classify_stim.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io as sio\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import iisignature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def shift_stim(stims : pd.Series, shift : int):\n",
    "    # shifts all stimuli by an amount\n",
    "    stims[stims != 0] += shift\n",
    "    return stims"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading data from two exercises for one subject  \n",
    "\n",
    "+ E1 - \"basic movements of the fingers\" \n",
    "\n",
    "+ E2 - \"Isometric, isotonic hand configurations and basic wrist movements\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "      0     1     2    3    4     5     6     7     8     9    10   11    12  \\\n",
       "0 -20.0   7.0 -11.0  2.0 -6.0   1.0  -1.0   3.0  -3.0  -6.0  -1.0  0.0   2.0   \n",
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       "2   8.0  18.0  30.0  6.0  8.0  37.0 -45.0 -12.0  -5.0 -10.0  -2.0  1.0   7.0   \n",
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       "\n",
       "     13    14    15  stimulus  repetition  \n",
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     "execution_count": 6,
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   ],
   "source": [
    "df = pd.DataFrame([])\n",
    "data_paths = ['./signatures_data/s1/S1_E2_A1.mat', './signatures_data/s1/S1_E3_A1.mat']\n",
    "tot_stim = 0\n",
    "for i, data_path in enumerate(data_paths):\n",
    "    mat = sio.loadmat(data_path)\n",
    "    if i == 0:\n",
    "        df = pd.DataFrame(mat['emg'])\n",
    "        df['stimulus'] = mat['restimulus']\n",
    "        df['repetition'] = mat['repetition']\n",
    "    else:\n",
    "        df2 = pd.DataFrame(mat['emg'])\n",
    "        df2['stimulus'] = shift_stim(pd.DataFrame(mat['restimulus']), tot_stim)\n",
    "        df2['repetition'] = mat['repetition']\n",
    "        df = pd.concat([df, df2], ignore_index=True)\n",
    "    tot_stim += len(np.unique(mat['restimulus'])) - 1\n",
    "\n",
    "df.head()\n",
    "    "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Contains 16 sEmg signals: columns 0-7 are spaced around the forearm, 8-15 are 22.5 degrees tilted (both sampled at 200 Hz)\n",
    "\n",
    "41 movements in total are analyzed and each movement is repeated 6 times\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
       "       34, 35, 36, 37, 38, 39, 40], dtype=int8)"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "np.unique(df['stimulus'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6], dtype=int8)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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    "np.unique(df['repetition'])"
   ]
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  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original DB5 paper utilizes repetitions 1, 3, 4, 5 for training classifiers and repetitions 2, 5 for validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_set = [1, 3, 4, 6]\n",
    "test_set = [2, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>963 rows × 18 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0     1     2    3    4    5    6     7     8    9   10   11   12  \\\n",
       "10922   1.0   0.0   4.0  1.0  0.0 -1.0 -1.0  -3.0  -2.0 -2.0  0.0 -1.0 -1.0   \n",
       "10923   0.0   0.0  -1.0  0.0 -1.0 -3.0 -4.0 -24.0  -1.0 -2.0 -2.0 -1.0  0.0   \n",
       "10924   7.0 -16.0  -3.0 -3.0 -1.0 -2.0  3.0  30.0  -1.0 -1.0 -2.0 -1.0 -1.0   \n",
       "10925  -9.0  10.0  -1.0 -2.0 -3.0 -2.0 -3.0 -20.0   2.0 -1.0 -3.0 -1.0  0.0   \n",
       "10926  -2.0   6.0   3.0  2.0  2.0 -1.0  0.0  -5.0   1.0  1.0 -1.0 -1.0 -1.0   \n",
       "...     ...   ...   ...  ...  ...  ...  ...   ...   ...  ...  ...  ...  ...   \n",
       "11880   1.0 -12.0   3.0 -2.0  0.0  0.0  1.0   1.0  10.0  0.0 -1.0  0.0 -1.0   \n",
       "11881  16.0  48.0   4.0  3.0 -1.0  2.0 -2.0  -3.0  -5.0 -2.0  3.0 -1.0  4.0   \n",
       "11882  -4.0  -9.0  -4.0 -1.0 -1.0 -2.0 -2.0  -1.0   3.0 -4.0 -3.0 -1.0  0.0   \n",
       "11883  14.0  -7.0  -1.0 -3.0 -3.0 -1.0  0.0   2.0   0.0 -3.0 -6.0  0.0 -1.0   \n",
       "11884  12.0  20.0  20.0  8.0  4.0  2.0  7.0   1.0   9.0  6.0  8.0 -4.0  1.0   \n",
       "\n",
       "        13   14   15  stimulus  repetition  \n",
       "10922 -1.0 -3.0 -1.0         1           6  \n",
       "10923  1.0 -1.0 -2.0         1           6  \n",
       "10924 -1.0  1.0  0.0         1           6  \n",
       "10925  2.0  3.0  1.0         1           6  \n",
       "10926 -2.0  0.0  0.0         1           6  \n",
       "...    ...  ...  ...       ...         ...  \n",
       "11880  1.0 -3.0 -1.0         1           6  \n",
       "11881  1.0  0.0 -1.0         1           6  \n",
       "11882  1.0 -2.0 -1.0         1           6  \n",
       "11883 -2.0 -1.0  1.0         1           6  \n",
       "11884  0.0 -1.0 -4.0         1           6  \n",
       "\n",
       "[963 rows x 18 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[(df.stimulus==1) & (df.repetition==6)]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The iisignature package handles the signature computations when given a path and specified depth. The library performs the computation on all multi-indices where each multi-index consists of values from $[0, \\ell]$ where $\\ell$ is the level. To verify this, we recreate Example 6 from Chevyrev-Kormilitzin. Let \n",
    "$$X_t = \\{ X_t ^1, X_t ^2\\} = \\{ 3 + t, (3+t)^2\\}, t \\in [0, 5]$$\n",
    "then the signature of the path can be computed up to specified levels and values can be confirmed against equation (1.23). "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The iisignature package handles the signature computations when given a path and a specified depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t1 = np.linspace(0, 5, 10)\n",
    "Xt = np.array([3 + t1, (3 + t1)**2])\n",
    "\n",
    "plt.plot(Xt[0], Xt[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   5.        ,   55.        ,   12.5       ,  158.07613169,\n",
       "        116.92386831, 1512.5       ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iisignature.sig(Xt.T, 2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above computes the signature up to level 2, which involves computing $$\\langle S^1_{0, 5}, S^2_{0,5} S^{1, 1}_{0,5}, S^{1, 2}_{0, 5}, S^{2, 1}_{0, 5}, S^{2, 2}_{0, 5}\\rangle = \\left\\langle 5, 55, \\frac{25}{2}, \\frac{475}{3}, \\frac{350}{3}, \\frac{3025}{2} \\right\\rangle$$ "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The package also computes logsignatures for us to a specified depth."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, we recreate Example 9 from Chevyrev-Kormilitzin.\n",
    "\n",
    "Consider the two-dimensional path \n",
    "\n",
    "$$X : [0, 2] \\mapsto \\R^2, X_t = \\begin{cases} \\{t , 0\\} & \\text{ if } t \\in [0, 1], \\\\ \\{1, t-1 \\} & \\text{ if } t \\in [1, 2] \\end{cases} $$\n",
    "\n",
    "which is the concatenation of two linear paths $Y: [0, 1] \\mapsto \\R^2, Y_t = \\{ t, 0 \\}$ and $Z : [1, 2] \\mapsto \\R^2, Z_t \\mapsto \\{ 0, t-1\\}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_log_signature(path, depth, dims=None):\n",
    "    if dims is None:\n",
    "        dims = path.shape[1] # take second, assumes (timesteps, dims)\n",
    "    s = iisignature.prepare(dims, depth)\n",
    "    return iisignature.logsig(path, s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = np.linspace(0, 1, 10) \n",
    "Yt = np.array([t1, np.zeros_like(t1)])\n",
    "\n",
    "t2 = np.linspace(1, 2, 10) \n",
    "Zt = np.array([np.ones_like(t2), t2 - 1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1, 2, 1) \n",
    "plt.plot(Yt.T)\n",
    "\n",
    "plt.subplot(1, 2, 2) \n",
    "plt.plot(Zt.T)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 0., 0.]), array([0., 1., 0.]))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_log_signature(Yt.T, 2), compute_log_signature(Zt.T, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "At = np.concatenate([Yt.T, Zt.T], axis=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa3416a9050>,\n",
       " <matplotlib.lines.Line2D at 0x7fa295476ed0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(At)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 1. , 0.5])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_log_signature(At, 2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a few utilities for dealing with the Ninapro data: a normalizer, which takes sEMG data and specific repetitions, then centers and scales those repetitions to unit variance as well as the notion of a path, which can be windowed to a specified size and designated overlap between successive windows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from normalizers import normalize\n",
    "\n",
    "\n",
    "class Path():\n",
    "    def __init__(self, vals, reps=range(1, 7), norm_vals=True):\n",
    "        self.vals = vals.reset_index(drop=True, inplace=False)\n",
    "        if norm_vals:\n",
    "            self.vals = normalize(self.vals, reps)\n",
    "\n",
    "class DB5Path(Path):\n",
    "    def __init__(self, vals, exercise, repetition, dims=None):\n",
    "        super().__init__(vals)\n",
    "        self.exercise = exercise\n",
    "        self.repetition = repetition\n",
    "        if dims is None:\n",
    "            self.dims = vals.shape[1] - 2\n",
    "        else:\n",
    "            self.dims = dims\n",
    "    \n",
    "    def naive_padding(self, length) -> np.array:\n",
    "        tempdf = pd.DataFrame(np.random.standard_normal(size = (length, self.dims)))\n",
    "        tempdf['stimulus'] = pd.Series(np.ones(length) * self.exercise)\n",
    "        tempdf['repetition'] = pd.Series(np.ones(length) * self.repetition)\n",
    "        return tempdf\n",
    "    \n",
    "    def get_windows(self, window_size, overlap, use_padding=False) -> np.array:\n",
    "        \"\"\"\n",
    "        returns a list of dataframes\n",
    "        \"\"\"\n",
    "        begin = 0\n",
    "        ans = []\n",
    "        n = len(self.vals)\n",
    "        while(begin < n):\n",
    "            if (begin + window_size < n):\n",
    "                ans.append(self.vals[begin:begin + window_size])\n",
    "            else:\n",
    "                # need to pad it out\n",
    "                if use_padding:\n",
    "                    overflow = (n - begin) % window_size\n",
    "                    ans.append(pd.concat([self.vals[begin:], self.naive_padding(window_size - overflow)], ignore_index=True))\n",
    "                else:\n",
    "                    pass  # other option is to drop the last bit\n",
    "            begin += window_size - overlap\n",
    "        return ans\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "stimulus = 1\n",
    "repetition = 6\n",
    "dbpth = DB5Path(df[(df.stimulus == stimulus) & (df.repetition == repetition)], stimulus, repetition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>stimulus</th>\n",
       "      <th>repetition</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.077548</td>\n",
       "      <td>0.041438</td>\n",
       "      <td>0.467218</td>\n",
       "      <td>0.482313</td>\n",
       "      <td>0.261318</td>\n",
       "      <td>-0.046611</td>\n",
       "      <td>-0.020667</td>\n",
       "      <td>-0.047810</td>\n",
       "      <td>-0.039871</td>\n",
       "      <td>-0.028218</td>\n",
       "      <td>0.069908</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>-0.002053</td>\n",
       "      <td>-0.001418</td>\n",
       "      <td>-0.125506</td>\n",
       "      <td>-0.000705</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.042071</td>\n",
       "      <td>0.041438</td>\n",
       "      <td>-0.013169</td>\n",
       "      <td>0.219159</td>\n",
       "      <td>-0.046322</td>\n",
       "      <td>-0.545344</td>\n",
       "      <td>-0.389227</td>\n",
       "      <td>-0.640613</td>\n",
       "      <td>0.001370</td>\n",
       "      <td>-0.028218</td>\n",
       "      <td>-0.065684</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>0.217669</td>\n",
       "      <td>0.271679</td>\n",
       "      <td>-0.000970</td>\n",
       "      <td>-0.043140</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.290407</td>\n",
       "      <td>-0.633480</td>\n",
       "      <td>-0.205324</td>\n",
       "      <td>-0.570305</td>\n",
       "      <td>-0.046322</td>\n",
       "      <td>-0.295977</td>\n",
       "      <td>0.470746</td>\n",
       "      <td>0.883737</td>\n",
       "      <td>0.001370</td>\n",
       "      <td>0.007027</td>\n",
       "      <td>-0.065684</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>-0.002053</td>\n",
       "      <td>-0.001418</td>\n",
       "      <td>0.123567</td>\n",
       "      <td>0.041730</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.277219</td>\n",
       "      <td>0.463261</td>\n",
       "      <td>-0.013169</td>\n",
       "      <td>-0.307150</td>\n",
       "      <td>-0.661601</td>\n",
       "      <td>-0.295977</td>\n",
       "      <td>-0.266373</td>\n",
       "      <td>-0.527698</td>\n",
       "      <td>0.125096</td>\n",
       "      <td>0.007027</td>\n",
       "      <td>-0.133480</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>0.217669</td>\n",
       "      <td>0.408227</td>\n",
       "      <td>0.248103</td>\n",
       "      <td>0.084164</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.028882</td>\n",
       "      <td>0.294532</td>\n",
       "      <td>0.371140</td>\n",
       "      <td>0.745468</td>\n",
       "      <td>0.876597</td>\n",
       "      <td>-0.046611</td>\n",
       "      <td>0.102186</td>\n",
       "      <td>-0.104267</td>\n",
       "      <td>0.083854</td>\n",
       "      <td>0.077517</td>\n",
       "      <td>0.002112</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>-0.002053</td>\n",
       "      <td>-0.137966</td>\n",
       "      <td>0.061298</td>\n",
       "      <td>0.041730</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6  \\\n",
       "0  0.077548  0.041438  0.467218  0.482313  0.261318 -0.046611 -0.020667   \n",
       "1  0.042071  0.041438 -0.013169  0.219159 -0.046322 -0.545344 -0.389227   \n",
       "2  0.290407 -0.633480 -0.205324 -0.570305 -0.046322 -0.295977  0.470746   \n",
       "3 -0.277219  0.463261 -0.013169 -0.307150 -0.661601 -0.295977 -0.266373   \n",
       "4 -0.028882  0.294532  0.371140  0.745468  0.876597 -0.046611  0.102186   \n",
       "\n",
       "          7         8         9        10        11        12        13  \\\n",
       "0 -0.047810 -0.039871 -0.028218  0.069908 -0.005159 -0.002053 -0.001418   \n",
       "1 -0.640613  0.001370 -0.028218 -0.065684 -0.005159  0.217669  0.271679   \n",
       "2  0.883737  0.001370  0.007027 -0.065684 -0.005159 -0.002053 -0.001418   \n",
       "3 -0.527698  0.125096  0.007027 -0.133480 -0.005159  0.217669  0.408227   \n",
       "4 -0.104267  0.083854  0.077517  0.002112 -0.005159 -0.002053 -0.137966   \n",
       "\n",
       "         14        15  stimulus  repetition  \n",
       "0 -0.125506 -0.000705         1           6  \n",
       "1 -0.000970 -0.043140         1           6  \n",
       "2  0.123567  0.041730         1           6  \n",
       "3  0.248103  0.084164         1           6  \n",
       "4  0.061298  0.041730         1           6  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dbpth.vals.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The specified path consists of 963 time step measurements with 18 columns - 16 for the sEMG data and two additional columns for the number of the exercise and repetition count to confirm that we are extracting the correct values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(963, 18)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dbpth.vals.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "windows = dbpth.get_windows(window_size=200, overlap=100)\n",
    "len(windows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2):\n",
    "    plt.plot(windows[0][i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60   -1.224033\n",
       "61   -0.802209\n",
       "62    3.289479\n",
       "63   -1.308397\n",
       "64    1.053814\n",
       "65   -0.000745\n",
       "66   -0.802209\n",
       "67   -0.127292\n",
       "68   -0.802209\n",
       "69    2.234920\n",
       "70    0.421079\n",
       "71   -0.042927\n",
       "72   -0.549115\n",
       "73   -0.464750\n",
       "74    0.167985\n",
       "75   -3.375333\n",
       "76    3.584755\n",
       "77   -1.139668\n",
       "78    2.192737\n",
       "79   -0.675662\n",
       "Name: 1, dtype: float32"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "windows[0][1][60:80]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "repetitions = [1, 2, 3, 4, 5, 6]\n",
    "stims = [1, 28]\n",
    "train_windows = []\n",
    "test_windows = []\n",
    "for stimulus in stims:\n",
    "    for repetition in repetitions:\n",
    "        dbpth = DB5Path(df[(df.stimulus == stimulus) & (df.repetition == repetition)], stimulus, repetition)\n",
    "        if repetition in train_set:\n",
    "            train_windows += dbpth.get_windows(window_size=200, overlap=100)\n",
    "        elif repetition in test_set:\n",
    "            test_windows += dbpth.get_windows(window_size=200, overlap=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(56, 26)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(train_windows), len(test_windows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def splitxy(dfs : list, x_cols, y_col):\n",
    "    x = []\n",
    "    y = []\n",
    "    for df in dfs:\n",
    "        x.append(df[x_cols].to_numpy())\n",
    "        y.append(df[y_col].to_numpy()[0]) # assume everything is of the same class\n",
    "    return np.array(x), np.array(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x, train_y = splitxy(train_windows, range(16), ['stimulus'])\n",
    "test_x, test_y = splitxy(test_windows, range(16), ['stimulus'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After performing a test-train split, we compute the log signatures on each window to a depth of 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 56/56 [00:00<00:00, 87.59it/s]\n",
      "100%|██████████| 26/26 [00:00<00:00, 82.47it/s]\n"
     ]
    }
   ],
   "source": [
    "train_signatures = []\n",
    "for window in tqdm(train_x):\n",
    "    train_signatures.append(compute_log_signature(window, depth=3))\n",
    "test_signatures = []\n",
    "for window in tqdm(test_x):\n",
    "    test_signatures.append(compute_log_signature(window, depth=3))\n",
    "train_signatures = np.array(train_signatures)\n",
    "test_signatures = np.array(test_signatures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((56, 1496), (26, 1496))"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_signatures.shape, test_signatures.shape"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a SVM since it's not immediately apparent what to do with such high-dimensional data. The human action recognition example used a linear classifier with a dropout layer, which was trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import svm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(pred, true):\n",
    "    assert len(pred) == len(true), \"check lengths match\"\n",
    "    return np.sum((pred == true)) / len(pred)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert accuracy(np.array([1, 1, 1, 2]), np.array([1, 2, 1, 2])) == 0.75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier = svm.LinearSVC()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((56, 200, 16), (56, 1))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_x.shape, train_y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(56, 136) (56, 1)\n",
      "(26, 136) (26, 1)\n"
     ]
    }
   ],
   "source": [
    "print(train_signatures.shape, train_y.shape)\n",
    "print(test_signatures.shape, test_y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alan/.miniconda3/envs/signatures/lib/python3.11/site-packages/sklearn/utils/validation.py:1143: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearSVC()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearSVC</label><div class=\"sk-toggleable__content\"><pre>LinearSVC()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearSVC()"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classifier.fit(train_signatures, train_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = classifier.predict(test_signatures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28,  1,  1,  1,  1,  1,  1,  1,  1, 28, 28, 28,  1,  1,  1, 28, 28,\n",
       "       28,  1,  1,  1,  1, 28, 28, 28, 28], dtype=int8)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, 28, 28, 28, 28,\n",
       "       28, 28, 28, 28, 28, 28, 28, 28, 28], dtype=int8)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_y.reshape(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6153846153846154"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(pred, test_y.reshape(-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix, ConfusionMatrixDisplay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "cm = confusion_matrix(test_y.reshape(-1), pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = fig.add_subplot(111)\n",
    "cm_display = ConfusionMatrixDisplay(cm,\n",
    "                                    display_labels=stims).plot(ax=ax,\n",
    "                                                                       xticks_rotation=\"vertical\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What about the training set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_pred = classifier.predict(train_signatures)\n",
    "accuracy(train_pred, train_y.reshape(-1))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Wait that's kinda interesting. You can get 100% training acc with just a Linear SVC."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we apply PCA as in a dimensionality reduction process. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "from sklearn.manifold import TSNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(82, 2)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(50)\n",
    "sne = TSNE(2)\n",
    "pca_fitted = pca.fit_transform(np.concatenate((train_signatures, test_signatures), axis=0))\n",
    "sne_fitted = sne.fit_transform(pca_fitted)\n",
    "sne_fitted.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = []\n",
    "c2 = []\n",
    "for i, pt in enumerate(sne_fitted):\n",
    "    if i < len(train_signatures):\n",
    "        if train_y[i] == 1:\n",
    "            c1.append(pt)\n",
    "        else:\n",
    "            c2.append(pt)\n",
    "    else:\n",
    "        if test_y[i - len(train_signatures)] == 1:\n",
    "            c1.append(pt)\n",
    "        else:\n",
    "            c2.append(pt)\n",
    "\n",
    "c1 = np.array(c1)\n",
    "c2 = np.array(c2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fa273db8fd0>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(c1[:, 0], c1[:, 1], color='blue')\n",
    "plt.scatter(c2[:, 0], c2[:, 1], color='red')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "wait... that's really impressive. nothing fancy, just dimensionality reduction methods. results are inconsistent though."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "signatures",
   "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": "3.11.0"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "bb9cc3eca2c8231e981fb1e0f6b02032d6d746c99299a8ed51289e761cd494c2"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}