3D卷积，代码实现
三维卷积：理解+用例-发现
在图像卷积神经网络内核中，包含3D卷积及其在3D MNIST数据集上的实现。
什么是卷积？
从数学上讲，卷积是一种积分函数，表示一个函数g在另一个函数f上移动时的重叠量。
直觉地说，卷积就像一个混合器，将一个函数与另一个函数混合在一起，在保留信息的同时，减少数据空间。
在神经网络和深度学习方面：
卷积是具有可训练参数的滤波器（矩阵/向量），用于从输入数据中提取低维特征。
具有保留输入数据点之间的空间或位置关系的特性。
卷积神经网络增强相邻层神经元之间的局部连接模式，空间局部相关性。
直观地说，卷积是在输入上应用滑动窗口（具有可训练权重的滤波器）的概念，产生（权重和输入的）加权和输出的步骤。加权下一层输入的特征空间。
例如，在人脸识别问题中，前几个卷积层训练输入图像中关键点，下一个卷积层训练边缘和形状，最后一个卷积层训练人脸。在本例中，首先将输入空间缩减为较低维空间（表示关于点/像素的信息），然后将该空间缩减为包含（边/形状）的另一空间，最后缩减对图像中的面进行分类。卷积可以应用于N维。
卷积类型：
让我们来讨论什么是不同类型的卷积
1D Convolutions 一维卷积
最简单的卷积是一维卷积，通常用于序列数据集（也可以用于其它用例）。可用于从输入序列中提取局部一维子序列，并在卷积窗口内识别局部模式。下图显示了如何将一维卷积滤波器应用于序列，获得新特征。一维卷积的其它常见用法见于NLP领域，其中每个句子都表示为一个单词序列。
2D Convolutions 二维卷积
在图像数据集上，CNN结构中主要使用二维卷积滤波器。二维卷积的主要思想，卷积滤波器在两个方向（x，y）上移动，从图像数据中计算低维特征。输出形状也是一个二维矩阵。
3D Convolutions 三维卷积
三维卷积对数据集应用三维过滤器，过滤器向3个方向（x，y，z）移动，计算低层特征表示。输出形状是一个三维体积空间，如立方体或长方体。有助于视频、三维医学图像等的目标物检测。不仅限于三维空间，还可以应用于二维空间输入，如图像。
在3D Mnist数据集上实现3D CNN。首先，导入key数据库。
此外，还有其他类型的卷积：
Dilated Convolutions 膨胀卷积/空洞卷积
扩展或高级卷积定义了内核中值之间的间距。在这种类型的卷积中，由于间距的原因，内核的可接受视图增加，例如，一个3x3内核的膨胀率为2，视野将与5x5内核相同。复杂性保持不变，但在这种情况下会生成不同的特征。
在3D mnist数据集上，创建一个3D卷积神经网络结构。
from keras.layers import Conv3D, MaxPool3D, Flatten, Dense
from keras.layers import Dropout, Input, BatchNormalization
from sklearn.metrics import confusion_matrix, accuracy_score
from plotly.offline import iplot, init_notebook_mode
from keras.losses import categorical_crossentropy
from keras.optimizers import Adadelta
import plotly.graph_objs as go
from matplotlib.pyplot import cm
from keras.models import Model
import numpy as np
import keras
import h5py
init_notebook_mode(connected=True)
%matplotlib inline
使用 TensorFlow backend后端.
3D MNIST数据以.h5格式给出，将完整的数据集加载到训练集和测试集中。
with h5py.File('../input/full_dataset_vectors.h5', 'r') as dataset:
x_train = dataset["X_train"][:]
x_test = dataset["X_test"][:]
y_train = dataset["y_train"][:]
y_test = dataset["y_test"][:]
观察数据集维度：
print ("x_train shape: ", x_train.shape)
print ("y_train shape: ", y_train.shape)
print ("x_test shape: ", x_test.shape)
print ("y_test shape: ", y_test.shape)
x_train shape: (10000, 4096)
y_train shape: (10000,)
x_test shape: (2000, 4096)
y_test shape: (2000,)
这个数据集是一个平面的一维数据，在一个单独的数据文件中共享了原始的x，y，z。在三维空间中绘制一个数字。旋转三维数字，查看效果。
现在，在这个数据集上实现一个三维卷积神经网络。为了使用二维卷积，首先将每个图像转换成三维形状：宽度、高度、通道。通道表示红色、绿色和蓝色层的切片。以类似的方式，将输入数据集转换为4D形状，以便使用三维卷积：长度、宽度、高度、通道（r/g/b）。
## Introduce the channel dimention in the input dataset
xtrain = np.ndarray((x_train.shape[0], 4096, 3))
xtest = np.ndarray((x_test.shape[0], 4096, 3))
## iterate in train and test, add the rgb dimention
def add_rgb_dimention(array):
scaler_map = cm.ScalarMappable(cmap="Oranges")
array = scaler_map.to_rgba(array)[:, : -1]
return array
for i in range(x_train.shape[0]):
xtrain[i] = add_rgb_dimention(x_train[i])
for i in range(x_test.shape[0]):
xtest[i] = add_rgb_dimention(x_test[i])
## convert to 1 + 4D space (1st argument represents number of rows in the dataset)
xtrain = xtrain.reshape(x_train.shape[0], 16, 16, 16, 3)
xtest = xtest.reshape(x_test.shape[0], 16, 16, 16, 3)
## convert target variable into one-hot
y_train = keras.utils.to_categorical(y_train, 10)
y_test = keras.utils.to_categorical(y_test, 10)
y_train.shape
(10000, 10)
Lets create the model architecture. The architecture is described below:
Input and Output layers:
One Input layer with dimentions 16, 16, 16, 3
Output layer with dimentions 10
Convolutions :
Apply 4 Convolutional layer with increasing order of filter size (standard size : 8, 16, 32, 64) and fixed kernel size = (3, 3, 3)
Apply 2 Max Pooling layers, one after 2nd convolutional layer and one after fourth convolutional layer.
MLP architecture:
Batch normalization on convolutiona architecture
Dense layers with 2 layers followed by dropout to avoid overfitting
## input layer
input_layer = Input((16, 16, 16, 3))
## convolutional layers
conv_layer1 = Conv3D(filters=8, kernel_size=(3, 3, 3), activation='relu')(input_layer)
conv_layer2 = Conv3D(filters=16, kernel_size=(3, 3, 3), activation='relu')(conv_layer1)
## add max pooling to obtain the most imformatic features
pooling_layer1 = MaxPool3D(pool_size=(2, 2, 2))(conv_layer2)
conv_layer3 = Conv3D(filters=32, kernel_size=(3, 3, 3), activation='relu')(pooling_layer1)
conv_layer4 = Conv3D(filters=64, kernel_size=(3, 3, 3), activation='relu')(conv_layer3)
pooling_layer2 = MaxPool3D(pool_size=(2, 2, 2))(conv_layer4)
## perform batch normalization on the convolution outputs before feeding it to MLP architecture
pooling_layer2 = BatchNormalization()(pooling_layer2)
flatten_layer = Flatten()(pooling_layer2)
## create an MLP architecture with dense layers : 4096 -> 512 -> 10
## add dropouts to avoid overfitting / perform regularization
dense_layer1 = Dense(units=2048, activation='relu')(flatten_layer)
dense_layer1 = Dropout(0.4)(dense_layer1)
dense_layer2 = Dense(units=512, activation='relu')(dense_layer1)
dense_layer2 = Dropout(0.4)(dense_layer2)
output_layer = Dense(units=10, activation='softmax')(dense_layer2)
## define the model with input layer and output layer
model = Model(inputs=input_layer, outputs=output_layer)
Compile the model and start training.
model.compile(loss=categorical_crossentropy, optimizer=Adadelta(lr=0.1), metrics=['acc'])
model.fit(x=xtrain, y=y_train, batch_size=128, epochs=50, validation_split=0.2)
Train on 8000 samples, validate on 2000 samples
Epoch 1/50
8000/8000 [==============================] - 8s 1ms/step - loss: 2.1643 - acc: 0.2400 - val_loss: 4.1364 - val_acc: 0.1595
Epoch 2/50
8000/8000 [==============================] - 3s 389us/step - loss: 1.7002 - acc: 0.4255 - val_loss: 2.6611 - val_acc: 0.2830
Epoch 3/50
8000/8000 [==============================] - 3s 389us/step - loss: 1.3900 - acc: 0.5319 - val_loss: 1.7843 - val_acc: 0.4425
Epoch 4/50
8000/8000 [==============================] - 3s 390us/step - loss: 1.2224 - acc: 0.5872 - val_loss: 2.4387 - val_acc: 0.3545
Epoch 5/50
8000/8000 [==============================] - 3s 393us/step - loss: 1.1250 - acc: 0.6149 - val_loss: 1.6011 - val_acc: 0.4820
Epoch 6/50
8000/8000 [==============================] - 3s 386us/step - loss: 1.0584 - acc: 0.6379 - val_loss: 1.9631 - val_acc: 0.3940
Epoch 7/50
8000/8000 [==============================] - 3s 385us/step - loss: 1.0012 - acc: 0.6509 - val_loss: 2.7977 - val_acc: 0.3435
Epoch 8/50
8000/8000 [==============================] - 3s 385us/step - loss: 0.9556 - acc: 0.6706 - val_loss: 1.3028 - val_acc: 0.5515
Epoch 9/50
8000/8000 [==============================] - 3s 388us/step - loss: 0.9101 - acc: 0.6893 - val_loss: 1.3699 - val_acc: 0.5525
Epoch 10/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.8759 - acc: 0.7000 - val_loss: 1.5005 - val_acc: 0.5080
Epoch 11/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.8387 - acc: 0.7126 - val_loss: 1.4767 - val_acc: 0.5215
Epoch 12/50
8000/8000 [==============================] - 3s 388us/step - loss: 0.8098 - acc: 0.7246 - val_loss: 1.6518 - val_acc: 0.5250
Epoch 13/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.7806 - acc: 0.7324 - val_loss: 1.2170 - val_acc: 0.5900
Epoch 14/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.7584 - acc: 0.7442 - val_loss: 1.3042 - val_acc: 0.5840
Epoch 15/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.7239 - acc: 0.7542 - val_loss: 1.0767 - val_acc: 0.6480
Epoch 16/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.6997 - acc: 0.7602 - val_loss: 1.1681 - val_acc: 0.6200
Epoch 17/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.6756 - acc: 0.7702 - val_loss: 1.1535 - val_acc: 0.6295
Epoch 18/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.6450 - acc: 0.7759 - val_loss: 1.3781 - val_acc: 0.5975
Epoch 19/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.6229 - acc: 0.7927 - val_loss: 1.2891 - val_acc: 0.6145
Epoch 20/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.6027 - acc: 0.7996 - val_loss: 1.2839 - val_acc: 0.6060
Epoch 21/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.5727 - acc: 0.8088 - val_loss: 1.7544 - val_acc: 0.5350
Epoch 22/50
8000/8000 [==============================] - 3s 387us/step - loss: 0.5555 - acc: 0.8151 - val_loss: 1.3720 - val_acc: 0.5965
Epoch 23/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.5308 - acc: 0.8246 - val_loss: 1.2582 - val_acc: 0.6400
Epoch 24/50
8000/8000 [==============================] - 3s 394us/step - loss: 0.5077 - acc: 0.8286 - val_loss: 1.3886 - val_acc: 0.6085
Epoch 25/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.4869 - acc: 0.8400 - val_loss: 1.2946 - val_acc: 0.6315
Epoch 26/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.4634 - acc: 0.8512 - val_loss: 1.3686 - val_acc: 0.6220
Epoch 27/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.4487 - acc: 0.8529 - val_loss: 1.8458 - val_acc: 0.5635
Epoch 28/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.4297 - acc: 0.8616 - val_loss: 1.7958 - val_acc: 0.5485
Epoch 29/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.4067 - acc: 0.8669 - val_loss: 1.2551 - val_acc: 0.6475
Epoch 30/50
8000/8000 [==============================] - 3s 388us/step - loss: 0.3832 - acc: 0.8762 - val_loss: 1.4216 - val_acc: 0.6190
Epoch 31/50
8000/8000 [==============================] - 3s 388us/step - loss: 0.3730 - acc: 0.8790 - val_loss: 1.3635 - val_acc: 0.6335
Epoch 32/50
8000/8000 [==============================] - 3s 388us/step - loss: 0.3535 - acc: 0.8840 - val_loss: 1.6396 - val_acc: 0.6040
Epoch 33/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.3298 - acc: 0.8970 - val_loss: 1.5481 - val_acc: 0.6355
Epoch 34/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.3281 - acc: 0.8912 - val_loss: 1.7711 - val_acc: 0.5945
Epoch 35/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.3013 - acc: 0.9031 - val_loss: 1.7350 - val_acc: 0.5885
Epoch 36/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.2862 - acc: 0.9096 - val_loss: 2.2285 - val_acc: 0.5195
Epoch 37/50
8000/8000 [==============================] - 3s 392us/step - loss: 0.2735 - acc: 0.9150 - val_loss: 1.8348 - val_acc: 0.5965
Epoch 38/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.2565 - acc: 0.9201 - val_loss: 1.5115 - val_acc: 0.6410
Epoch 39/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.2498 - acc: 0.9205 - val_loss: 1.6900 - val_acc: 0.6300
Epoch 40/50
8000/8000 [==============================] - 3s 387us/step - loss: 0.2228 - acc: 0.9335 - val_loss: 1.6331 - val_acc: 0.6475
Epoch 41/50
8000/8000 [==============================] - 3s 387us/step - loss: 0.2137 - acc: 0.9320 - val_loss: 1.6562 - val_acc: 0.6305
Epoch 42/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.2053 - acc: 0.9399 - val_loss: 1.7376 - val_acc: 0.6190
Epoch 43/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.1885 - acc: 0.9436 - val_loss: 1.8600 - val_acc: 0.6155
Epoch 44/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.1756 - acc: 0.9481 - val_loss: 1.9500 - val_acc: 0.6335
Epoch 45/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.1688 - acc: 0.9496 - val_loss: 2.2368 - val_acc: 0.5805
Epoch 46/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.1582 - acc: 0.9540 - val_loss: 2.0403 - val_acc: 0.6175
Epoch 47/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.1462 - acc: 0.9603 - val_loss: 1.8678 - val_acc: 0.6270
Epoch 48/50
8000/8000 [==============================] - 3s 390us/step - loss: 0.1376 - acc: 0.9624 - val_loss: 2.4479 - val_acc: 0.5640
Epoch 49/50
8000/8000 [==============================] - 3s 391us/step - loss: 0.1304 - acc: 0.9641 - val_loss: 2.5482 - val_acc: 0.5750
Epoch 50/50
8000/8000 [==============================] - 3s 389us/step - loss: 0.1260 - acc: 0.9634 - val_loss: 2.0320 - val_acc: 0.6220
<keras.callbacks.History at 0x7fd2bcb420b8>
在模型训练中，可以观察到验证集的精度是波动的，表明网络可以进一步改进。预测和测量当前模型的准确性
pred = model.predict(xtest)
pred = np.argmax(pred, axis=1)
pred
array([7, 6, 1, ..., 3, 4, 4])
目前，该模型并不精确，但可以通过架构改进和超参数调整，进一步改进。
参考链接：
https://www.kaggle.com/shivamb/3d-convolutions-understanding-use-case?scriptVersionId=9626233