Liu Yang, Liu Yan, Chan Keith C C
Department of Computing, the Hong Kong Polytechnic University, Kowloon, Hong Kong, China.
IEEE Trans Neural Netw. 2010 Nov;21(11):1848-54. doi: 10.1109/TNN.2010.2066574. Epub 2010 Sep 27.
This brief paper presents a unified framework for tensor-based dimensionality reduction (DR) with a new tensor distance (TD) metric and a novel multilinear locality-preserved maximum information embedding (MLPMIE) algorithm. Different from traditional Euclidean distance, which is constrained by the orthogonality assumption, TD measures the distance between data points by considering the relationships among different coordinates. To preserve the natural tensor structure in low-dimensional space, MLPMIE directly works on the high-order form of input data and iteratively learns the transformation matrices. In order to preserve the local geometry and to maximize the global discrimination simultaneously, MLPMIE keeps both local and global structures in a manifold model. By integrating TD into tensor embedding, TD-MLPMIE performs tensor-based DR through the whole learning procedure, and achieves stable performance improvement on various standard datasets.
本文简要介绍了一种基于张量的降维（DR）统一框架，该框架具有一种新的张量距离（TD）度量和一种新颖的多线性局部保持最大信息嵌入（MLPMIE）算法。与受正交性假设约束的传统欧几里得距离不同，TD通过考虑不同坐标之间的关系来测量数据点之间的距离。为了在低维空间中保留自然张量结构，MLPMIE直接对输入数据的高阶形式进行操作，并迭代学习变换矩阵。为了同时保留局部几何结构并最大化全局判别力，MLPMIE在流形模型中保留局部和全局结构。通过将TD集成到张量嵌入中，TD-MLPMIE在整个学习过程中执行基于张量的DR，并在各种标准数据集上实现了稳定的性能提升。
