2021-03-02 08:32:40 +01:00
{
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2021-05-19 07:49:54 +02:00
"## Uczenie maszynowe –
"### Zajęcia laboratoryjne\n",
"# 10. Wprowadzenie do sieci neuronowych"
2021-03-02 08:32:40 +01:00
]
},
{
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"source": [
"Poniżej znajduje się implementacja prostej sieci neuronowej dla problemu klasyfikacji binarnej na przykładzie losowo wygenerowanego zestawu danych.\n",
"\n",
"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",
"$$a^{(i)} = g^{(i)}\\left( a^{(i-1)} \\Theta^{(i)} + \\beta^{(i)} \\right) \\; , $$\n",
"gdzie $g^{(i)}$ to tzw. **funkcje aktywacji**"
]
},
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"source": [
"## Zadanie 10"
]
},
{
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"### 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."
]
},
{
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"### Część zaawansowana (2 punkty)\n",
"\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."
]
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"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"
]
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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"
]
},
{
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