池化

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在通过卷积获得了特征(features)之后,下一步我们希望利用这些特征去做分类。理论上讲,人们可以用所有提取得到的特征去训练分类器,例如softmax分类器,但这样做面临计算量的挑战。例如:对于一个96X96像素的图像,假设我们已经学习得到了400个定义在8X8输入上的特征,每一个特征和图像卷积都会得到一个(96 − 8 + 1) * (96 − 8 + 1) = 7921维的卷积特征,由于有400个特征,所以每个样例(example)都会得到一个892 * 400 = 3,168,400维的卷积特征向量。学习一个拥有超过3百万特征输入的分类器十分不便,并且容易出现过拟合(over-fitting)。
在通过卷积获得了特征(features)之后,下一步我们希望利用这些特征去做分类。理论上讲,人们可以用所有提取得到的特征去训练分类器,例如softmax分类器,但这样做面临计算量的挑战。例如:对于一个96X96像素的图像,假设我们已经学习得到了400个定义在8X8输入上的特征,每一个特征和图像卷积都会得到一个(96 − 8 + 1) * (96 − 8 + 1) = 7921维的卷积特征,由于有400个特征,所以每个样例(example)都会得到一个892 * 400 = 3,168,400维的卷积特征向量。学习一个拥有超过3百万特征输入的分类器十分不便,并且容易出现过拟合(over-fitting)。
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To address this, first recall that we decided to obtain convolved features because images have the "stationarity" property, which implies that features that are useful in one region are also likely to be useful for other regions. Thus, to describe a large image, one natural approach is to aggregate statistics of these features at various locations. For example, one could compute the mean (or max) value of a particular feature over a region of the image. These summary statistics are much lower in dimension (compared to using all of the extracted features) and can also improve results (less over-fitting). We aggregation operation is called this operation pooling, or sometimes mean pooling or max pooling (depending on the pooling operation applied).  
To address this, first recall that we decided to obtain convolved features because images have the "stationarity" property, which implies that features that are useful in one region are also likely to be useful for other regions. Thus, to describe a large image, one natural approach is to aggregate statistics of these features at various locations. For example, one could compute the mean (or max) value of a particular feature over a region of the image. These summary statistics are much lower in dimension (compared to using all of the extracted features) and can also improve results (less over-fitting). We aggregation operation is called this operation pooling, or sometimes mean pooling or max pooling (depending on the pooling operation applied).  
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下图显示池化如何应用于一个图像的四块不重合区域。
下图显示池化如何应用于一个图像的四块不重合区域。
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[http://deeplearning.stanford.edu/wiki/images/0/08/Pooling_schematic.gif 点击查看原图]
[http://deeplearning.stanford.edu/wiki/images/0/08/Pooling_schematic.gif 点击查看原图]
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== Pooling for Invariance ==
== Pooling for Invariance ==
If one chooses the pooling regions to be contiguous areas in the image and only pools features generated from the same (replicated) hidden units. Then, these pooling units will then be translation invariant. This means that the same (pooled) feature will be active even when the image undergoes (small) translations. Translation-invariant features are often desirable; in many tasks (e.g., object detection, audio recognition), the label of the example (image) is the same even when the image is translated. For example, if you were to take an MNIST digit and translate it left or right, you would want your classifier to still accurately classify it as the same digit regardless of its final position.  
If one chooses the pooling regions to be contiguous areas in the image and only pools features generated from the same (replicated) hidden units. Then, these pooling units will then be translation invariant. This means that the same (pooled) feature will be active even when the image undergoes (small) translations. Translation-invariant features are often desirable; in many tasks (e.g., object detection, audio recognition), the label of the example (image) is the same even when the image is translated. For example, if you were to take an MNIST digit and translate it left or right, you would want your classifier to still accurately classify it as the same digit regardless of its final position.  
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【初译】:
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Revision as of 11:44, 7 March 2013

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