curtisallen · August 14, 2013 20:43
diff --git a/HyperbolicTangent.ipynb b/HyperbolicTangent.ipynb
 {
 "metadata": {
  "name": "Hyperbolic tangent tanh"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "[How to represent an unbounded variable as number between 0 and 1](http://stats.stackexchange.com/a/1113)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%load_ext rmagic \n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "A very common trick to do so (e.g., in connectionist modeling) is to use the [hyperbolic tangent tanh](http://en.wikipedia.org/wiki/Tanh) as the 'squashing function\". It automatically fits all numbers into the interval between -1 and 1. Which in your case restricts the range from 0 to 1. In r and matlab you get it via tanh().\n\nAnother squashing function is the logistic function (thanks to Simon for the name), provided by f(x)=1/(1+e\u2212x), which restricts the range from 0 to 1 (with 0 mapped to .5). So you would have to multiply the result by 2 and subtract 1 to fit your data into the interval between 0 and 1.\n\nHere is some simple R code which plots both functions (tanh in red, logistic in blue) so you can see how both squash:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%%R\nx <- seq(0,20,0.001)\nplot(x,tanh(x),pch=\".\", col=\"red\", ylab=\"y\")\npoints(x,(1 / (1 + exp(-x)))*2-1, pch=\".\",col=\"blue\")",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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nnFF3XqcnugWp08K2T4AAgeIJJBnAIxk3btwYBw4ciPXr14+cXPf96aef3vAD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\njwzPzfbnt7/97XHhhRfGpZd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      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
 }
	{
	"metadata": {
	"name": "Hyperbolic tangent tanh"
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": "[How to represent an unbounded variable as number between 0 and 1](http://stats.stackexchange.com/a/1113)"
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "%load_ext rmagic \n",
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 6
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": "A very common trick to do so (e.g., in connectionist modeling) is to use the [hyperbolic tangent tanh](http://en.wikipedia.org/wiki/Tanh) as the 'squashing function\". It automatically fits all numbers into the interval between -1 and 1. Which in your case restricts the range from 0 to 1. In r and matlab you get it via tanh().\n\nAnother squashing function is the logistic function (thanks to Simon for the name), provided by f(x)=1/(1+e\u2212x), which restricts the range from 0 to 1 (with 0 mapped to .5). So you would have to multiply the result by 2 and subtract 1 to fit your data into the interval between 0 and 1.\n\nHere is some simple R code which plots both functions (tanh in red, logistic in blue) so you can see how both squash:"
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "%%R\nx <- seq(0,20,0.001)\nplot(x,tanh(x),pch=\".\", col=\"red\", ylab=\"y\")\npoints(x,(1 / (1 + exp(-x)))*2-1, pch=\".\",col=\"blue\")",
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "display_data",
	"png": 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nnFF3XqcnugWp08K2T4AAgeIJJBnAIxk3btwYBw4ciPXr14+cXPf96aef3vAD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\njwzPzfbnt7/97XHhhRfGpZd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	}
	],
	"prompt_number": 7
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "",
	"language": "python",
	"metadata": {},
	"outputs": []
	}
	],
	"metadata": {}
	}
	]
	}
No results found