基于峭度的矩阵值数据投影寻踪
Kurtosis-based projection pursuit for matrix-valued data
摘要：
我们开发的数据，承认一个自然的矩阵形式表示的投影追求。对于投影指数，我们提出了经典的峰度和Mardia的多变量峰度的扩展。第一个索引同时估计矩阵两侧的投影，而第二个索引分别找到两个投影。这两个指数恢复最佳分离投影两组高斯混合物在完全没有任何标签信息。我们进一步建立了相应样本估计的强相合性。仿真和手写邮政编码数据的实际数据的例子来证明该方法。
英文摘要：
We develop projection pursuit for data that admit a natural representation in matrix form. For projection indices, we propose extensions of the classical kurtosis and Mardia's multivariate kurtosis. The first index estimates projections for both sides of the matrices simultaneously, while the second index finds the two projections separately. Both indices are shown to recover the optimally separating projection for two-group Gaussian mixtures in the full absence of any label information. We further establish the strong consistency of the corresponding sample estimators. Simulations and a real data example on hand-written postal code data are used to demonstrate the method.
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