03-08-22 Baseline Experiment SVD.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import LogNorm\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### File Directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_file_name = \"Lohmans SupplementaryData Ligation observation tables.xlsx\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_data_matrix(data_file_name): \n",
    "    dir_path = os.path.dirname(os.path.realpath(\"Data Workflow\"))\n",
    "    # pandas dataframe [this is the matrix right from xlsx file]\n",
    "    df = pd.read_excel(dir_path + \"/\" + data_file_name)\n",
    "    # this is changing the index to TTT or AAA as we would like\n",
    "    df.set_index(df.columns[0], inplace = True)\n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# getting data from the file to a matrix\n",
    "matrix = get_data_matrix(data_file_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           AAA   AAC   AAG   AAT   ACA  ACC  ACG  ACT  AGA  AGC  ...  TCG  \\\n",
      "Overhang                                                         ...        \n",
      "TTT       5294     0    16     7     0    0    0    0   13    0  ...    0   \n",
      "GTT          2  4748     2   588     0   91    0    1    0   37  ...    0   \n",
      "CTT          2     1  4826     2     0    0   39    0    0    0  ...    0   \n",
      "ATT          5    20     9  6179     0    1    0    5    0    0  ...    0   \n",
      "TGT          4     0     0     0  5420    3   74   21    1    0  ...    0   \n",
      "...        ...   ...   ...   ...   ...  ...  ...  ...  ...  ...  ...  ...   \n",
      "ACA          0     0     0     0     0    0    0    0    0    0  ...    0   \n",
      "TAA          0     0     0     0     0    0    0    0    0    0  ...    0   \n",
      "GAA          0     0     0     0     0    2    0    0    0    6  ...    1   \n",
      "CAA          0     0     2     0     0    0    1    0    0    0  ...    1   \n",
      "AAA          0     0     0     0     0    0    0    0    0    0  ...    0   \n",
      "\n",
      "          TCT  TGA  TGC  TGG   TGT  TTA   TTC   TTG   TTT  \n",
      "Overhang                                                   \n",
      "TTT         0    0    0    0     0    0     0     0     0  \n",
      "GTT         0    0    0    0     0    0     0     0     0  \n",
      "CTT         0    0    0    1     0    0     0     2     0  \n",
      "ATT         0    0    0    0     0    0     0     0     0  \n",
      "TGT         0    0    0    0     0    0     0     0     0  \n",
      "...       ...  ...  ...  ...   ...  ...   ...   ...   ...  \n",
      "ACA         0   25  103   30  5420    0     1     0     0  \n",
      "TAA         0    0    0    0     0  788     0     2     3  \n",
      "GAA         0    0    2    0     1    4  6065     3   294  \n",
      "CAA         0    0    0    2     0    2     0  6254     1  \n",
      "AAA         1    0    0    0     4    4    18     4  5294  \n",
      "\n",
      "[64 rows x 64 columns]\n"
     ]
    }
   ],
   "source": [
    "print(matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform SVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f88f17b3450>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "col_seq = matrix.columns\n",
    "row_seq = matrix.index\n",
    "matrix_np = matrix.to_numpy()\n",
    "U, s, VT = np.linalg.svd(matrix_np)\n",
    "\n",
    "plt.semilogy(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us print out the most important features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_svd_char(importance_index):\n",
    "    s = len(importance_index)\n",
    "    fig, ax = plt.subplots(s,1,figsize = (10,6))\n",
    "    plt.xticks(rotation=90)\n",
    "    \n",
    "    # picking up random colors here\n",
    "    c = [\"#\" + ''.join([random.choice('0123456789ABCDEF') for j in range(6)]) for i in range(s)]\n",
    "    \n",
    "    for num in importance_index:\n",
    "        ax[num].bar(row_seq,U[:,num], label = 'Sequence Priority: ' + str(num), alpha = 0.6, color = c[num])\n",
    "        ax[num].set_ylim(-0.6,0.6)\n",
    "        ax[num].set_xticks([])\n",
    "        \n",
    "    ax[-1].set_xticks(range(len(row_seq)))\n",
    "    ax[-1].set_xticklabels(row_seq)\n",
    "    \n",
    "    fig.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# three most import decompositions\n",
    "plot_svd_char([0,1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 5 least important parts\n",
    "plot_svd_char([-1,-2,-3,-4,-5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What I think I have constructed here is an interaction basis. If I take AAA and I want its interaction profile, I would in theory use a reduced representation of it. How good is this interaction basis? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Could this be somehow used to derive the hurestics we talked about before? Maybe the point system can be assigned based on something in the reduced data set? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}