freqgen.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Echo State Network as a tunable frequency generator\n",
    "\n",
    "This is a simplified implementation of Herbert Jaeger's task of learning a simple non-autonomous system, [a frequency generator controlled by an external signal](http://www.scholarpedia.org/article/Echo_state_network). Plots at the end.\n",
    "\n",
    "[See the ESN implementation](https://github.com/cknd/pyESN).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "from pyESN import ESN\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Task\n",
    "\n",
    "The network will learn to generate a wave signal whose frequency is determined by some slowly changing control input.\n",
    "\n",
    "#### 1) Generate some sample data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(42)\n",
    "def frequency_generator(N,min_period,max_period,n_changepoints):\n",
    "    \"\"\"returns a random step function with N changepoints\n",
    "       and a sine wave signal that changes its frequency at\n",
    "       each such step, in the limits given by min_ and max_period.\"\"\"\n",
    "    # vector of random indices < N, padded with 0 and N at the ends:\n",
    "    changepoints = np.insert(np.sort(rng.randint(0,N,n_changepoints)),[0,n_changepoints],[0,N])\n",
    "    # list of interval boundaries between which the control sequence should be constant:\n",
    "    const_intervals = list(zip(changepoints,np.roll(changepoints,-1)))[:-1]\n",
    "    # populate a control sequence\n",
    "    frequency_control = np.zeros((N,1))\n",
    "    for (t0,t1) in const_intervals:\n",
    "        frequency_control[t0:t1] = rng.rand()\n",
    "    periods = frequency_control * (max_period - min_period) + max_period\n",
    "    # run time through a sine, while changing the period length\n",
    "    frequency_output = np.zeros((N,1))\n",
    "    z = 0\n",
    "    for i in range(N):\n",
    "        z = z + 2 * np.pi / periods[i]\n",
    "        frequency_output[i] = (np.sin(z) + 1)/2\n",
    "    return np.hstack([np.ones((N,1)),1-frequency_control]),frequency_output\n",
    "\n",
    "\n",
    "N = 15000 # signal length\n",
    "min_period = 2\n",
    "max_period = 10\n",
    "n_changepoints = int(N/200)\n",
    "frequency_control,frequency_output = frequency_generator(N,min_period,max_period,n_changepoints)\n",
    "\n",
    "traintest_cutoff = int(np.ceil(0.7*N))\n",
    "\n",
    "train_ctrl,train_output = frequency_control[:traintest_cutoff],frequency_output[:traintest_cutoff]\n",
    "test_ctrl, test_output  = frequency_control[traintest_cutoff:],frequency_output[traintest_cutoff:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) Instantiate, train & test the network\n",
    "Parameters are mostly the same as in Herbert Jaeger's original Matlab code. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "harvesting states...\n",
      "fitting...\n",
      "training error:\n",
      "0.00367775097729\n",
      "test error:\n",
      "0.390371124559\n"
     ]
    }
   ],
   "source": [
    "esn = ESN(n_inputs = 2,\n",
    "          n_outputs = 1,\n",
    "          n_reservoir = 200,\n",
    "          spectral_radius = 0.25,\n",
    "          sparsity = 0.95,\n",
    "          noise = 0.001,\n",
    "          input_shift = [0,0],\n",
    "          input_scaling = [0.01, 3],\n",
    "          teacher_scaling = 1.12,\n",
    "          teacher_shift = -0.7,\n",
    "          out_activation = np.tanh,\n",
    "          inverse_out_activation = np.arctanh,\n",
    "          random_state = rng,\n",
    "          silent = False)\n",
    "\n",
    "pred_train = esn.fit(train_ctrl,train_output)\n",
    "\n",
    "print(\"test error:\")\n",
    "pred_test = esn.predict(test_ctrl)\n",
    "print(np.sqrt(np.mean((pred_test - test_output)**2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3) Plots\n",
    "First, a look at the control signal, the target signal and the output of the model both during training and during testing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   "source": [
    "window_tr = range(int(len(train_output)/4),int(len(train_output)/4+2000))\n",
    "plt.figure(figsize=(10,1.5))\n",
    "plt.plot(train_ctrl[window_tr,1],label='control')\n",
    "plt.plot(train_output[window_tr],label='target')\n",
    "plt.plot(pred_train[window_tr],label='model')\n",
    "plt.legend(fontsize='x-small')\n",
    "plt.title('training (excerpt)')\n",
    "plt.ylim([-0.1,1.1])\n",
    "\n",
    "window_test = range(2000)\n",
    "plt.figure(figsize=(10,1.5))\n",
    "plt.plot(test_ctrl[window_test,1],label='control')\n",
    "plt.plot(test_output[window_test],label='target')\n",
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   "source": [
    "What we see is that we can't see much, except that the amplitude is systematically too small (any ideas why that is?).\n",
    "\n",
    "So let's look at a few spectrograms to see how the frequency spectrum of these signals changes over time."
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   "cell_type": "code",
   "execution_count": 10,
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "def draw_spectogram(data):\n",
    "    plt.specgram(data,Fs=4,NFFT=256,noverlap=150,cmap=plt.cm.bone,detrend=lambda x:(x-0.5))\n",
    "    plt.gca().autoscale('x')\n",
    "    plt.ylim([0,0.5])\n",
    "    plt.ylabel(\"freq\")\n",
    "    plt.yticks([])\n",
    "    plt.xlabel(\"time\")\n",
    "    plt.xticks([])\n",
    "\n",
    "plt.figure(figsize=(7,1.5))\n",
    "draw_spectogram(train_output.flatten())\n",
    "plt.title(\"training: target\")\n",
    "plt.figure(figsize=(7,1.5))\n",
    "draw_spectogram(pred_train.flatten())\n",
    "plt.title(\"training: model\")\n",
    "\n",
    "plt.figure(figsize=(3,1.5))\n",
    "draw_spectogram(test_output.flatten())\n",
    "plt.title(\"test: target\")\n",
    "plt.figure(figsize=(3,1.5))\n",
    "draw_spectogram(pred_test.flatten())\n",
    "plt.title(\"test: model\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's a frequency generator!"
   ]
  }
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