稀疏编码
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'''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 <math>\mathbf{x}\in\mathbb{R}^n</math> (i.e. such that <math>k > n</math>). 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 <math>a_i</math> are no longer uniquely determined by the input vector <math>\mathbf{x}</math>. Therefore, in sparse coding, we introduce the additional criterion of '''sparsity''' to resolve the degeneracy introduced by over-completeness. 【初译】因主成分分析技术允许有效地学习一组完备基向量集合,希望能够学习一组过完备的基向量集合,来表示输入向量 <math>\mathbf{x}\in\mathbb{R}^n</math> (即,如<math>k > n</math>)。过完备基的优点是该基向量能更好地捕捉输入数据内在的结构和模式。然而,对于过完备基,其系数 <math>a_i</math> 不在由输入向量 <math>\mathbf{x}</math>唯一确定。因此,在稀疏编中引入稀疏的附加标准,解决因引入过完备基所导致的退化问题。 【一审】虽然形如主成分分析技术(PCA)能使我们方便地找到一组“完备”基向量,但是这里我们想要做的是找到一组“超完备”基向量来表示输入向量 <math>\mathbf{x}\in\mathbb{R}^n</math> (也就是说,<math>k > n</math>)。超完备基的好处是它们能更有效地找出输入数据的结构与模式。然而,对于超完备基来说,系数 <math>a_i</math> 不再由输入向量 <math>\mathbf{x}</math>唯一确定。因此,在稀疏编码算法中,我们另加了一个评判标准“稀疏性”来解决因超完备而导致的退化(degeneracy)问题。 Here, we define sparsity as having few non-zero components or having few components not close to zero. The requirement that our coefficients <math>a_i</math> be sparse means that given a input vector, we would like as few of our coefficients to be far from zero as possible. The choice of sparsity as a desired characteristic of our representation of the input data can be motivated by the observation that most sensory data such as natural images may be described as the superposition of a small number of atomic elements such as surfaces or edges. Other justifications such as comparisons to the properties of the primary visual cortex have also been advanced. 【初译】此处,定义的稀疏性为具有很少的非零分量或很少不接近零的分量。针对系数 <math>a_i</math> 的稀疏处理是对于输入向量,要求得到尽可能少的不为零的系数。作为输入表示数据的期望特征,即稀疏性的选择可由多数传感器数据描述受到启发,如自然图像可被描述为少量的元成分(表面或边缘)的叠加。其他理由,如和主要视觉皮层的属性相比已取得进展。 【一审】这里,我们把“稀疏性”定义为:只有很少的几个非零元素或只有很少的几个远大于零的元素。要求系数 <math>a_i</math> 是稀疏的意思就是说:对于一组输入向量,我们只想有尽可能少的几个系数远大于零。要使输入数据的表示方式符合我们所期望的这个样子,稀疏性的选择可以从对感观数据的观察得到启示,比如,自然图像有时可以通过少量的基本元素如图像表层或边缘的叠加来表示。(一审:这东西没接触过)其它的选择标准如初级视觉皮层神经元特性的比较,这在之前的课程中也有提及。
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