关键词: 非线性维数约简, 流形学习, k近邻

Abstract: Unlike most traditional manifold-based data classification algorithms assume that all the data points are on a single manifold，it supposes that multiple classes data may reside on different manifolds.A data classification algorithm on multiple manifolds is presented.The algorithm roughly divides into two steps：learning process and testing process.In learning process，the manifolds are firstly learned for each class separately using linear manifold learning，and then low dimensionality coordinates and mapping matrix of the training data is obtained.In testing process，classification is performed using minimum reconstruction error between test data and its k-nearest neighbors in embedding space.The experimental results on both synthetic data and coil-20 databases show the effectiveness of the proposed algorithm.

Key words: Nonlinear Dimensionality Reduction（NLDR）, manifold learning, k nearest neighbors