Abstract: For resolving the problem of the existing noise sample and large number of dimensions, the k-nearest neighbors classifier over manifolds was presented in this paper. Firstly the classic k-nearest neighbors was extended by Bayes theorem and local joint probability density was estimated by kernel density estimation in classifier. In addition, after building the noise sample model, an objective function was defined via improved marginal intrinsic graph and its weight matrix for searching the optimal dimension reduction mapping matrix. At last, details about k-nearest neighbors algorithm over manifolds were provided. The experimental results demonstrate that the presented method has lower classification error rate than six kinds of classic methods in most cases on twelve data sets.

Key words: k-Nearest Neighbors, noise sample, dimensionality reduction, classifier, manifold

摘要： 针对分类数据中存在噪声样本和维数问题，提出了流形上的k最近邻方法。首先，利用贝叶斯公式对经典k最近邻方法进行扩展，并采用核概率密度方法估计样本的局部联合概率密度；其次，建立噪声样本点对模型，并构建改进的边际本征图和相应的权值矩阵，通过定义目标函数寻找最优降维映射矩阵；最后，提出一个完整的流形上k最近邻算法。与6种经典方法在12个常用数据集上的实验比较表明，在大多数情况下所提方法的分类性能要优于其他方法。

关键词: k最近邻, 噪声样本, 降维, 分类器, 流形