Abstract: Most of the real-world data，such as images and videos，are always represented by tensor and high-dimensionality form，which make tensor data dimensionality reduction the hot issue in recent research.Due to the supervised view of point，most of the present tensor dimensionality reduction methods cannot take full advantage of the unlabeled data.Combining the advantages of traditional semi-supervised methods and tensor-based methods，Tensor Dimensionality Reduction via Harmonic Function（TDRHF） can make full use of the unlabeled data while maintaining the natural tensor structure of the data.The effectiveness of the method is verified by both simulations and real-world data.

Key words: harmonic function, tensor data, dimensionality reduction

摘要： 实际应用中的许多数据，如图像，视频，通常具有张量性和高维性特征，张量数据的维数约简便成为近期的研究热点。现有的张量维数约简方法大都是监督的，它们不能有效利用未标签样本数据的信息。基于调和函数的张量数据维数约简方法综合了传统半监督方法和张量方法的优点，能够在有效利用未标签样本信息的同时，保持数据天然的张量结构特征。仿真实验和真实数据上的结果都验证了其有效性。

关键词: 调和函数, 张量数据, 维数约简