{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Função Sigmoid\n", "\n", "A **função Sigmoid** é uma função matemática que tem a característica de uma curva com formato de 'S' ou 'curva sigmoid'. \n", "\n", "Frequentemente, a função sigmoid refere-se ao caso especial de [função logística](https://pt.wikipedia.org/wiki/Fun%C3%A7%C3%A3o_log%C3%ADstica), ela é limitada, diferenciável e real e é definida para todos os valores de entrada reais e tem uma derivada não-negativa em cada ponto. \n", "\n", "Ela é definida pela fórmula:\n", "\n", "\\begin{equation}\n", "\\sigma(x)=\\frac{1}{1+e^{-x}}\n", "\\end{equation}\n", "\n", "Como podemos observar, ela basicamente recebe um número de valor real como entrada e coloca ele entre $0$ e $1$. Seu objetivo é introduzir não-linearidade no espaço de entrada. Baseado na representação matemática acima, um número negativo grande passado pela função sigmoid se torna $0$ e um número positivo grande se torna $1$. \n", "\n", "Por causa desta propriedade, a função sigmoid normalmente tem uma interpretação associada com a taxa de disparo de um neurônio em [Deep Neural Networks](https://www.kdnuggets.com/2020/02/deep-neural-networks.html), onde o não disparo seria dado como $0$, para um disparo completamente saturado em uma frequência máxima assumida, nesse caso seria $1$. Entretanto, é válido lembrar que a função de ativação sigmoid se tornou menos popular nas aplicações de redes neurais por questões técnicas, as funções mais utilizadas atualmente nesse contexto são as funções de Unidade Linear Retificada ([ReLU](https://machinelearningmastery.com/rectified-linear-activation-function-for-deep-learning-neural-networks/)).\n", "\n", "Vamos então importar as bibliotecas necessárias para vermos um exemplo da função sigmoid em ação:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Definimos a função sigmoid:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def sigma(x):\n", " return 1 / (1 + np.exp(-x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Definimos os valores de entrada **X**:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "X = np.linspace(-5, 5, 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculamos os valores de saída **Y**:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "Y = sigma(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotamos o gráfico da função sigmoid:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(16,9))\n", "plt.axis([-5,5, 0,1])\n", "plt.plot(X, Y, linewidth=3, color='b')\n", "plt.xlabel('Eixo X')\n", "plt.ylabel('Eixo Y')\n", "plt.title('Função Sigmoid', fontsize=16)\n", "plt.grid()\n", "plt.text(3.3, 0.85, r'$\\sigma(x)=\\frac{1}{1+e^{-x}}$', fontsize=20)\n", "plt.show()" ] } ], "metadata": { "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": "3.7.10" } }, "nbformat": 4, "nbformat_minor": 4 }