Discriminant adaptive nearest neighbor classification
Discriminant adaptive nearest neighbor classification
复制标题
DOI：
10.1109/34.506411
复制
发表时间：
1996-06-01
影响因子：
23.6
通讯作者：
Tibshirani, R
中科院分区：
文献类型：
--
作者：
Hastie, T;Tibshirani, R
最近邻分类期望类的条件概率局部恒定，并且在高维中存在偏差。我们提出了一种局部自适应形式的最近邻分类，试图改善这种维度的诅咒。我们使用局部线性判别分析来估计计算邻域的有效度量。我们从质心信息中确定局部决策边界，然后在与这些局部决策边界正交的方向上缩小邻域，并将其平行于边界拉长。此后，任何基于邻域的分类器都可以使用修改后的邻域。后验概率在修改后的邻域内趋于均匀。我们还提出了一种结合局部维数信息的全局降维方法。在许多例子中，这些方法证明了比最近邻分类有很大改进的潜力。
Nearest neighbor classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbor classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighborhoods. We determine the local decision boundaries from centroid information, and then shrink neighborhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighborhood-based classifier can be employed, using the modified neighborhoods. The posterior probabilities tend to be more homogeneous in the modified neighborhoods. We also propose a method for global dimension reduction, that combines local dimension information. In a number of examples, the methods demonstrate the potential for substantial improvements over nearest neighbor classification.