正交化近邻关系保持的降维及分类算法

针对近邻关系保持嵌入（NPE）算法易于受到降低后的维数影响，而且性能依赖于正确的维数估计的问题，提出了一种正交化的近邻关系保持的嵌入降维方法——ONPE。ONPE方法是使用数据点间的近邻关系来构造邻接图，假设每个数据点都能由其近邻点的线性组合表示，则可以通过提取数据点的局部几何信息，并在降维中保持提取的局部几何信息，迭代地计算正交基来得到数据的低维嵌入坐标。同时，在ONPE算法的基础上，利用局部几何信息，提出了一种在低维空间中使用标签传递（LNP）的分类算法——ONPC。其是假设高维空间中的局部近邻关系在降维后的空间中依然得到保持，并且数据点的类别可由近邻点的类别得到。在人工数据和人脸数据上的实验表明，该算法在减少维数依赖的同时，能有效提高NPE算法的分类性能。

Orthogonal Neighborhood Preserving Embedding Based Dimension Reduction and Classification Method

To overcome the sensitivity to the dimensions of reduced space, and performance degradation with wrong dimension estimation of neighborhood preserving embedding (NPE) method, an orthogonal neighborhood preserving embedding (ONPE) method is proposed for manifold dimension reduction. ONPE uses neighborhood information to construct the adjacent graph, and assuming that each data point can be represented by linear combination of its neighbor points. ONPE then extracts local geometry information embedded in reconstruction weights, and obtains the low dimensional coordinates by iteratively computes the mutually orthogonal basis functions. Moreover, utilizing the local geometry during ONPE dimension reduction, a new classification method (ONPC) based on a label propagation method (LNP) is proposed. The reasonable assumption is that local neighbor information in high dimensional space is also preserved in reduced space, and the class label of a data point can be obtained through the class labels of its neighbors. Several experiments on artificial datasets and face database demonstrate the effectiveness of the algorithm.