{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Uczenie maszynowe\n", "# 13. Splotowe sieci neuronowe" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Splotowe sieci neuronowe, inaczej konwolucyjne sieci neuronowe (*convolutional neural networks*, CNN, ConvNet)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Konwolucyjne sieci neuronowe wykorzystuje się do:\n", "\n", "* rozpoznawania obrazu\n", "* analizy wideo\n", "* innych zagadnień o podobnej strukturze" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Innymi słowy, CNN przydają się, gdy mamy bardzo dużo danych wejściowych, w których istotne jest ich sąsiedztwo." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Warstwy konwolucyjne" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Dla uproszczenia przyjmijmy, że mamy dane w postaci jednowymiarowej – np. chcemy stwierdzić, czy na danym nagraniu obecny jest głos człowieka." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Nasze nagranie możemy reprezentować jako ciąg $n$ próbek dźwiękowych:\n", "$$(x_0, x_1, \\ldots, x_n)$$\n", "(możemy traktować je jak jednowymiarowe „piksele”)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Najprostsza metoda – „zwykła” jednowarstwowa sieć neuronowa (każdy z każdym) nie poradzi sobie zbyt dobrze w tym przypadku:\n", "\n", "* dużo danych wejściowych\n", "* nie wykrywa własności „lokalnych” wejścia" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Chcielibyśmy wykrywać pewne lokalne „wzory” w danych wejściowych.\n", "\n", "W tym celu tworzymy mniejszą sieć neuronową (mniej neuronów wejściowych) i _kopiujemy_ ją tak, żeby każda jej kopia działała na pewnym fragmencie wejścia (fragmenty mogą nachodzić na siebie)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Warstwę sieci A nazywamy **warstwą konwolucyjną** (konwolucja = splot).\n", "\n", "Warstw konwolucyjnych może być więcej niż jedna." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Tak definiujemy formalnie funckję splotu dla 2 wymiarów:\n", "\n", "$$\n", "\\left[\\begin{array}{ccc}\n", "a & b & c\\\\\n", "d & e & f\\\\\n", "g & h & i\\\\\n", "\\end{array}\\right]\n", "*\n", "\\left[\\begin{array}{ccc}\n", "1 & 2 & 3\\\\\n", "4 & 5 & 6\\\\\n", "7 & 8 & 9\\\\\n", "\\end{array}\\right] \n", "=\\\\\n", "(1 \\cdot a)+(2 \\cdot b)+(3 \\cdot c)+(4 \\cdot d)+(5 \\cdot e)\\\\+(6 \\cdot f)+(7 \\cdot g)+(8 \\cdot h)+(9 \\cdot i)\n", "$$\n", "\n", "Więcej: https://en.wikipedia.org/wiki/Kernel_(image_processing)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Ilustracja działania funkcji splotu:\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Jednostka warstwy konwolucyjnej może się składać z jednej lub kilku warstw neuronów." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Jeden neuron może odpowiadać np. za wykrywanie pionowych krawędzi, drugi poziomych, a jeszcze inny np. krzyżujących się linii." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### _Pooling_" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Obrazy składają się na ogół z milionów pikseli. Oznacza to, że nawet po zastosowaniu kilku warstw konwolucyjnych mielibyśmy sporo parametrów do wytrenowania.\n", "\n", "Żeby zredukować liczbę parametrów, a dzięki temu uprościć obliczenia, stosuje się warstwy ***pooling***.\n", "\n", "*Pooling* to rodzaj próbkowania. Najpopularniejszą jego odmianą jest *max-pooling*, czyli wybieranie najwyższej wartości spośród kilku sąsiadujących pikseli (rys. 13.1)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![Rys. 13.1. Pooling](Max_pooling.png \"Rys. 13.1. Pooling\")\n", "\n", "Rys. 13.1. - źródło: [Aphex34](https://commons.wikimedia.org/wiki/File:Max_pooling.png), [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0), Wikimedia Commons" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Warstwy _pooling_ i konwolucyjne można przeplatać ze sobą (rys. 13.2)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "![Rys. 13.2. CNN](Typical_cnn.png \"Rys. 13.2. CNN\")\n", "\n", "Rys. 13.2. - źródło: [Aphex34](https://commons.wikimedia.org/wiki/File:Typical_cnn.png), [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0), Wikimedia Commons" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "_Pooling_ – idea: nie jest istotne, w którym *dokładnie* miejscu na obrazku dana cecha (krawędź, oko, itp.) się znajduje, wystarczy przybliżona lokalizacja." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Do sieci konwolucujnych możemy dokładać też warstwy ReLU." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "https://www.youtube.com/watch?v=FmpDIaiMIeA" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Zobacz też: https://colah.github.io/posts/2014-07-Conv-Nets-Modular/" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Przykład: MNIST" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import math\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import random\n", "\n", "from IPython.display import YouTubeVideo" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2023-01-27 12:50:47.601029: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA\n", "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n", "2023-01-27 12:50:48.662241: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory\n", "2023-01-27 12:50:48.662268: I tensorflow/compiler/xla/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine.\n", "2023-01-27 12:50:51.653864: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory\n", "2023-01-27 12:50:51.654326: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory\n", "2023-01-27 12:50:51.654341: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.\n" ] } ], "source": [ "import keras\n", "from keras.datasets import mnist\n", "\n", "from keras.models import Sequential\n", "from keras.layers import Dense, Dropout, Flatten\n", "from keras.layers import Conv2D, MaxPooling2D\n", "\n", "# załaduj dane i podziel je na zbiory uczący i testowy\n", "(x_train, y_train), (x_test, y_test) = mnist.load_data()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def draw_examples(examples, captions=None):\n", " plt.figure(figsize=(16, 4))\n", " m = len(examples)\n", " for i, example in enumerate(examples):\n", " plt.subplot(100 + m * 10 + i + 1)\n", " plt.imshow(example, cmap=plt.get_cmap('gray'))\n", " plt.show()\n", " if captions is not None:\n", " print(6 * ' ' + (10 * ' ').join(str(captions[i]) for i in range(m)))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " 5 0 4 1 9 2 1\n" ] } ], "source": [ "draw_examples(x_train[:7], captions=y_train)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "batch_size = 128\n", "num_classes = 10\n", "epochs = 12\n", "\n", "# input image dimensions\n", "img_rows, img_cols = 28, 28" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "if keras.backend.image_data_format() == 'channels_first':\n", " x_train = x_train.reshape(x_train.shape[0], 1, img_rows, img_cols)\n", " x_test = x_test.reshape(x_test.shape[0], 1, img_rows, img_cols)\n", " input_shape = (1, img_rows, img_cols)\n", "else:\n", " x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)\n", " x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)\n", " input_shape = (img_rows, img_cols, 1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x_train shape: (60000, 28, 28, 1)\n", "60000 train samples\n", "10000 test samples\n" ] } ], "source": [ "x_train = x_train.astype('float32')\n", "x_test = x_test.astype('float32')\n", "x_train /= 255\n", "x_test /= 255\n", "print('x_train shape: {}'.format(x_train.shape))\n", "print('{} train samples'.format(x_train.shape[0]))\n", "print('{} test samples'.format(x_test.shape[0]))\n", "\n", "# convert class vectors to binary class matrices\n", "y_train = keras.utils.to_categorical(y_train, num_classes)\n", "y_test = keras.utils.to_categorical(y_test, num_classes)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2023-01-27 12:51:13.294000: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory\n", "2023-01-27 12:51:13.295301: W tensorflow/compiler/xla/stream_executor/cuda/cuda_driver.cc:265] failed call to cuInit: UNKNOWN ERROR (303)\n", "2023-01-27 12:51:13.295539: I tensorflow/compiler/xla/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (ELLIOT): /proc/driver/nvidia/version does not exist\n", "2023-01-27 12:51:13.298310: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 FMA\n", "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n" ] } ], "source": [ "model = Sequential()\n", "model.add(Conv2D(32, kernel_size=(3, 3),\n", " activation='relu',\n", " input_shape=input_shape))\n", "model.add(Conv2D(64, (3, 3), activation='relu'))\n", "model.add(MaxPooling2D(pool_size=(2, 2)))\n", "model.add(Dropout(0.25))\n", "model.add(Flatten())\n", "model.add(Dense(128, activation='relu'))\n", "model.add(Dropout(0.5))\n", "model.add(Dense(num_classes, activation='softmax'))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: \"sequential\"\n", "_________________________________________________________________\n", " Layer (type) Output Shape Param # \n", "=================================================================\n", " conv2d (Conv2D) (None, 26, 26, 32) 320 \n", " \n", " conv2d_1 (Conv2D) (None, 24, 24, 64) 18496 \n", " \n", " max_pooling2d (MaxPooling2D (None, 12, 12, 64) 0 \n", " ) \n", " \n", " dropout (Dropout) (None, 12, 12, 64) 0 \n", " \n", " flatten (Flatten) (None, 9216) 0 \n", " \n", " dense (Dense) (None, 128) 1179776 \n", " \n", " dropout_1 (Dropout) (None, 128) 0 \n", " \n", " dense_1 (Dense) (None, 10) 1290 \n", " \n", "=================================================================\n", "Total params: 1,199,882\n", "Trainable params: 1,199,882\n", "Non-trainable params: 0\n", "_________________________________________________________________\n" ] } ], "source": [ "model.summary()" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "ename": "NameError", "evalue": "name 'model' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn [1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m model\u001b[38;5;241m.\u001b[39mcompile(loss\u001b[38;5;241m=\u001b[39mkeras\u001b[38;5;241m.\u001b[39mlosses\u001b[38;5;241m.\u001b[39mcategorical_crossentropy,\n\u001b[1;32m 2\u001b[0m optimizer\u001b[38;5;241m=\u001b[39mkeras\u001b[38;5;241m.\u001b[39moptimizers\u001b[38;5;241m.\u001b[39mAdadelta(),\n\u001b[1;32m 3\u001b[0m metrics\u001b[38;5;241m=\u001b[39m[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124maccuracy\u001b[39m\u001b[38;5;124m'\u001b[39m])\n", "\u001b[0;31mNameError\u001b[0m: name 'model' is not defined" ] } ], "source": [ "model.compile(loss=keras.losses.categorical_crossentropy,\n", " optimizer=keras.optimizers.Adadelta(),\n", " metrics=['accuracy'])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Train on 60000 samples, validate on 10000 samples\n", "Epoch 1/12\n", "60000/60000 [==============================] - 333s - loss: 0.3256 - acc: 0.9037 - val_loss: 0.0721 - val_acc: 0.9780\n", "Epoch 2/12\n", "60000/60000 [==============================] - 342s - loss: 0.1088 - acc: 0.9683 - val_loss: 0.0501 - val_acc: 0.9835\n", "Epoch 3/12\n", "60000/60000 [==============================] - 366s - loss: 0.0837 - acc: 0.9748 - val_loss: 0.0429 - val_acc: 0.9860\n", "Epoch 4/12\n", "60000/60000 [==============================] - 311s - loss: 0.0694 - acc: 0.9788 - val_loss: 0.0380 - val_acc: 0.9878\n", "Epoch 5/12\n", "60000/60000 [==============================] - 325s - loss: 0.0626 - acc: 0.9815 - val_loss: 0.0334 - val_acc: 0.9886\n", "Epoch 6/12\n", "60000/60000 [==============================] - 262s - loss: 0.0552 - acc: 0.9835 - val_loss: 0.0331 - val_acc: 0.9890\n", "Epoch 7/12\n", "60000/60000 [==============================] - 218s - loss: 0.0494 - acc: 0.9852 - val_loss: 0.0291 - val_acc: 0.9903\n", "Epoch 8/12\n", "60000/60000 [==============================] - 218s - loss: 0.0461 - acc: 0.9859 - val_loss: 0.0294 - val_acc: 0.9902\n", "Epoch 9/12\n", "60000/60000 [==============================] - 219s - loss: 0.0423 - acc: 0.9869 - val_loss: 0.0287 - val_acc: 0.9907\n", "Epoch 10/12\n", "60000/60000 [==============================] - 218s - loss: 0.0418 - acc: 0.9875 - val_loss: 0.0299 - val_acc: 0.9906\n", "Epoch 11/12\n", "60000/60000 [==============================] - 218s - loss: 0.0388 - acc: 0.9879 - val_loss: 0.0304 - val_acc: 0.9905\n", "Epoch 12/12\n", "60000/60000 [==============================] - 218s - loss: 0.0366 - acc: 0.9889 - val_loss: 0.0275 - val_acc: 0.9910\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.fit(x_train, y_train,\n", " batch_size=batch_size,\n", " epochs=epochs,\n", " verbose=1,\n", " validation_data=(x_test, y_test))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "('Test loss:', 0.027530849870144449)\n", "('Test accuracy:', 0.99099999999999999)\n" ] } ], "source": [ "score = model.evaluate(x_test, y_test, verbose=0)\n", "print('Test loss:', score[0])\n", "print('Test accuracy:', score[1])" ] } ], "metadata": { "author": "Paweł Skórzewski", "celltoolbar": "Slideshow", "email": "pawel.skorzewski@amu.edu.pl", "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "lang": "pl", "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" }, "livereveal": { "start_slideshow_at": "selected", "theme": "white" }, "subtitle": "12.Splotowe sieci neuronowe[wykład]", "title": "Uczenie maszynowe", "vscode": { "interpreter": { "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6" } }, "year": "2021" }, "nbformat": 4, "nbformat_minor": 4 }