only facilitates efficient regression like SDPP but also successfully classifies data into different classes. We have formulated the proposed optimization problem as a Semidefinite Least Square (SLS) SDPP problem. A two block Alternating Direction Method of Multipliers have been developed to learn the transformation matrix solving the SLS-SDPP which can easily handle out of sample data.

中文翻译：

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乘子交替方向法的有监督保距投影

监督距离保护投影（SDPP）是Zhu等人最近提出的一种在监督环境中的降维方法。在[43]。该方法学习从输入空间到精简特征空间的线性映射。尽管该方法在回归任务中显示出非常有希望的结果，但对于分类问题，性能却不令人满意。与邻近点的距离关系的保留迫使数据在投影空间中彼此非常接近地投影，而不管其类别如何，最终以低分类率结束。为了避免SDPP方法的拥挤，我们提出了SDPP的修改版本，它既解决了回归问题又解决了分类问题，并显着提高了SDPP的性能。我们已将预测协变量的总方差纳入SDPP问题，该问题已最大化以保留全局结构。这种方法不仅可以促进像SDPP这样的有效回归，而且可以成功地将数据分类到不同的类别中。我们将拟议的优化问题表述为半定最小二乘（SLS）SDPP问题。已经开发了一种两块乘法器的交替方向方法，以学习求解可以轻松处理样本数据的SLS-SDPP的变换矩阵。