提交 e0b65164 编写于 作者: Y Yuanpeng

Translate model overview.

上级 6615c737
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<p align="center">
<img src="image/mnist_example_image.png" width="400"><br/>
图1. MNIST图片示例
Fig 1. MNIST image examples
Fig. 1. MNIST image examples
</p>
MNIST数据集是从 [NIST](https://www.nist.gov/srd/nist-special-database-19) 的Special Database 3(SD-3)和Special Database 1(SD-1)构建而来。由于SD-3是由美国人口调查局的员工进行标注,SD-1是由美国高中生进行标注,因此SD-3比SD-1更干净也更容易识别。Yann LeCun等人从SD-1和SD-3中各取一半作为MNIST的训练集(60000条数据)和测试集(10000条数据),其中训练集来自250位不同的标注员,此外还保证了训练集和测试集的标注员是不完全相同的。
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- $Y$是输出:分类器的输出是10类数字(0-9),即$Y=\left ( y_0, y_1, \dots, y_9 \right )$,每一维$y_i$代表图片分类为第$i$类数字的概率。
- $L$是图片的真实标签:$L=\left ( l_0, l_1, \dots, l_9 \right )$也是10维,但只有一维为1,其他都为0。
## Model Overview
Before introducing the classification algorithms and training procedure, we provide some definitions:
- $X$ is input:MNIST image is $28\times28$ two dimensional matrix. It is reshaped to $784$ dimensional vector. $X=\left ( x_0, x_1, \dots, x_{783} \right )$。
- $Y$ is output:Output of classifier is 10 class digits from 0 to 9. $Y=\left ( y_0, y_1, \dots, y_9 \right )$,Each dimension $y_i$ represents a probability that the image belongs to $i$.
- $L$ is a image's ground truth label:$L=\left ( l_0, l_1, \dots, l_9 \right )$ It is also 10 dimensional, but only one dimension is 1 and others are all 0.
### Softmax回归(Softmax Regression)
最简单的Softmax回归模型是先将输入层经过一个全连接层得到的特征,然后直接通过softmax 函数进行多分类\[[9](#参考文献)\]
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