(10000, 10)\n"
]
}
],
"source": [
"print(type(mnist.test.images), mnist.test.images.shape)\n",
"print(type(mnist.test.labels), mnist.test.labels.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Simple Neural Network Model (No Hidden Layer)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1) Tensor Operation and Shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Input Layer to Output Layer\n",
" - $i=1...784$\n",
" - $j=1...10$\n",
"$$ u_j = \\sum_i W_{ji} x_i + b_j $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Presentation of Matrix and Vector\n",
" - Shape of ${\\bf W}: (10, 784)$\n",
" - Shape of ${\\bf x}: (784, 1)$\n",
" - Shape of ${\\bf b}: (10,)$\n",
" - Shape of ${\\bf u}: (10,)$\n",
"$$ {\\bf u} = {\\bf Wx + b} $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- **Transposed Matrix** Operation in Tensorflow\n",
" - Shape of ${\\bf W}: (784, 10)$\n",
" - Shape of ${\\bf x}: (1, 784)$\n",
" - Shape of ${\\bf b}: (10,)$\n",
" - Shape of ${\\bf u}: (10,)$\n",
"$$ {\\bf u} = {\\bf xW + b} $$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Small Sized Example"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2, 3) (1, 2) (1, 3)\n",
"[[ 9 12 15]]\n",
"\n",
"(3,) (1, 3)\n",
"[[19 32 45]]\n"
]
}
],
"source": [
"W_ = np.array([[1, 2, 3], [4, 5, 6]]) #shape of W: (2, 3)\n",
"x_ = np.array([[1, 2]]) #shape of x: (1, 2)\n",
"xW_ = np.dot(x_, W_) #shape of xW: (1, 3)\n",
"print(W_.shape, x_.shape, xW_.shape)\n",
"print(xW_)\n",
"\n",
"print()\n",
"\n",
"b_ = np.array([10, 20, 30]) #shape of b: (3,)\n",
"u_ = xW_ + b_ #shape of u: (1, 3) \n",
"print(b_.shape, u_.shape)\n",
"print(u_)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2) Mini Batch"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(100, 784)\n",
"(100, 10)\n"
]
}
],
"source": [
"batch_images, batch_labels = mnist.train.next_batch(100)\n",
"print(batch_images.shape)\n",
"#print batch_images\n",
"print\n",
"\n",
"print(batch_labels.shape)\n",
"#print batch_labels"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Mini Batch (ex. batch size = 100) \n",
" - Shape of ${\\bf W}: (784, 10)$\n",
" - Shape of ${\\bf x}: (100, 784)$\n",
" - Shape of ${\\bf b}: (10,)$\n",
" - Shape of ${\\bf u}: (100, 10)$\n",
"$$ {\\bf U} = {\\bf XW + B} $$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Small Sized Example"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(2, 3) (5, 2) (5, 3)\n",
"[[ 9 12 15]\n",
" [ 9 12 15]\n",
" [ 9 12 15]\n",
" [ 9 12 15]\n",
" [ 9 12 15]]\n",
"\n",
"(3,) (5, 3)\n",
"[[19 32 45]\n",
" [19 32 45]\n",
" [19 32 45]\n",
" [19 32 45]\n",
" [19 32 45]]\n"
]
}
],
"source": [
"W_ = np.array([[1, 2, 3], [4, 5, 6]]) #shape of W: (2, 3)\n",
"x_ = np.array([[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) #shape of x: (5, 2)\n",
"xW_ = np.dot(x_, W_) #shape of xW: (5, 3)\n",
"print(W_.shape, x_.shape, xW_.shape)\n",
"print(xW_)\n",
"\n",
"print()\n",
"\n",
"b_ = np.array([10, 20, 30]) #shape of b: (3,)\n",
"u_ = xW_ + b_ #shape of u: (1, 3) \n",
"print(b_.shape, u_.shape)\n",
"print(u_)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3) Model Construction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- The placeholder to store the training data:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x - (?, 784)\n"
]
}
],
"source": [
"x = tf.placeholder(tf.float32, [None, 784])\n",
"print(\"x -\", x.get_shape())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- The placeholder to store the correct answers (ground truth):"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y_target = tf.placeholder(tf.float32, [None, 10])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- A single (output) layer neural network model"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"W - (784, 10)\n",
"b - (10,)\n"
]
}
],
"source": [
"weight_init_std = 0.01\n",
"W = tf.Variable(weight_init_std * tf.random_normal([784, 10]))\n",
"b = tf.Variable(tf.zeros([10]))\n",
"print(\"W -\", W.get_shape())\n",
"print(\"b -\", b.get_shape())"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"u - (?, 10)\n"
]
}
],
"source": [
"u = tf.matmul(x, W) + b\n",
"print(\"u -\", u.get_shape())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4) Target Setup"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- softmax\n",
"\n",
"$$ {\\bf z} = softmax({\\bf u}) $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Error functions: Cross entropy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Suppose you have two tensors, where $u$ contains computed scores for each class (for example, from $u = W*x + b$) and $y_target$ contains one-hot encoded true labels.\n",
"\n",
"\n",
"u = ... # Predicted label, e.g. $u = tf.matmul(X, W) + b\n",
"y_target = ... # True label, one-hot encoded\n",
"\n",
"\n",
"- We call $u$ **logits** (if you interpret the scores in u as unnormalized log probabilities).\n",
"\n",
"- Additionally, the total cross-entropy loss computed in this manner:\n",
"\n",
"\n",
"z = tf.nn.softmax(u)\n",
"total_loss = tf.reduce_mean(-tf.reduce_sum(y_target * tf.log(z), [1]))\n",
"\n",
"\n",
"- is essentially equivalent to the total cross-entropy loss computed with the function softmax_cross_entropy_with_logits():\n",
"\n",
"\n",
"total_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=u, labels=y_target))\n",
""
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"learning_rate = 0.1\n",
"error = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=u, labels=y_target))\n",
"optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(error)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Learning (Training) & Evaluation"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total batch: 550\n",
"Epoch: 0, Train Error: 2.30572, Validation Error: 2.30698, Test Accuracy: 0.12840\n",
"Epoch: 1, Train Error: 0.39198, Validation Error: 0.37061, Test Accuracy: 0.90180\n",
"Epoch: 2, Train Error: 0.34676, Validation Error: 0.32587, Test Accuracy: 0.90890\n",
"Epoch: 3, Train Error: 0.32534, Validation Error: 0.30698, Test Accuracy: 0.91660\n",
"Epoch: 4, Train Error: 0.31445, Validation Error: 0.29831, Test Accuracy: 0.91660\n",
"Epoch: 5, Train Error: 0.30418, Validation Error: 0.28912, Test Accuracy: 0.91790\n",
"Epoch: 6, Train Error: 0.29866, Validation Error: 0.28601, Test Accuracy: 0.91850\n",
"Epoch: 7, Train Error: 0.29390, Validation Error: 0.28150, Test Accuracy: 0.91900\n",
"Epoch: 8, Train Error: 0.29029, Validation Error: 0.27967, Test Accuracy: 0.91980\n",
"Epoch: 9, Train Error: 0.28661, Validation Error: 0.27622, Test Accuracy: 0.92200\n",
"Epoch: 10, Train Error: 0.28457, Validation Error: 0.27407, Test Accuracy: 0.92190\n",
"Epoch: 11, Train Error: 0.28074, Validation Error: 0.27155, Test Accuracy: 0.92230\n",
"Epoch: 12, Train Error: 0.27949, Validation Error: 0.27210, Test Accuracy: 0.92440\n",
"Epoch: 13, Train Error: 0.27634, Validation Error: 0.26903, Test Accuracy: 0.92230\n",
"Epoch: 14, Train Error: 0.27572, Validation Error: 0.26896, Test Accuracy: 0.92290\n",
"Epoch: 15, Train Error: 0.27364, Validation Error: 0.26740, Test Accuracy: 0.92340\n",
"Epoch: 16, Train Error: 0.27223, Validation Error: 0.26725, Test Accuracy: 0.92270\n",
"Epoch: 17, Train Error: 0.27102, Validation Error: 0.26595, Test Accuracy: 0.92290\n",
"Epoch: 18, Train Error: 0.27071, Validation Error: 0.26719, Test Accuracy: 0.92330\n",
"Epoch: 19, Train Error: 0.26938, Validation Error: 0.26507, Test Accuracy: 0.92190\n",
"Epoch: 20, Train Error: 0.26838, Validation Error: 0.26431, Test Accuracy: 0.92210\n",
"Epoch: 21, Train Error: 0.26776, Validation Error: 0.26610, Test Accuracy: 0.92200\n",
"Epoch: 22, Train Error: 0.26633, Validation Error: 0.26555, Test Accuracy: 0.92400\n",
"Epoch: 23, Train Error: 0.26622, Validation Error: 0.26398, Test Accuracy: 0.92470\n",
"Epoch: 24, Train Error: 0.26345, Validation Error: 0.26242, Test Accuracy: 0.92270\n",
"Epoch: 25, Train Error: 0.26297, Validation Error: 0.26230, Test Accuracy: 0.92380\n",
"Epoch: 26, Train Error: 0.26315, Validation Error: 0.26254, Test Accuracy: 0.92380\n",
"Epoch: 27, Train Error: 0.26165, Validation Error: 0.26105, Test Accuracy: 0.92450\n",
"Epoch: 28, Train Error: 0.26111, Validation Error: 0.26239, Test Accuracy: 0.92470\n",
"Epoch: 29, Train Error: 0.25995, Validation Error: 0.26142, Test Accuracy: 0.92350\n",
"Epoch: 30, Train Error: 0.25970, Validation Error: 0.26080, Test Accuracy: 0.92450\n",
"Epoch: 31, Train Error: 0.25900, Validation Error: 0.26151, Test Accuracy: 0.92420\n",
"Epoch: 32, Train Error: 0.26040, Validation Error: 0.26189, Test Accuracy: 0.92400\n",
"Epoch: 33, Train Error: 0.25777, Validation Error: 0.25990, Test Accuracy: 0.92350\n",
"Epoch: 34, Train Error: 0.25738, Validation Error: 0.26107, Test Accuracy: 0.92430\n",
"Epoch: 35, Train Error: 0.25743, Validation Error: 0.26133, Test Accuracy: 0.92400\n",
"Epoch: 36, Train Error: 0.25644, Validation Error: 0.26034, Test Accuracy: 0.92460\n",
"Epoch: 37, Train Error: 0.25596, Validation Error: 0.26001, Test Accuracy: 0.92440\n",
"Epoch: 38, Train Error: 0.25591, Validation Error: 0.26088, Test Accuracy: 0.92520\n",
"Epoch: 39, Train Error: 0.25558, Validation Error: 0.26054, Test Accuracy: 0.92540\n",
"Epoch: 40, Train Error: 0.25539, Validation Error: 0.26121, Test Accuracy: 0.92550\n",
"Epoch: 41, Train Error: 0.25400, Validation Error: 0.25911, Test Accuracy: 0.92520\n",
"Epoch: 42, Train Error: 0.25396, Validation Error: 0.25937, Test Accuracy: 0.92360\n",
"Epoch: 43, Train Error: 0.25311, Validation Error: 0.25945, Test Accuracy: 0.92460\n",
"Epoch: 44, Train Error: 0.25310, Validation Error: 0.25960, Test Accuracy: 0.92520\n",
"Epoch: 45, Train Error: 0.25337, Validation Error: 0.26013, Test Accuracy: 0.92450\n",
"Epoch: 46, Train Error: 0.25380, Validation Error: 0.26053, Test Accuracy: 0.92570\n",
"Epoch: 47, Train Error: 0.25286, Validation Error: 0.25917, Test Accuracy: 0.92560\n",
"Epoch: 48, Train Error: 0.25228, Validation Error: 0.26081, Test Accuracy: 0.92410\n",
"Epoch: 49, Train Error: 0.25221, Validation Error: 0.26051, Test Accuracy: 0.92410\n"
]
}
],
"source": [
"prediction_and_ground_truth = tf.equal(tf.argmax(u, 1), tf.argmax(y_target, 1))\n",
"accuracy = tf.reduce_mean(tf.cast(prediction_and_ground_truth, tf.float32))\n",
"with tf.Session() as sess:\n",
" init = tf.global_variables_initializer()\n",
" sess.run(init)\n",
" \n",
" batch_size = 100\n",
" total_batch = int(math.ceil(mnist.train.num_examples/float(batch_size)))\n",
" print(\"Total batch: %d\" % total_batch) \n",
"\n",
" training_epochs = 50\n",
" epoch_list = []\n",
" train_error_list = []\n",
" validation_error_list = []\n",
" test_accuracy_list = []\n",
" for epoch in range(training_epochs):\n",
" epoch_list.append(epoch)\n",
" # Train Error Value\n",
" train_error_value = sess.run(error, feed_dict={x: mnist.train.images, y_target: mnist.train.labels})\n",
" train_error_list.append(train_error_value)\n",
" \n",
" validation_error_value = sess.run(error, feed_dict={x: mnist.validation.images, y_target: mnist.validation.labels})\n",
" validation_error_list.append(validation_error_value)\n",
" \n",
" test_accuracy_value = sess.run(accuracy, feed_dict={x: mnist.test.images, y_target: mnist.test.labels})\n",
" test_accuracy_list.append(test_accuracy_value) \n",
" print(\"Epoch: {0:2d}, Train Error: {1:0.5f}, Validation Error: {2:0.5f}, Test Accuracy: {3:0.5f}\".format(epoch, train_error_value, validation_error_value, test_accuracy_value))\n",
" \n",
" for i in range(total_batch):\n",
" batch_images, batch_labels = mnist.train.next_batch(batch_size)\n",
" sess.run(optimizer, feed_dict={x: batch_images, y_target: batch_labels})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. Analysis with Graph"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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W7SvASncfDlQCPzazosj5se5+rrtXtETMIiIi0j6oyJStAQOCV90yJyIirUyvXr0YPXo0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\nWIkI8+qjw6OJCo8iKhB10DI6PLp0PT4mnqZRTWs82XYJlwBe0mntnrW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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3 8 5 ..., 8 8 8]\n",
"[7 2 1 ..., 4 5 6]\n",
"Number of False Prediction: 8971\n",
"False Prediction Index: 0, Prediction: 3, Ground Truth: 7\n",
"False Prediction Index: 1, Prediction: 8, Ground Truth: 2\n",
"False Prediction Index: 2, Prediction: 5, Ground Truth: 1\n",
"False Prediction Index: 3, Prediction: 8, Ground Truth: 0\n",
"False Prediction Index: 4, Prediction: 0, Ground Truth: 4\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Draw Graph about Error Values & Accuracy Values\n",
"def draw_error_values_and_accuracy(epoch_list, train_error_list, validation_error_list, test_accuracy_list):\n",
" # Draw Error Values and Accuracy\n",
" fig = plt.figure(figsize=(20, 5))\n",
" plt.subplot(121)\n",
" plt.plot(epoch_list[1:], train_error_list[1:], 'r', label='Train')\n",
" plt.plot(epoch_list[1:], validation_error_list[1:], 'g', label='Validation')\n",
" plt.ylabel('Total Error')\n",
" plt.xlabel('Epochs')\n",
" plt.grid(True)\n",
" plt.legend(loc='upper right')\n",
"\n",
" plt.subplot(122)\n",
" plt.plot(epoch_list[1:], test_accuracy_list[1:], 'b', label='Test')\n",
" plt.ylabel('Accuracy')\n",
" plt.xlabel('Epochs')\n",
" plt.yticks(np.arange(0.0, 1.0, 0.05))\n",
" plt.grid(True)\n",
" plt.legend(loc='lower right')\n",
" plt.show()\n",
"\n",
"draw_error_values_and_accuracy(epoch_list, train_error_list, validation_error_list, test_accuracy_list)\n",
" \n",
"def draw_false_prediction(diff_index_list):\n",
" fig = plt.figure(figsize=(20, 5))\n",
" for i in range(5):\n",
" j = diff_index_list[i]\n",
" print(\"False Prediction Index: %s, Prediction: %s, Ground Truth: %s\" % (j, prediction[j], ground_truth[j]))\n",
" img = np.array(mnist.test.images[j])\n",
" img.shape = (28, 28)\n",
" plt.subplot(150 + (i+1))\n",
" plt.imshow(img, cmap='gray')\n",
" \n",
"with tf.Session() as sess: \n",
" init = tf.global_variables_initializer()\n",
" sess.run(init)\n",
" # False Prediction Profile\n",
" prediction = sess.run(tf.argmax(u, 1), feed_dict={x:mnist.test.images})\n",
" ground_truth = sess.run(tf.argmax(y_target, 1), feed_dict={y_target:mnist.test.labels})\n",
"\n",
" print(prediction)\n",
" print(ground_truth)\n",
"\n",
" diff_index_list = []\n",
" for i in range(mnist.test.num_examples):\n",
" if (prediction[i] != ground_truth[i]):\n",
" diff_index_list.append(i)\n",
" \n",
" print(\"Number of False Prediction:\", len(diff_index_list))\n",
" draw_false_prediction(diff_index_list)"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
![](\"https://www.tensorflow.org/versions/r0.11/images/MNIST-Matrix.png\")
\n",
"\n",
"- flatten 1-D tensor of size 28x28 = 784.\n",
" - Each entry in the tensor is a pixel intensity between 0 and 1, for a particular pixel in a particular image.\n",
"$$[0, 0, 0, ..., 0.6, 0.7, 0.7, 0.5, ... 0.8, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9, 0.3, ..., 0.4, 0.4, 0.4, ... 0, 0, 0]$$ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1) Training Data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"![](\"https://www.tensorflow.org/versions/r0.11/images/mnist-train-xs.png\")
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- A one-hot vector is a vector which is 0 in most entries, and 1 in a single entry.\n",
"- In this case, the $n$th digit will be represented as a vector which is 1 in the nth entry. \n",
" - For example, 3 would be $[0,0,0,1,0,0,0,0,0,0]$. \n",
"- **mnist.train.labels** is a tensor with a shape of [55000, 10]. \n",
"![](\"https://www.tensorflow.org/versions/r0.11/images/mnist-train-ys.png\")
"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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