论文标题
流形分区判别分析
Manifold Partition Discriminant Analysis
论文作者
论文摘要
我们提出了一种新型算法，用于降低维度降低歧管分析（MPDA）。它的目的是找到一个线性嵌入空间，在该空间中，沿着与数据歧管的局部变化相一致的方向实现了类相似性，而附近属于不同类别的数据则很好地分开。通过将数据歧管划分为多个线性子空间并利用一阶泰勒扩展，MPDA明确参数化了切线空间的连接，并以分段方式表示数据歧管。尽管图拉普拉斯方法仅捕获数据点之间的成对相互作用，但我们的方法捕获了数据点之间的成对和高阶交互（使用区域一致性）。这种歧管表示可以帮助提高阶级相似性的度量，从而进一步改善了降低维度的性能。对多个现实世界数据集的实验结果证明了该方法的有效性。
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is consistent with the local variation of the data manifold, while nearby data belonging to different classes are well separated. By partitioning the data manifold into a number of linear subspaces and utilizing the first-order Taylor expansion, MPDA explicitly parameterizes the connections of tangent spaces and represents the data manifold in a piecewise manner. While graph Laplacian methods capture only the pairwise interaction between data points, our method capture both pairwise and higher order interactions (using regional consistency) between data points. This manifold representation can help to improve the measure of within-class similarity, which further leads to improved performance of dimensionality reduction. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.
