独立成分分析

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== Introduction介绍 ==
== Introduction介绍 ==
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'''原文''':
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试着回想一下,在介绍稀疏编码算法中我们想为样本数据学习得到一个超完备基(over-complete basis)。具体来说,这意味着用稀疏编码学习得到的基向量之间不一定线性独立。尽管在某些情况下这已经满足需要,但有时我们仍然希望得到的是一组线性独立基。独立成分分析算法(ICA)正实现了这一点。而且,在ICA中,我们希望学习到的基不仅要线性独立,而且还是一组标准正交基。(一组标准正交基<math>(\phi_1, \ldots \phi_n)</math>需要满足条件:<math>\phi_i \cdot \phi_j = 0</math>(如果<math>i \ne j</math>)或者<math>\phi_i \cdot \phi_j = 1</math>(如果i = j)
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If you recall, in [[Sparse Coding | sparse coding]], we wanted to learn an '''over-complete''' basis for the data. In particular, this implies that the basis vectors that we learn in sparse coding will not be linearly independent. While this may be desirable in certain situations, sometimes we want to learn a linearly independent basis for the data. In independent component analysis (ICA), this is exactly what we want to do. Further, in ICA, we want to learn not just any linearly independent basis, but an '''orthonormal''' basis for the data. (An orthonormal basis is a basis <math>(\phi_1, \ldots \phi_n)</math> such that <math>\phi_i \cdot \phi_j = 0</math> if <math>i \ne j</math> and <math>1</math> if <math>i = j</math>).
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'''译文''':
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如果你还记得,在稀疏编码中我们希望为数据学习一个过完备基(over-complete basis).具体来说,这意味着我们在稀疏编码中学习的基向量不一定是线性独立的.虽然在某些情况下这是可以的,但有时我们希望学习一个线性独立基.这正是我们在独立成份分析(ICA)中要做的.而且,在ICA中,我们希望学习的不仅是线性独立基,而且是标准正交基.(一个标准正交基是一个基<math>(\phi_1, \ldots \phi_n)</math>,满足<math>\phi_i \cdot \phi_j = 0</math> if <math>i \ne j</math> and <math>1</math> if <math>i = j</math>).
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'''一审''':
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如果你还记得,在稀疏编码中我们希望为数据学习一个过完备基(over-complete basis).具体来说,这意味着在稀疏编码中学习到的基向量之间不一定线性独立.尽管在某些情况下这已经满足需要,但有时我们仍然希望得到一组线性独立基.例如在独立成份分析(ICA)中,这正是我们想要的.而且,在ICA中,我们希望学习到的基不仅要线性独立,而且还是一组标准正交基.(一个标准正交基<math>(\phi_1, \ldots \phi_n)</math>需要满足条件:<math>\phi_i \cdot \phi_j = 0</math> if <math>i \ne j</math> and <math>1</math> if <math>i = j</math>).
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'''原文''':
'''原文''':

Revision as of 02:16, 20 March 2013

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