稀疏编码自编码表达
From Ufldl
| Line 33: | Line 33: | ||
Formally, in sparse coding, we have some data x we would like to learn features on. In particular, we would like to learn s, a set of sparse features useful for representing the data, and A, a basis for transforming the features from the feature space to the data space. Our objective function is hence: | Formally, in sparse coding, we have some data x we would like to learn features on. In particular, we would like to learn s, a set of sparse features useful for representing the data, and A, a basis for transforming the features from the feature space to the data space. Our objective function is hence: | ||
| + | |||
| + | [初译] | ||
| + | |||
| + | 在稀疏编码中，通常有很多数据x供我们进行特征学习。例如：s是一个用于表示数据的稀疏特征集，A是特征集从特征空间转换到数据空间的基。因此，为了计算s和A构建如下目标函数： | ||
| + | |||
| + | [一审] | ||
| + | |||
| + | 在稀疏编码中，对于从数据x中进行特征学习的情况。例如学习一个用于表示数据的稀疏特征集s，和一个将特征从特征空间转换到数据空间的基A,我们可以构建如下目标函数： | ||
| + | |||
| + | [原文] | ||
| + | |||
:<math>J(A, s) = \lVert As - x \rVert_2^2 + \lambda \lVert s \rVert_1</math> | :<math>J(A, s) = \lVert As - x \rVert_2^2 + \lambda \lVert s \rVert_1</math> | ||
| + | (If you are unfamiliar with the notation,<math>\lVert x \rVert_k</math> refers to the Lk norm of the x which is equal to <math>\sum x^k_i</math>. The L2 norm is the familiar Euclidean norm, while the L1 norm is the sum of absolute values of the elements of the vector) | ||
[初译] | [初译] | ||
| Line 42: | Line 54: | ||
在稀疏编码中，对于从数据x中进行特征学习的情况。例如学习一个用于表示数据的稀疏特征集s，和一个将特征从特征空间转换到数据空间的基A,我们可以构建如下目标函数： | 在稀疏编码中，对于从数据x中进行特征学习的情况。例如学习一个用于表示数据的稀疏特征集s，和一个将特征从特征空间转换到数据空间的基A,我们可以构建如下目标函数： | ||
| + | |||
| + | |||
| + | :<math>J(A, s) = \lVert As - x \rVert_2^2 + \lambda \lVert s \rVert_1</math> | ||
