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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Uczenie maszynowe –
"### Zajęcia laboratoryjne\n",
"# 10. Wprowadzenie do sieci neuronowych"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Poniżej znajduje się implementacja prostej sieci neuronowej dla problemu klasyfikacji binarnej na przykładzie losowo wygenerowanego zestawu danych.\n",
"\n",
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"W sieciach jednokierunkowych (ang. *feedforward*) wartości neuronów w $i$-tej warstwie są obliczane na podstawie wartości neuronów warstwy $i-1$. Mając daną $n$-warstwową sieć neuronową oraz jej parametry $\\Theta^{(1)}, \\ldots, \\Theta^{(n)} $ oraz $\\beta^{(1)}, \\ldots, \\beta^{(n)}$ liczymy: \n",
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"$$a^{(i)} = g^{(i)}\\left( a^{(i-1)} \\Theta^{(i)} + \\beta^{(i)} \\right) \\; , $$\n",
"gdzie $g^{(i)}$ to tzw. **funkcje aktywacji**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Zadanie 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Część podstawowa (4 punkty)\n",
"\n",
" * Zaimplementuj funkcję `accuracy()` liczącą skuteczność klasyfikacji.\n",
" * Za jej pomocą oblicz i wypisz końcową skuteczność klasyfikatora.\n",
" * Wypisuj również wartość `accuracy` podczas trenowania (przy okazji wypisywania wartości funkcji kosztu).\n",
" * Zbuduj sieci neuronowe dla różnych wielkości warstwy ukrytej (`dim_hid` = 1, 2, 5, 10, 25). Porównaj skuteczność tych modeli."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"### Część zaawansowana (3 punkty)\n",
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"\n",
"Zastosuj poniższą implementację sieci neuronowej do klasyfikacji binarnej zbioru wygenerowanego za pomocą wybranej funkcji [sklearn.datasets](http://scikit-learn.org/stable/modules/classes.html#samples-generator). Ustal rozmiary warstw wejściowej ($n \\gt 2$) i ukrytej, dobierz odpowiednie parametry sieci (parametr $\\alpha$, liczba epok, wielkość warstwy ukrytej). Podaj skuteczność klasyfikacji."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"from sklearn import datasets\n",
"import matplotlib.pyplot as plt\n",
"\n",
"\n",
"def generate_data():\n",
" # Keep results deterministic\n",
" np.random.seed(1234)\n",
" X, y = datasets.make_moons(200, noise=0.25)\n",
" # X, y = datasets.make_classification(200, 2, 2, 0)\n",
" return X, y\n",
"\n",
"def visualize(X, y, model=None):\n",
" x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
" y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
" h = 0.01\n",
" xx, yy = np.meshgrid(\n",
" np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
" if model:\n",
" Z = predict(model, np.c_[xx.ravel(), yy.ravel()])\n",
" Z = Z.reshape(xx.shape)\n",
" plt.contourf(xx, yy, Z, cmap=plt.cm.viridis)\n",
" plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.viridis)\n",
" plt.show()\n",
"\n",
"def initialize_model(dim_in=2, dim_hid=3, dim_out=2):\n",
" # Keep results deterministic\n",
" np.random.seed(1234)\n",
" W1 = np.random.randn(dim_in, dim_hid) / np.sqrt(dim_in)\n",
" b1 = np.zeros((1, dim_hid))\n",
" W2 = np.random.randn(dim_hid, dim_out) / np.sqrt(dim_hid)\n",
" b2 = np.zeros((1, dim_out))\n",
" return W1, b1, W2, b2\n",
"\n",
"def softmax(X):\n",
" e = np.exp(X)\n",
" return e / np.sum(e, axis=1, keepdims=True)\n",
"\n",
"def predict(model, X):\n",
" W1, b1, W2, b2 = model\n",
" z1 = X.dot(W1) + b1\n",
" a1 = np.tanh(z1)\n",
" z2 = a1.dot(W2) + b2\n",
" probs = softmax(z2)\n",
" return np.argmax(probs, axis=1)\n",
"\n",
"def calculate_cost(model, X, y):\n",
" W1, b1, W2, b2 = model\n",
" z1 = X.dot(W1) + b1\n",
" a1 = np.tanh(z1)\n",
" z2 = a1.dot(W2) + b2\n",
" probs = softmax(z2)\n",
" preds = probs[:, 1]\n",
" return -1. / len(y) * np.sum(\n",
" np.multiply(y, np.log(preds)) + np.multiply(1 - y, np.log(1 - preds)),\n",
" axis=0)\n",
"\n",
"def accuracy(model, X, y):\n",
" # TODO: Napisz funkcję obliczającą skuteczność.\n",
" pass\n",
"\n",
"def train(model, X, y, alpha=0.01, epochs=10000, debug=False):\n",
" W1, b1, W2, b2 = model\n",
" m = len(X)\n",
"\n",
" for i in range(epochs):\n",
" # Forward propagation\n",
" z1 = X.dot(W1) + b1\n",
" a1 = np.tanh(z1)\n",
" z2 = a1.dot(W2) + b2\n",
" probs = softmax(z2)\n",
"\n",
" # Backpropagation\n",
" delta3 = probs\n",
" delta3[range(m), y] -= 1\n",
" dW2 = (a1.T).dot(delta3)\n",
" db2 = np.sum(delta3, axis=0, keepdims=True)\n",
" delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))\n",
" dW1 = np.dot(X.T, delta2)\n",
" db1 = np.sum(delta2, axis=0)\n",
"\n",
" # Parameter update\n",
" W1 -= alpha * dW1\n",
" b1 -= alpha * db1\n",
" W2 -= alpha * dW2\n",
" b2 -= alpha * db2\n",
"\n",
" # Print loss\n",
" if debug and i % 1000 == 0:\n",
" model = (W1, b1, W2, b2)\n",
" print(\"Cost after iteration {}: {:.4f}\".format(i, calculate_cost(\n",
" model, X, y)))\n",
" # TODO: Wypisz skuteczność (accuracy) klasyfikacji w tym miejscu\n",
"\n",
" return W1, b1, W2, b2"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X, y = generate_data()\n",
"visualize(X, y)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost after iteration 0: 0.4692\n",
"Cost after iteration 1000: 0.1527\n",
"Cost after iteration 2000: 0.1494\n",
"Cost after iteration 3000: 0.1478\n",
"Cost after iteration 4000: 0.1458\n",
"Cost after iteration 5000: 0.1444\n",
"Cost after iteration 6000: 0.1433\n",
"Cost after iteration 7000: 0.1423\n",
"Cost after iteration 8000: 0.1415\n",
"Cost after iteration 9000: 0.1407\n"
]
},
{
"data": {
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"image/png": "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
2021-03-02 08:32:40 +01:00
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"model = train(initialize_model(dim_hid=5), X, y, debug=True)\n",
"visualize(X, y, model)"
]
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},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
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}
],
"metadata": {
"hide_input": false,
"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": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
