稀疏编码

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-	稀疏编码	+	'''Sparse Coding'''
		+
		+	'''稀疏编码'''
		+
		+	初译：@寅莹
		+
		+	一审：@大黄蜂的思索
		+
		+	Sparse coding is a class of unsupervised methods for learning sets of over-complete bases to represent data efficiently. The aim of sparse coding is to find a set of basis vectors <math>\mathbf{\phi}_i</math> such that we can represent an input vector <math>\mathbf{x}</math> as a linear combination of these basis vectors:
		+	:<math>\begin{align}
		+	\mathbf{x} = \sum_{i=1}^k a_i \mathbf{\phi}_{i}
		+	\end{align}</math>
		+	【初译】针对超完备基的学习集，稀疏编码是一类有效表示数据的非监督方法。稀疏编码的目的是找到一组基向量 <math>\mathbf{\phi}_i</math> 集合，以致能将输入向量 <math>\mathbf{x}</math> 表示为这组基向量的线性组合。
		+	:<math>\begin{align}
		+	\mathbf{x} = \sum_{i=1}^k a_i \mathbf{\phi}_{i}
		+	\end{align}</math>
		+	【一审】稀疏编码算法是一种无监督学习方法，它用来寻找一组“超完备”基向量来更高效地表示样本数据。稀疏编码算法的目的就是找到一组基向量 <math>\mathbf{\phi}_i</math> ，使得我们能将输入向量 <math>\mathbf{x}</math> 表示为这些基向量的线性组合。
		+	:<math>\begin{align}
		+	\mathbf{x} = \sum_{i=1}^k a_i \mathbf{\phi}_{i}
		+	\end{align}</math>
		+	While techniques such as Principal Component Analysis (PCA) allow us to learn a complete set of basis vectors efficiently, we wish to learn an '''over-complete''' set of basis vectors to represent input vectors  (i.e. such that k>n). The advantage of having an over-complete basis is that our basis vectors are better able to capture structures and patterns inherent in the input data. However, with an over-complete basis, the coefficients ai are no longer uniquely determined by the input vector x. Therefore, in sparse coding, we introduce the additional criterion of sparsity to resolve the degeneracy introduced by over-completeness.

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Revision as of 01:51, 8 March 2013