高维数据的低维表示综述 - 图文(9)

(7) 流形重构与有监督学习

现有的流形学习方法主要应用于聚类与可视化，这是由于数据降维的点对点嵌入性质决定的。但由于难以得到流形空间与其降维空间的对应映射函数关系，使其难以广泛用于模式识别和分类等问题。如何找到两个空间的映射关系，包括线性与非线性映射关系，以重构流形是监督与半监督学习需要解决的关键问题之一。如果能得到数据降维中观测空间到特征空间的映射，则以训练数据划分空间对测试数据进行分类的有监督流形学习将成为可能。

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