AIX360-CEMExplainer: MNIST Example

news2024/11/20 3:29:48

CEMExplainer: MNIST Example

  • 这一部分屁话有点多，导包没问题的话可以跳过
  • 加载MNIST数据集
  • 加载经过训练的MNIST模型
  • 加载经过训练的卷积自动编码器模型（可选）
  • 初始化CEM解释程序以解释模型预测
  • 解释输入实例
  • 获得相关否定（Pertinent Negative,PN）解释
  • 获得相关的肯定（Pertinent Positive,PP）解释
  • 相关负（PN）和相关正（PP）解释图

CEMBexplainer:MNIST示例

  • 本文了如何使用AIX360的CEMBexplainer来获得对比解释的示例，即对MNIST数据训练的模型所做预测的相关否定（PN）和相关肯定（PP）。
  • CEMBexplainer是对比解释方法的一种实现。
  • 此案例使用经过训练的模型，这些模型可从aix360/models/CEM/文件夹访问。

官方代码在https://github.com/Trusted-AI/AIX360/blob/master/examples/contrastive/CEM-MNIST.ipynb

这一部分屁话有点多，导包没问题的话可以跳过

pip install keras

pip install --user tensorflow

import os
import sys
from keras.models import model_from_json
from PIL import Image
from matplotlib import pyplot as plt
import numpy as np

from aix360.algorithms.contrastive import CEMExplainer, KerasClassifier
from aix360.datasets import MNISTDataset

经典一步一bug，眼睛一睁一闭，休眠升天修仙。。。
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TensorFlow 2.0中contrib被弃用，尝试安装旧版tensorflow

conda install tensorflow==1.14.0

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看到这我真的高兴坏了，之前不小心把python版本装高了，没办法，就是这么倒霉，推倒重来，官网怎么喜欢用那么老的版本，为什么我的眼里常含泪水，因为对知识爱得深沉。。。

重新创建个虚拟环境，
python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6
https://blog.csdn.net/weixin_45735391/article/details/133197625
python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6python3.6

清华源似乎没有这个古老的版本。。。
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emmmm，又是一个坑。。。

python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7
https://blog.csdn.net/weixin_45735391/article/details/133197625
python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7python3.7
此倒霉蛋已疯。。。

tensorflow装好了，又多活了一天，欧耶！！！
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可是
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此人g了。。。那就pip吧。。。

pip install aix360

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看着它那么红，就让它红这吧。。。

人生嘛，惊喜不断，不然多无聊，哈哈哈。。。
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pip install skimage

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pip install scikit-image

还差亿点点。。。
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conda install pytorch

还差亿点点。。。
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conda install requests

不想看见这坨警告的话，可以加上

import warnings
warnings.filterwarnings("ignore")

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好了，导包这块终于结束了。
又多活了一天，真不错，今天是个好日子。。。

加载MNIST数据集

# load MNIST data and normalize it in the range [-0.5, 0.5]
data = MNISTDataset()

花的时间有亿点点久。。。真的等不下去了。。。脑子已经在修仙了。。。
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看看源码写的啥

class MNISTDataset():
    def __init__(self, custom_preprocessing=None, dirpath=None): 
        self._dirpath = dirpath
        if not self._dirpath:
            self._dirpath = os.path.join(os.path.dirname(os.path.abspath(__file__)),
                '..', 'data','mnist_data')

        files = ["train-images-idx3-ubyte.gz",
                 "t10k-images-idx3-ubyte.gz",
                 "train-labels-idx1-ubyte.gz",
                 "t10k-labels-idx1-ubyte.gz"]
        for name in files:
            if not os.path.exists(self._dirpath + "/" + name):
                print("retrieving file", name)
                urllib.request.urlretrieve('http://yann.lecun.com/exdb/mnist/' + name, self._dirpath + "/" + name)
                print("retrieved")

        train_data       = extract_data(self._dirpath + "/train-images-idx3-ubyte.gz", 60000)
        train_labels     = extract_labels(self._dirpath + "/train-labels-idx1-ubyte.gz", 60000)
        self.test_data   = extract_data(self._dirpath + "/t10k-images-idx3-ubyte.gz", 10000)
        self.test_labels = extract_labels(self._dirpath + "/t10k-labels-idx1-ubyte.gz", 10000)
        
        VALIDATION_SIZE = 5000
        
        self.validation_data = train_data[:VALIDATION_SIZE, :, :, :]
        self.validation_labels = train_labels[:VALIDATION_SIZE]
        self.train_data = train_data[VALIDATION_SIZE:, :, :, :]
        self.train_labels = train_labels[VALIDATION_SIZE:]

直接百度搜一下下载MNIST数据集，找到别人分享的资源，把这四个文件["train-images-idx3-ubyte.gz","t10k-images-idx3-ubyte.gz","train-labels-idx1-ubyte.gz", "t10k-labels-idx1-ubyte.gz"]下载下来。

然后代码改一下，dirpath就是那四个文件的保存路径。

dirpath = r'C:\Users\gxx\Desktop\jupter\aix360\MNIST'
data = MNISTDataset(dirpath=dirpath)

# print the shape of train and test data
print("MNIST train data range  :", "(", np.min(data.train_data), ",", np.max(data.train_data), ")")
print("MNIST test data range   :", "(", np.min(data.train_data), ",",  np.max(data.train_data), ")")
print("MNIST train data shape  :", data.train_data.shape)
print("MNIST test data shape   :", data.test_data.shape)
print("MNIST train labels shape:", data.test_labels.shape)
print("MNIST test labels shape :", data.test_labels.shape)

输出结果

MNIST train data range  : ( -0.5 , 0.5 )
MNIST test data range   : ( -0.5 , 0.5 )
MNIST train data shape  : (55000, 28, 28, 1)
MNIST test data shape   : (10000, 28, 28, 1)
MNIST train labels shape: (10000, 10)
MNIST test labels shape : (10000, 10)

加载经过训练的MNIST模型

此notebook使用经过训练的MNIST模型。此处提供了训练此模型的代码。请注意，该模型输出logits，并且不使用softmax函数。
把官网上的文件复制到本地，改一下路径。

# path to mnist related models
# model_path = '../../aix360/models/CEM'
model_path = r'C:\Users\gxx\Desktop\jupter\aix360\CEM'

def load_model(model_json_file, model_wt_file):
    
    # read model json file
    with open(model_json_file, 'r') as f:
        model = model_from_json(f.read())
    
    # read model weights file
    model.load_weights(model_wt_file)
    
    return model
    

# load MNIST model using its json and wt files
mnist_model = load_model(os.path.join(model_path, 'mnist.json'), os.path.join(model_path, 'mnist'))

# print model summary
mnist_model.summary()

不出意外，bug又来了。。。
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在安装 tensorflow 时，默认安装 h5py 为3.7.0，而报错是因为安装的 TF 不支持过高版本的 h5py。
卸 载 h5py 3.7.0版本，安装 h5py 2.10.0 版本。

pip uninstall --user h5py
pip install --user h5py==2.10.0

结果输出：
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加载经过训练的卷积自动编码器模型（可选）

这个notebook使用了一个经过训练的卷积自动编码器模型。此处提供了训练此模型的代码。

# load the trained convolutional autoencoder model
ae_model = load_model(os.path.join(model_path, 'mnist_AE_1_decoder.json'), 
                      os.path.join(model_path, 'mnist_AE_1_decoder.h5'))
# print model summary
ae_model.summary()

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初始化CEM解释程序以解释模型预测

# wrap mnist_model into a framework independent class structure
mymodel = KerasClassifier(mnist_model)

# initialize explainer object
explainer = CEMExplainer(mymodel)

解释输入实例

# choose an input image
image_id = 340
input_image = data.test_data[image_id]

# rescale values from [-0.5, 0.5] to [0, 255] for plotting
plt.imshow((input_image[:,:,0] + 0.5)*255, cmap="gray")

# check model prediction
print("Predicted class:", mymodel.predict_classes(np.expand_dims(input_image, axis=0)))
print("Predicted logits:", mymodel.predict(np.expand_dims(input_image, axis=0)))

结果输出：
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观察结果：

尽管上面的图像被模型分类为数字3，但是由于它与数字5具有相似性，所以它也可以被分类为数字5。我们现在使用AIX360的CEMBexplainer来计算相关的正面和负面解释，这有助于我们理解为什么图像被模型分类为数字3而不是数字5。

获得相关否定（Pertinent Negative,PN）解释

arg_mode = "PN" # Find pertinent negative

arg_max_iter = 1000 # Maximum number of iterations to search for the optimal PN for given parameter settings
arg_init_const = 10.0 # Initial coefficient value for main loss term that encourages class change
arg_b = 9 # No. of updates to the coefficient of the main loss term

arg_kappa = 0.9 # Minimum confidence gap between the PNs (changed) class probability and original class' probability
arg_beta = 1.0 # Controls sparsity of the solution (L1 loss)
arg_gamma = 100 # Controls how much to adhere to a (optionally trained) autoencoder
arg_alpha = 0.01 # Penalizes L2 norm of the solution
arg_threshold = 0.05 # Automatically turn off features <= arg_threshold if arg_threshold < 1
arg_offset = 0.5 # the model assumes classifier trained on data normalized
                # in [-arg_offset, arg_offset] range, where arg_offset is 0 or 0.5


(adv_pn, delta_pn, info_pn) = explainer.explain_instance(np.expand_dims(input_image, axis=0), arg_mode, ae_model, arg_kappa, arg_b, 
                                            arg_max_iter, arg_init_const, arg_beta, arg_gamma, arg_alpha, arg_threshold, arg_offset)

结果输出：

WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\aix360\algorithms\contrastive\CEM_aen.py:60: The name tf.placeholder is deprecated. Please use tf.compat.v1.placeholder instead.

WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\aix360\algorithms\contrastive\CEM_aen.py:151: The name tf.assign is deprecated. Please use tf.compat.v1.assign instead.

WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\aix360\algorithms\contrastive\CEM_aen.py:213: The name tf.train.polynomial_decay is deprecated. Please use tf.compat.v1.train.polynomial_decay instead.

WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\tensorflow\python\keras\optimizer_v2\learning_rate_schedule.py:409: div (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.
Instructions for updating:
Deprecated in favor of operator or tf.math.divide.
WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\aix360\algorithms\contrastive\CEM_aen.py:216: The name tf.train.GradientDescentOptimizer is deprecated. Please use tf.compat.v1.train.GradientDescentOptimizer instead.

WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\tensorflow\python\ops\math_grad.py:1250: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.
Instructions for updating:
Use tf.where in 2.0, which has the same broadcast rule as np.where
WARNING:tensorflow:From C:\Users\gxx\anaconda3\envs\tf-py37\lib\site-packages\aix360\algorithms\contrastive\CEM_aen.py:230: The name tf.variables_initializer is deprecated. Please use tf.compat.v1.variables_initializer instead.

iter:0 const:[10.]
Loss_Overall:2737.2244, Loss_Attack:58.5389
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:500 const:[10.]
Loss_Overall:2737.2244, Loss_Attack:58.5389
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[100.]
Loss_Overall:3152.3984, Loss_Attack:0.0000
Loss_L2Dist:12.6054, Loss_L1Dist:16.5280, AE_loss:3123.264892578125
target_lab_score:9.0004, max_nontarget_lab_score:29.0375

iter:500 const:[100.]
Loss_Overall:2977.4854, Loss_Attack:0.0000
Loss_L2Dist:7.0313, Loss_L1Dist:10.1030, AE_loss:2960.35107421875
target_lab_score:9.2486, max_nontarget_lab_score:28.5018

iter:0 const:[55.]
Loss_Overall:2840.0422, Loss_Attack:0.0000
Loss_L2Dist:4.8674, Loss_L1Dist:7.2291, AE_loss:2827.94580078125
target_lab_score:9.7374, max_nontarget_lab_score:27.1471

iter:500 const:[55.]
Loss_Overall:2670.4844, Loss_Attack:0.0000
Loss_L2Dist:0.8409, Loss_L1Dist:2.1313, AE_loss:2667.51220703125
target_lab_score:15.5937, max_nontarget_lab_score:19.4013

iter:0 const:[32.5]
Loss_Overall:2644.0203, Loss_Attack:2.0429
Loss_L2Dist:0.5595, Loss_L1Dist:1.8527, AE_loss:2639.565185546875
target_lab_score:16.7141, max_nontarget_lab_score:17.5513

iter:500 const:[32.5]
Loss_Overall:2868.9368, Loss_Attack:190.2513
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[21.25]
Loss_Overall:2782.8979, Loss_Attack:117.1809
Loss_L2Dist:0.0176, Loss_L1Dist:0.2093, AE_loss:2665.490234375
target_lab_score:19.1928, max_nontarget_lab_score:14.5784

iter:500 const:[21.25]
Loss_Overall:2803.0806, Loss_Attack:124.3951
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[26.875]
Loss_Overall:2738.9089, Loss_Attack:91.5858
Loss_L2Dist:0.1530, Loss_L1Dist:0.9359, AE_loss:2646.234130859375
target_lab_score:18.1907, max_nontarget_lab_score:15.6829

iter:500 const:[26.875]
Loss_Overall:2836.0088, Loss_Attack:157.3232
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[24.0625]
Loss_Overall:2774.3594, Loss_Attack:117.5742
Loss_L2Dist:0.0524, Loss_L1Dist:0.4683, AE_loss:2656.2646484375
target_lab_score:18.8622, max_nontarget_lab_score:14.8760

iter:500 const:[24.0625]
Loss_Overall:2819.5447, Loss_Attack:140.8591
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[25.46875]
Loss_Overall:2754.6963, Loss_Attack:104.3005
Loss_L2Dist:0.0950, Loss_L1Dist:0.7232, AE_loss:2649.57763671875
target_lab_score:18.5058, max_nontarget_lab_score:15.3106

iter:500 const:[25.46875]
Loss_Overall:2827.7766, Loss_Attack:149.0911
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

iter:0 const:[24.765625]
Loss_Overall:2762.2129, Loss_Attack:109.3322
Loss_L2Dist:0.0725, Loss_L1Dist:0.6168, AE_loss:2652.191650390625
target_lab_score:18.6550, max_nontarget_lab_score:15.1403

iter:500 const:[24.765625]
Loss_Overall:2823.6606, Loss_Attack:144.9751
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:2678.685546875
target_lab_score:19.3967, max_nontarget_lab_score:14.4428

print(info_pn)

结果输出：

[INFO]kappa:0.9, Orig class:3, Perturbed class:5, Delta class: 1, Orig prob:[[-11.279339    0.73625    -9.008647   19.396711   -8.286123   14.442826   -1.3170443 -11.587322   -0.992185    1.0182207]], Perturbed prob:[[ -6.6607647   -1.9869652   -7.4231925   13.461045    -6.341817   13.8300295    1.2803447  -11.60892      0.31489015   1.1112802 ]], Delta prob:[[-0.11039171  1.0537697  -0.0954444  -0.2623107  -0.3357536   0.24241148  -0.0948096  -0.00691785 -0.31975082 -0.56200165]]

获得相关的肯定（Pertinent Positive,PP）解释

arg_mode = "PP"  # Find pertinent positive
arg_beta = 0.1 # Controls sparsity of the solution (L1 loss)
(adv_pp, delta_pp, info_pp) = explainer.explain_instance(np.expand_dims(input_image, axis=0), arg_mode, ae_model, arg_kappa, arg_b, 
                                            arg_max_iter, arg_init_const, arg_beta, arg_gamma, arg_alpha, arg_threshold, arg_offset)

结果输出：


iter:0 const:[10.]
Loss_Overall:1186.7114, Loss_Attack:20.4772
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:500 const:[10.]
Loss_Overall:1186.7114, Loss_Attack:20.4772
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:0 const:[100.]
Loss_Overall:1374.8175, Loss_Attack:224.8764
Loss_L2Dist:0.0581, Loss_L1Dist:0.5667, AE_loss:1149.8262939453125
target_lab_score:-0.1908, max_nontarget_lab_score:1.1579

iter:500 const:[100.]
Loss_Overall:1177.7847, Loss_Attack:0.0000
Loss_L2Dist:9.0615, Loss_L1Dist:26.9499, AE_loss:1166.0281982421875
target_lab_score:9.1723, max_nontarget_lab_score:5.3354

iter:0 const:[55.]
Loss_Overall:1278.8588, Loss_Attack:112.6245
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:500 const:[55.]
Loss_Overall:1278.8588, Loss_Attack:112.6245
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:0 const:[77.5]
Loss_Overall:1324.9324, Loss_Attack:158.6981
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:500 const:[77.5]
Loss_Overall:1324.9324, Loss_Attack:158.6981
Loss_L2Dist:0.0000, Loss_L1Dist:0.0000, AE_loss:1166.2342529296875
target_lab_score:-0.1036, max_nontarget_lab_score:1.0441

iter:0 const:[88.75]
Loss_Overall:1347.3350, Loss_Attack:190.4548
Loss_L2Dist:0.0195, Loss_L1Dist:0.2384, AE_loss:1156.8367919921875
target_lab_score:-0.1378, max_nontarget_lab_score:1.1082

iter:500 const:[88.75]
Loss_Overall:1182.4167, Loss_Attack:0.0000
Loss_L2Dist:10.1261, Loss_L1Dist:29.5733, AE_loss:1169.3333740234375
target_lab_score:10.9503, max_nontarget_lab_score:8.5652

iter:0 const:[83.125]
Loss_Overall:1336.9946, Loss_Attack:176.8078
Loss_L2Dist:0.0096, Loss_L1Dist:0.1385, AE_loss:1160.1634521484375
target_lab_score:-0.1352, max_nontarget_lab_score:1.0918

iter:500 const:[83.125]
Loss_Overall:1177.7847, Loss_Attack:0.0000
Loss_L2Dist:9.0615, Loss_L1Dist:26.9499, AE_loss:1166.0281982421875
target_lab_score:9.1723, max_nontarget_lab_score:5.3355

iter:0 const:[80.3125]
Loss_Overall:1330.7108, Loss_Attack:169.8772
Loss_L2Dist:0.0070, Loss_L1Dist:0.1182, AE_loss:1160.8148193359375
target_lab_score:-0.1306, max_nontarget_lab_score:1.0846

iter:500 const:[80.3125]
Loss_Overall:1187.8037, Loss_Attack:0.0000
Loss_L2Dist:9.0935, Loss_L1Dist:26.5365, AE_loss:1176.0565185546875
target_lab_score:10.0619, max_nontarget_lab_score:2.9340

iter:0 const:[78.90625]
Loss_Overall:1327.5865, Loss_Attack:166.4040
Loss_L2Dist:0.0058, Loss_L1Dist:0.1080, AE_loss:1161.1658935546875
target_lab_score:-0.1282, max_nontarget_lab_score:1.0807

iter:500 const:[78.90625]
Loss_Overall:1176.6401, Loss_Attack:0.0000
Loss_L2Dist:8.3147, Loss_L1Dist:24.4263, AE_loss:1165.8828125
target_lab_score:8.1241, max_nontarget_lab_score:4.7113

iter:0 const:[78.203125]
Loss_Overall:1326.0416, Loss_Attack:164.6752
Loss_L2Dist:0.0053, Loss_L1Dist:0.1030, AE_loss:1161.350830078125
target_lab_score:-0.1270, max_nontarget_lab_score:1.0788

iter:500 const:[78.203125]
Loss_Overall:1180.0135, Loss_Attack:0.0000
Loss_L2Dist:9.0324, Loss_L1Dist:26.5381, AE_loss:1168.327392578125
target_lab_score:9.0967, max_nontarget_lab_score:5.0136

print(info_pp)

结果输出：

[INFO]kappa:0.9, Orig class:3, Perturbed class:3, Delta class: 3, Orig prob:[[-11.279339    0.73625    -9.008647   19.396711   -8.286123   14.442826   -1.3170443 -11.587322   -0.992185    1.0182207]], Perturbed prob:[[ -6.0453925   -0.16173983  -6.025815    11.575153    -3.0273986   11.318211     4.259432   -11.328725    -1.0278873   -2.3766122 ]], Delta prob:[[-2.3122752   0.60199463 -0.6148693   4.709517   -2.2623286   1.0073487  -2.2190797  -0.83646446 -1.5357832   0.9802128 ]]

相关负（PN）和相关正（PP）解释图

# rescale values from [-0.5, 0.5] to [0, 255] for plotting
fig0 = (input_image[:,:,0] + 0.5)*255

fig1 = (adv_pn[0,:,:,0] + 0.5) * 255
fig2 = (fig1 - fig0) #rescaled delta_pn
fig3 = (adv_pp[0,:,:,0] + 0.5) * 255
fig4 = (delta_pp[0,:,:,0] + 0.5) * 255 #rescaled delta_pp

f, axarr = plt.subplots(1, 5, figsize=(10,10))
axarr[0].set_title("Original" + "(" + str(mymodel.predict_classes(np.expand_dims(input_image, axis=0))[0]) + ")")
axarr[1].set_title("Original + PN" + "(" + str(mymodel.predict_classes(adv_pn)[0]) + ")")
axarr[2].set_title("PN")
axarr[3].set_title("Original + PP")
axarr[4].set_title("PP" + "(" + str(mymodel.predict_classes(delta_pp)[0]) + ")")

axarr[0].imshow(fig0, cmap="gray")
axarr[1].imshow(fig1, cmap="gray")
axarr[2].imshow(fig2, cmap="gray")
axarr[3].imshow(fig3, cmap="gray")
axarr[4].imshow(fig4, cmap="gray")
plt.show()

结果输出：
在这里插入图片描述
说明：

  • PP突出显示图像中存在的最小像素集，以便将其分类为数字3。注意，原始图像和PP都被分类器分类为数字3。
  • PN在顶部突出显示一条小水平线，该水平线的存在会将原始图像的分类改变为数字5，因此应该不存在，以便分类保持为数字3。

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