isim_sigma_RR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# iSIM - sigma\n",
    "\n",
    "## Notebook contents:\n",
    "- Generation of random fingerprints\n",
    "- Testing of RR standard deviation approximation on random fingerprints\n",
    "- Testing of RR standard deviation on fingerprints from real molecules\n",
    "- Testing of the exact RR standard deviation calculation\n",
    "\n",
    "Miranda-Quintana Group\n",
    "University of Florida\n",
    "\n",
    "Kenneth Lopez Perez"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generation of random fingerprints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Generation of 1000 random binary fingerprints\n",
    "np.random.seed(72)\n",
    "random_fp =  np.random.randint(0, 2, (1000, 2048))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing of the RR standard deviation approximation\n",
    "\n",
    "With the iSIM module it was possible to calculate the average pairwise similarity without doing all the possible pairs, only the columnwise sum was required. If we follow a similar approach we could get the approximation of the standard deviation of the similarities just with the columnwise sum. \n",
    "\n",
    "Russell-Rao is defined by:\n",
    "\n",
    "$$\n",
    "RR = \\frac{a}{p}\n",
    "$$\n",
    "\n",
    "where a corresponds to the number of one-one matches between fingerprints and p to the total of comparisons. \n",
    "\n",
    "With the columnwise vector, we can get the number of one-one coincidences for each column. Let the columwise sum vector be:\n",
    "\n",
    "$$\n",
    "column \\ sum = [k_1, k_2, ..., k_m]\n",
    "$$\n",
    "\n",
    "for fingerprints of length m. \n",
    "\n",
    "Then the number of one-one coincidences per column will be equal to:\n",
    "\n",
    "$$\n",
    "a_i = \\frac{k_i(k_i-1)}{2}\n",
    "$$\n",
    "\n",
    "And we can get a vector for the a values per column as shown below, and to gather the information of the whole vector we sum them.\n",
    "\n",
    "$$\n",
    "a = \\Sigma a_i = \\sum{\\frac{k_i(k_i-1)}{2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[123256. 132870. 127765. ... 121771. 115921. 131328.]\n",
      "a: 255357076.0\n"
     ]
    }
   ],
   "source": [
    "# Columnwise sum of the random fingerprints\n",
    "column_sum = np.sum(random_fp, axis=0)\n",
    "\n",
    "# Calculation of the number of pairs of 1s in each column\n",
    "a_per_column = column_sum * (column_sum - 1) / 2\n",
    "print(a_per_column)\n",
    "\n",
    "# Calculation of the total number of pairs of 1s in the whole matrix\n",
    "a = np.sum(a_per_column)\n",
    "print('a:', a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to get the total number of comparissons we calculate:\n",
    "$$\n",
    "p = \\frac{n(n-1)m}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p: 1022976000.0\n"
     ]
    }
   ],
   "source": [
    "n, m = random_fp.shape\n",
    "\n",
    "# Calculation of the total number of comparisons with the iSIM method\n",
    "p = n * (n - 1) * m / 2\n",
    "print('p:', p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to obtain the average RR pairwise value, we simply do a/p."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RR: 0.24962176629754754\n"
     ]
    }
   ],
   "source": [
    "RR = a / p\n",
    "print('RR:', RR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function is implemented in the iSIM module, and we can compare it to the average pariwise value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "isim_RR: 0.24962176629754754\n",
      "Time: 0.0022423267364501953 s\n",
      "--------------------\n",
      "Average pairwise RR: 0.24962176629754754\n",
      "Time: 1.9558014869689941 s\n",
      "--------------------\n",
      "Difference: 0.0\n",
      "Timing ratio: 872.2196703880915\n"
     ]
    }
   ],
   "source": [
    "from isim_comp import calculate_isim\n",
    "from isim_utils import pairwise_average\n",
    "import time\n",
    "\n",
    "# Calculation of the iSIM value\n",
    "start1 = time.time()\n",
    "isim_RR = calculate_isim(random_fp, n_ary='RR')\n",
    "end1 = time.time()\n",
    "\n",
    "print('isim_RR:', isim_RR)\n",
    "print('Time:', end1 - start1, 's')\n",
    "print(\"--------------------\")\n",
    "\n",
    "\n",
    "# Calculation of the average pairwise similarity\n",
    "start2 = time.time()\n",
    "average_pairwise, standard_deviation = pairwise_average(random_fp, n_ary='RR')\n",
    "end2 = time.time()\n",
    "\n",
    "print('Average pairwise RR:', average_pairwise)\n",
    "print('Time:', end2 - start2, 's')\n",
    "print(\"--------------------\")\n",
    "\n",
    "# Calculation of the difference between the iSIM value and the average pairwise similarity and the timing ratio\n",
    "print('Difference:', isim_RR - average_pairwise)\n",
    "print('Timing ratio:', (end2 - start2) / (end1 - start1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it can be apreaciated, doing the pairwise average takes way longer than the iSIM method, but the values are exactly the same.\n",
    "\n",
    "As the reader may have noticed, the average RR index is basically the proportion of total one-one coincidences in all the posible columnwise bit comparisons that can be done. When comparing only bits, the RR index has only two possible values: RR = 1 for a one-one match, or RR for a nonmatches or zero-zero matches. Hence, when calculating the average pairwise RR with the iSIM metric, what we are basically doing is getting the average of a binomial distribution. \n",
    "\n",
    "It would be intuitive then to calculate the variance of the average pairwise comparisons as the variance of a binomial distribution. \n",
    "\n",
    "The normal approximation of a binomial distribution is given by:\n",
    "\n",
    "$$\n",
    "\\sigma = \\sqrt{\\frac{p(1-p)}{n}}\n",
    "$$\n",
    "\n",
    "where p is the proportion of 1s in the distribution and n the total number of samples. Translating the formula to our framework, the standard deviation could be calculated with the following:\n",
    "\n",
    "$$\n",
    "\\sigma = \\sqrt{\\frac{RR(1-RR)}{m}}\n",
    "$$\n",
    "\n",
    "In our case, RR is the proportion of 1s in all the bit comparisons anb since we are using a columnwise approach, our number of samples would be the number of columns, m."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "isim_sigma: 0.00956348902381413\n",
      "Standard deviation: 0.009235858966327233\n"
     ]
    }
   ],
   "source": [
    "isim_sigma = np.sqrt(RR * (1 - RR)/m)\n",
    "print('isim_sigma:', isim_sigma)\n",
    "\n",
    "print('Standard deviation:', standard_deviation) ### Calculated above when compared to the pairwise average\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it can be seen, the number is not exact, we are using the normal approximation, hance the fingerprints do not have exactly a normal binomial distribution. Below we compare the approximation for multiple sets of different number of fingerprints and lengths. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Plot of the average pairwise similarity and the iSIM value for standard deviation calculation\n",
    "fig = plt.figure()\n",
    "for i in range(50):\n",
    "    fps = np.random.randint(0, 2, (np.random.randint(100, 500), np.random.randint(100, 2048)))\n",
    "    isim_RR = calculate_isim(fps, n_ary='RR')\n",
    "    isim_std = np.sqrt(isim_RR * (1 - isim_RR)/fps.shape[1])\n",
    "    average_pairwise, standard_deviation = pairwise_average(fps, n_ary='RR')\n",
    "\n",
    "    plt.scatter(standard_deviation, isim_std, color='blue')\n",
    "\n",
    "plt.plot([0, 0.1], [0, 0.1], color='black')\n",
    "plt.ylabel('iSIM sigma RR', fontsize=14)\n",
    "plt.xlabel('Pairwise standard deviation RR', fontsize=14)\n",
    "\n",
    "plt.savefig('figures/RR_normal_binomial_random.png', dpi = 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this exercise, we can see that the approximation despite of not being excat, is quite good. However, the fingerprints for real molecules are far from having a normal binomial distribution. Then we expect our trick not to work as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing of RR on fingerprints from real molecules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import glob\n",
    "\n",
    "fig = plt.figure()\n",
    "for file in glob.glob(\"rdkit/*.npy\"):\n",
    "    # Load fingerprint files\n",
    "    fps = np.load(file, mmap_mode='r')\n",
    "\n",
    "    # Calculate the iSIM sigma RR standard deviation\n",
    "    isim_RR = calculate_isim(fps, n_ary='RR')\n",
    "    isim_std = np.sqrt(isim_RR * (1 - isim_RR)/fps.shape[1])\n",
    "\n",
    "    # Calculate the pairwise standard deviation of RR\n",
    "    pairwise_std = pairwise_average(fps, n_ary=\"RR\")[1]\n",
    "\n",
    "    # Plot the point\n",
    "    plt.scatter(pairwise_std, isim_std, color = 'blue')\n",
    "\n",
    "plt.plot([0,0.1],[0, 0.1], color = 'black')\n",
    "plt.ylabel('iSIM sigma RR', fontsize=14)\n",
    "plt.xlabel('Pairwise standard deviation RR', fontsize=14)\n",
    "\n",
    "plt.savefig('figures/RR_normal_binomial_chembl.png', dpi = 400)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this section we confirmed that the distribution of bits in real-molecule fingerprints is far from normality. Hence the distribution of them across the fingerprints must be taken into consideration. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing of the exact RR standard deviation calculation\n",
    "\n",
    "For a given pair of fingerprints, $a$ is defined according to the following formula.\n",
    "\n",
    "$$\n",
    "a = \\sum_{i=1}^{M} p_i\n",
    "$$\n",
    "\n",
    "Where $p_i$ is 1 if both molecules have a value of 1 at position $i$, and 0 otherwise. For iSIM, to compute the average value of $a$, $E(a)$, we used linearity of expectation according to equation 7, where $E(p_i)$ is simply $\\frac{k_i(k_i-1)}{n(n-1)}$.\n",
    "\n",
    "$$\n",
    "E(a) = \\sum_{i=1}^{M} E(p_i)\n",
    "$$\n",
    "\n",
    "The variance of $a$ doesn't follow this same linearity, but instead expands to include covariances between terms, where $\\sigma_{p_i, p_j}$ is the covariance between $p_i$ and $p_j$.\n",
    "\n",
    "$$\n",
    "\\sigma^2_a = \\sum_{i=1}^{M}{\\sigma^2_{p_i}} + 2\\sum_{i=1}^{M}\\sum_{j=i+1}^{M}{\\sigma_{p_i, p_j}}\n",
    "$$\n",
    "\n",
    "Since $p_i$ can only have a value of 0 or 1, it follows a Bernoulli distribution, and has a variance following equation.\n",
    "\n",
    "$$\n",
    "\\sigma^2_{p_i} = E(p_i)(1-E(p_i))\n",
    "$$\n",
    "\n",
    "We additionally note that covariance is defined according to:\n",
    "\n",
    "$$\n",
    "\\sigma_{p_i, p_j} = E(p_ip_j) - E(p_i)E(p_j)\n",
    "$$\n",
    "\n",
    "From the previous equations we can therefore compute $\\sigma^2_a$ if we know $E(p_i  p_j)$ for any pair of $i$ and $j$, and $E(p_i)$ for any $i$. $E(p_i)$, as previously mentioned, is computed from iSIM and takes $O(N)$ time. $E(p_i  p_j)$ is simply the probability that when selecting a pair of two molecules, there is a value of 1 for both molecules at positions $i$ and $j$. Thus, similar to how we computed $E(p_i)$, we go through each of the molecules and enumerate the number of instances where there is a 1 in both positions $i$ and $j$, defined as $\\alpha_{ij}$. Since there are $\\frac{\\alpha_{ij}(\\alpha_{ij}-1)}{2}$ pairs where $p_i p_j$ is 1, and $\\frac{N(N-1)}{2}$ total pairs, $E(p_i  p_j)$ simply follows equation:\n",
    "\n",
    "$$\n",
    "E(p_i p_j) = \\frac{\\alpha_{ij}(\\alpha_{ij}-1)}{N(N-1)}\n",
    "$$\n",
    "\n",
    "Determining $\\alpha_{ij}$ takes $O(N)$ time, and we must do this for all $O(M^2)$ pairs, thus, determining all the covariances takes $O(NM^2)$ time. We can therefore obtain the variance of $a$ in $O(NM^2)$ time, and all we need to do is square root this, and then divide it by $m$ to get the standard deviation of the RR metric."
   ]
  },
  {
   "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": [
    "from isim_sigma import get_stdev_russell_fast\n",
    "\n",
    "fig = plt.figure()\n",
    "for file in glob.glob(\"rdkit/*.npy\"):\n",
    "    # Load fingerprint files\n",
    "    fps = np.load(file, mmap_mode='r')\n",
    "\n",
    "    # Calculate the iSIM sigma RR standard deviation\n",
    "    RR_exact = get_stdev_russell_fast(fps)\n",
    "\n",
    "    # Calculate the pairwise standard deviation of RR\n",
    "    pairwise_std = pairwise_average(fps, n_ary=\"RR\")[1]\n",
    "\n",
    "    # Plot the point\n",
    "    plt.scatter(pairwise_std, RR_exact, color = 'blue')\n",
    "\n",
    "plt.plot([0,0.1],[0, 0.1], color = 'black')\n",
    "plt.ylabel('iSIM sigma RR exact', fontsize=14)\n",
    "plt.xlabel('Pairwise standard deviation RR', fontsize=14)\n",
    "\n",
    "plt.savefig('figures/RR_fast_exact_chembl.png', dpi = 400)\n"
   ]
  }
 ],
 "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}