sgd.py

# USAGE
# python gradient_descent.py

# import the necessary packages
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
import numpy as np
import argparse

def sigmoid_activation(x):
	# compute the sigmoid activation value for a given input
	return 1.0 / (1 + np.exp(-x))

def predict(X, W):
	# take the dot product between our features and weight matrix
	preds = sigmoid_activation(X.dot(W))

	# apply a step function to threshold the outputs to binary
	# class labels
	preds[preds <= 0.5] = 0
	preds[preds > 0] = 1

	# return the predictions
	return preds

def next_batch(X,y,batchSize):
	for i in np.arange(0,X.shape[0],batchSize):
		yield(X[i:i+batchSize],y[i:i+batchSize])
	# note: if i+batchSize is out of bounds for X or y it does not crib
	# will only return the balance elements

##def next_batch(X, y, batchSize):
##    # loop over our dataset ‘X‘ in mini-batches, yielding a tuple of
##    # the current batched data and labels
##    for i in np.arange(0, X.shape[0], batchSize):
##		yield (X[i:i + batchSize], y[i:i + batchSize])


# construct the argument parse and parse the arguments
ap = argparse.ArgumentParser()
ap.add_argument("-e", "--epochs", type=float, default=100,
	help="# of epochs")
ap.add_argument("-a", "--alpha", type=float, default=0.01,
	help="learning rate")
ap.add_argument("-b", "--batch-size", type=int, default=32,
	help="Size of SGD mini-batches")
args = vars(ap.parse_args())

# generate a 2-class classification problem with 1,000 data points,
# where each data point is a 2D feature vector
(X, y) = make_blobs(n_samples=1000, n_features=2, centers=2,
	cluster_std=1.5, random_state=1)
y = y.reshape((y.shape[0], 1))

# insert a column of 1's as the last entry in the feature
# matrix -- this little trick allows us to treat the bias
# as a trainable parameter within the weight matrix
X = np.c_[X, np.ones((X.shape[0]))]

# partition the data into training and testing splits using 50% of
# the data for training and the remaining 50% for testing
(trainX, testX, trainY, testY) = train_test_split(X, y,
	test_size=0.5, random_state=42)

# initialize our weight matrix and list of losses
print("[INFO] training...")
W = np.random.randn(X.shape[1], 1)
losses = []

# loop over the desired number of epochs
for epoch in np.arange(0, args["epochs"]):
	# initialize epoch loss
	epochLoss = []

	# loop over data in mini batches
	for (batchX, batchY) in next_batch(X, y, args["batch_size"]):
		preds = sigmoid_activation(batchX.dot(W))

		# now that we have our predictions, we need to determine the
		# `error`, which is the difference between our predictions and
		# the true values
		error = preds - batchY
		epochLoss.append(np.sum(error ** 2))

		# the gradient descent update is the dot product between our
		# features and the error of the predictions
		gradient = batchX.T.dot(error)

		# in the update stage, all we need to do is "nudge" the weight
		# matrix in the negative direction of the gradient (hence the
		# term "gradient descent" by taking a small step towards a set
		# of "more optimal" parameters
		W += -args["alpha"] * gradient
	# update our loss history by taking the average loss across all
	# batches
	loss = np.average(epochLoss)
	losses.append(loss)

	# check to see if an update should be displayed
	if epoch == 0 or (epoch + 1) % 5 == 0:
		print("[INFO] epoch={}, loss={:.7f}".format(int(epoch + 1),
			loss))

# evaluate our model
print("[INFO] evaluating...")
preds = predict(testX, W)
print(classification_report(testY, preds))

# plot the (testing) classification data
plt.style.use("ggplot")
plt.figure()
plt.title("Data")
plt.scatter(testX[:, 0], testX[:, 1], marker="o", c=testY[:,0], s=30)

# construct a figure that plots the loss over time
plt.style.use("ggplot")
plt.figure()
plt.plot(np.arange(0, args["epochs"]), losses)
plt.title("Training Loss")
plt.xlabel("Epoch #")
plt.ylabel("Loss")
plt.show()