MNIST 上的 PCA 有效，但验证数据的表现非常糟糕

Question

我在 MNIST 上应用了 PCA，降维为 32。然后，为了测试它，我创建了一个简单的分类网络。训练准确率不错：96%，但另一方面，测试准确率是2%。

那怎么了？

import tensorflow as tf
from tensorflow.keras.datasets import mnist
import tensorflow.keras.layers as layers
from tensorflow.keras.models import Sequential
import numpy as np

(x,y),(x2,y2) = mnist.load_data()

y = tf.keras.utils.to_categorical(y)  
y2 = tf.keras.utils.to_categorical(y2)  

def pca(x):
    x = np.reshape(x, (x.shape[0], 784)).astype("float32") / 255.
    mean = x.mean(axis=1)
    #print(mean)
    #print(mean[:,None])
    x -= mean[:,None]
    
    s, u, v = tf.linalg.svd(x)
    s = tf.linalg.diag(s)
    
    k = 32 # DIM_REDUCED
    pca = tf.matmul(u[:,0:k], s[0:k,0:k])
    
    #print(pca)
    #print(pca.shape)
    return pca

x = pca(x)
x2 = pca(x2)

## BUILD A SUPER SIMPLE CLASSIFIC. NET
model = Sequential()
model.add(layers.Dense(32, activation="relu", input_shape=(32,)))
model.add(layers.Dense(16, activation="relu"))
model.add(layers.Dense(10, activation="softmax"))

model.compile(loss = "categorical_crossentropy", optimizer = "adam", metrics = ["acc"])

model.fit(x,y, epochs = 5, verbose = 1, batch_size = 64, validation_data = (x2,y2))

输出：

Epoch 5/5
60000/60000 [==============================] - 1s 23us/sample - loss: 0.1278 - acc: 0.9626 - val_loss: 11.0141 - val_acc: 0.0202

Answer 1

首先，您为每组应用两个不同的“pca”。 train的特征向量和特征值可以与测试集不同。

其次，您正在使用 SVD 获取主成分，但该成分不是您想要的结果。像投影矩阵一样使用主轴来获得更好/压缩的数据表示。

import tensorflow as tf
from tensorflow.keras.datasets import mnist
import tensorflow.keras.layers as layers
from tensorflow.keras.models import Sequential
import numpy as np

(x,y),(x2,y2) = mnist.load_data()

y = tf.keras.utils.to_categorical(y)  
y2 = tf.keras.utils.to_categorical(y2)  

def pca(x):
    x = np.reshape(x, (x.shape[0], 784)).astype("float32") / 255.
    mean = x.mean(axis=0)
    #print(mean)
    #print(mean[:,None])
    x -= mean[None, :]
    
    s, u, v = tf.linalg.svd(x)
    s = tf.linalg.diag(s)
    
    k = 32 # DIM_REDUCED
    projM = v[:, 0:k] #tf.matmul(u[:,0:k], s[0:k,0:k])  
    return mean, projM

def apply_pca(mean, projM, x):
    x = np.reshape(x, (x.shape[0], 784)).astype("float32") / 255.
    #print(mean)
    #print(mean[:,None])
    x -= mean[None, :]

    return tf.matmul(x, projM)
   
mean, projM = pca(x) 

x = apply_pca(mean, projM, x) 
x2 = apply_pca(mean, projM, x2) 

## BUILD A SUPER SIMPLE CLASSIFIC. NET
model = Sequential()
model.add(layers.Dense(32, activation="relu", input_shape=(32,)))
model.add(layers.Dense(16, activation="relu"))
model.add(layers.Dense(10, activation="softmax"))

model.compile(loss = "categorical_crossentropy", optimizer = "adam", metrics = ["acc"])

model.fit(x,y, epochs = 5, verbose = 1, batch_size = 64, validation_data = (x2,y2))