Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition
Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition
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DOI：
10.1016/s0262-8856(02)00114-2
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发表时间：
2002-12-01
影响因子：
4.7
通讯作者：
Martin, R
中科院分区：
文献类型：
--
作者：
Hall, P;Marshall, D;Martin, R
本文提供了添加和减去特征空间的算法，从而实现了数据模型的增量更新和减量更新。重要的是，与以往的工作不同，我们准确跟踪了数据的平均值，这使得我们的方法可以用于分类应用。将每组数据的特征空间相加，得到的结果近似于这组数据相加后的结果。减去特征空间得到的结果近似于使用一个数据子集得到的结果。利用我们的算法，可以在不参考原始数据的情况下对特征空间进行 "运算"。特征空间可以使用特征值分解（EVD）或奇异值分解（SVD）来构建。我们为这两种方法提供了加法运算符，但只为 EVD 提供了减法运算符，因为 SVD 没有闭式解。围绕 SVD 的方法和讨论是本文的主要创新点。我们将在三个一般应用（包括高斯混合物模型的动态构建）中说明我们算法的使用。(C) 2002 Elsevier Science B.V. 版权所有。保留所有权利。
This paper provides algorithms for adding and subtracting eigenspaces, thus allowing for incremental updating and downdating of data models. Importantly, and unlike previous work, we keep an accurate track of the mean of the data, which allows our methods to be used in classification applications. The result of adding eigenspaces, each made from a set of data, is an approximation to that which would obtain were the sets of data taken together. Subtracting eigenspaces yields a result approximating that which would obtain were a subset of data used. Using our algorithms, it is possible to perform 'arithmetic' on eigenspaces without reference to the original data. Eigenspaces can be constructed using either eigenvalue decomposition (EVD) or singular value decomposition (SVD). We provide addition operators for both methods, but subtraction for EVD only, arguing there is no closed-form solution for SVD. The methods and discussion surrounding SVD provide the principle novelty in this paper. We illustrate the use of our algorithms in three generic applications, including the dynamic construction of Gaussian mixture models. (C) 2002 Elsevier Science B.V. All rights reserved.