Invariant co-ordinate selection
Invariant co-ordinate selection
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DOI：
10.1111/j.1467-9868.2009.00706.x
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发表时间：
2009-01-01
影响因子：
5.8
通讯作者：
Oja, Hannu
中科院分区：
文献类型：
--
作者：
Tyler, David E.;Critchley, Frank;Oja, Hannu
提出了一种通过比较多变量离散度的不同估计来探索多变量数据的一般方法。该方法基于一个散布矩阵相对于另一个散布矩阵的特征值-特征向量分解。特别地，证明了特征向量可用于生成多变量数据的仿射不变坐标系。因此，我们将该方法视为一种不变坐标选择方法。通过绘制关于这个新的不变坐标系的数据，可以揭示各种数据结构。例如，在某些独立分量模型下，证明了不变坐标对应于独立分量。另一个例子与椭圆分布的混合有关。在这种情况下，即使数据点的类别标识未知，也证明了不变坐标的一个子集对应于Fisher线性判别式子空间。文中给出了一些例证。
A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.