使用自动编码器重建潜在空间

Question

import numpy as np
import numpy.matlib
import numpy as np
import pandas as pd
from keras.layers import Input, Dense
from keras.models import Model
from keras.optimizers import RMSprop
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import MinMaxScaler

sgx=np.random.randn(25200, 100)
normx = MinMaxScaler().fit(sgx)
sgxx=normx.fit_transform(sgx)

encoding_dim = 32
input_img = Input(shape=(100,))
encoded = Dense(80, activation='relu')(input_img)
encoded = Dense(64, activation='relu')(encoded)
encoded = Dense(32, activation='relu')(encoded)
decoded = Dense(64, activation='relu')(encoded)
decoded = Dense(90, activation='relu')(decoded)
decoded = Dense(100, activation='sigmoid')(decoded)

autoencoder = Model(input_img, decoded)
autoencoder.compile(loss='mean_squared_error', optimizer = RMSprop())
# this model maps an input to its encoded representation
encoder = Model(input_img, encoded)
# create the decoder model
encoded_input = Input(shape=(encoding_dim,))
deco = autoencoder.layers[-3](encoded_input)
deco = autoencoder.layers[-2](deco)
deco = autoencoder.layers[-1](deco)
decoder = Model(encoded_input, deco)
autoencoder.fit(sgxx, sgxx,
                epochs=100,
                batch_size=560)

encoded_imgs = encoder.predict(sgx)
decoded_imgs = decoder.predict(encoded_imgs)

in the code above, I reconstructed same initial dimension, can we use AE to reconstruct a lower dimension from initial one, I mean for ex in my case I have 100 dimensions, then after reducing the dimension I would like reconstruct only 30??

Answer 1

From the way your question is stated no , but I think there is just a miss understanding.

A typical way of training an auto-encoder is using reconstruction error. This is defined simply as ||x - f(g(x))|| where g is your encoder network, f is your decoder network and x is some input example. According to this particular loss f(g(x)) must have the same dimension as x (100 in your case).

You need to think about what it means to reconstruct something with a decoder, what exactly are you wanting to produce that has dimension 30? To rephrase your question, can we create a representation of x that has 30 dimensions? Answer: Yes! This is what auto-encoders are often used for, the encoder can take a 100 dimensional input and reduce its dimension to 30. To get this representation, (which in the code given above will be 32 dimensional) simply run x through g (your encoder) and stop. If the goal is only to construct this representation, the decoder is only used for training.

I hope this clarifies things!