Element Rearrangement for Tensor-Based Subspace Learning
Element Rearrangement for Tensor-Based Subspace Learning
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DOI：
10.1109/cvpr.2007.382984
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
Shuicheng Yan;Dong Xu;Stephen Lin;Thomas S. Huang;Shih-Fu Chang
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文献类型：
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作者：
Shuicheng Yan;Dong Xu;Stephen Lin;Thomas S. Huang;Shih-Fu Chang
基于张量的子空间学习的成功在很大程度上取决于减少沿着模式k平坦矩阵的列向量的相关性。在这项工作中，我们研究的问题，重新安排张量内的元素，以最大限度地提高这些相关性，使信息冗余的张量数据可以更广泛地删除现有的基于张量的降维算法。提出了一种有效的迭代算法来解决这个本质上是整数优化问题。在每一步中，张量结构都是用空间约束的地球移动器距离过程来细化的，该过程增量地重新排列张量，使其变得更类似于它们的低秩近似，这些低秩近似在沿着某些张量维度的特征之间具有高度相关性。单调收敛的算法证明使用辅助功能类似于用于证明收敛的期望最大化算法。此外，我们提出了一个扩展的算法进行监督子空间学习张量数据。在无监督和有监督子空间学习中的实验证明了我们提出的算法在提高数据压缩性能和分类精度方面的有效性。
The success of tensor-based subspace learning depends heavily on reducing correlations along the column vectors of the mode-k flattened matrix. In this work, we study the problem of rearranging elements within a tensor in order to maximize these correlations, so that information redundancy in tensor data can be more extensively removed by existing tensor-based dimensionality reduction algorithms. An efficient iterative algorithm is proposed to tackle this essentially integer optimization problem. In each step, the tensor structure is refined with a spatially-constrained Earth Mover's Distance procedure that incrementally rearranges tensors to become more similar to their low rank approximations, which have high correlation among features along certain tensor dimensions. Monotonic convergence of the algorithm is proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. In addition, we present an extension of the algorithm for conducting supervised subspace learning with tensor data. Experiments in both unsupervised and supervised subspace learning demonstrate the effectiveness of our proposed algorithms in improving data compression performance and classification accuracy.