Deep Learning (5) Softmax Regression: Introduction to Classification Algorithms, How to Load the Fashion-MINIST Data Set

Softmax returns

Fundamental

Regression and classification are two common methods of deep learning. Regression is a continuous prediction (for example, I predict the next two-color ball number based on the past lottery list), and classification is a prediction of discrete categories (handwritten speech recognition, picture recognition).

Now that we have a certain understanding of processing regression, how do we transition to classification?

Suppose we have n classes, first we need to encode these classes to turn them into data. All classes become a column vector.

$and=[y_1,{and}_2,...y_n{]}^T$

There is a data belonging to the i-th category, then its column vector is:

$and=[0,0,...,1,...,0,0{]}^T$

That is, only the elements of the class it belongs to =1.

You can use mean square loss training and determine which one to use based on probability.

Softmax regression is a classification method (the generalization of regression problems to multi-classification). First determine the number of input features and the number of output categories. For example, in the picture above we have 4 features and 3 possible categories, then the formula for calculating their respective probabilities includes 3 linear regressions:

It can be seen that Softmax is a fully connected single-layer neural network.

After normalizing all the output results, we select the largest possible classification result with the highest confidence.

Taking the exponent of e makes all values ​​nonnegative.

Use the real probability vector - the probability vector we predict is the loss. The real value is a column vector with only one 1.

Cross entropy loss:

It can be seen that in the classification problem, we don't care about the incorrect prediction value, we only care about whether the correct prediction value is large enough. **Because the correct value is a column vector with only one element being 1.

Commonly used loss functions

L2 Loss: Mean square loss.

L1 Loss: Absolute value loss.

The L2 gradient is a sloping straight line, which is more suitable for gradient descent algorithms; L1 is a jump, and the gradient is either -1 or 1. As shown in the figure, the gradient of L1 L2.

We can combine the two to get a new loss function (robust loss Huber Robust):

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Image classification dataset

MINIST is a commonly used image classification data set, but it is too simple. The later upgraded version was called Fashion-MINIST (clothing classification).

First, we study how to load the training data set for later testing of the algorithm.

# 导包
%matplotlib inline
import torch
import torchvision
from torch.utils import data
from torchvision import transforms
from d2l import torch as d2l

d2l.use_svg_display()

d2l.use_svg_display()

# 下载数据集并读取到内存
trans = transforms.ToTensor()
mnist_train = torchvision.datasets.FashionMNIST(
    root="../data", train=True, transform=trans, download=True)		# 训练数据集
mnist_test = torchvision.datasets.FashionMNIST(
    root="../data", train=False, transform=trans, download=True)	# 测试数据集用于评估性能

# 定义函数用于返回对应索引的标签
def get_fashion_mnist_labels(labels):  #@save
    """返回Fashion-MNIST数据集的文本标签"""
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]

# 图像可视化，让结果看着更直观，比如下面那个绿色图的样子
def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  #@save
    """绘制图像列表"""
    figsize = (num_cols * scale, num_rows * scale)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        if torch.is_tensor(img):
            # 图片张量
            ax.imshow(img.numpy())
        else:
            # PIL图片
            ax.imshow(img)
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])
    return axes

# 我们先读一点数据集看看啥样的
X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))
show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y));

# 通过内置数据加载器读取一批量数据，自动随机打乱读取，不需要我们自己定义
batch_size = 256

def get_dataloader_workers():  #@save
    """使用4个进程来读取数据"""
    return 4

train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True,
                             num_workers=get_dataloader_workers())

The above measurement time is basically 2-3 seconds.

To summarize and integrate the above data reading process, the code is as follows:

def load_data_fashion_mnist(batch_size, resize=None):  #@save
    """下载Fashion-MNIST数据集，然后将其加载到内存中"""
    trans = [transforms.ToTensor()]
    if resize:
        trans.insert(0, transforms.Resize(resize))
    trans = transforms.Compose(trans)
    mnist_train = torchvision.datasets.FashionMNIST(
        root="../data", train=True, transform=trans, download=True)
    mnist_test = torchvision.datasets.FashionMNIST(
        root="../data", train=False, transform=trans, download=True)
    return (data.DataLoader(mnist_train, batch_size, shuffle=True,
                            num_workers=get_dataloader_workers()),
            data.DataLoader(mnist_test, batch_size, shuffle=False,
                            num_workers=get_dataloader_workers()))

Loading an image also allows you to resize it.