{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An often used tool in my toolbox is polynomial regression to reduce smooth curves down to just a few best fit polynomial coefficients. These coefficients can then be used to do additional analysis that would have been difficult to do with the original (often patchily sampled) curves.\n",
    "\n",
    "An important question then becomes, \"how do I compare two polynomial curves?\". It is tempting to use the euclidean distance between the coefficient vectors as a distance between polynomials. However, this (dis)similarity measure doesn't correspond very well to our intuitive understanding of the differences in shape between the corresponding curves.\n",
    "\n",
    "<!-- TEASER_END --> \n",
    "\n",
    "In the past when I have searched for things like \"distance between polynomials\", \"metrics on polynomial coefficient space\", \"similarity measures between polynomials\", etc the search results have not been helpful. They tend to talk about things like using the ordered roots of a polynomial to represent it. A very intuitive sort of distance between two polynomials is the distance between the sampled curves. That is to say pick a grid of $N$ points $x_i$, evaluate the polynomials at those points $y_i = P(x_i)$ and then treat the resulting $y$ vectors as points in euclidean space $R^N$. But the quality of your results depends on the grid that you choose and actually carrying out this calculation can be very computationally expensive. Fortunately it turns out to not be too difficult to calculate the distance you would get in the analytic limit as $N \\to \\infty$ directly from the polynomial coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(111222)\n",
    "import scipy.spatial\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.rcParams.update(\n",
    "    {\n",
    "        \"figure.figsize\":(12, 6),\n",
    "        \"font.size\":16,\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the following set of polynomials on the interval -1 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Residual Magnitude')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f040dc89fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example_coeffs = np.array([\n",
    "    [0, 0, -2, 0],\n",
    "    [0, 1, 0, 1],\n",
    "    [-3, 0, 0, 0],\n",
    "])\n",
    "\n",
    "poly_labels = [\"-2x\", \"x^2+1\", \"-3x^3\"]\n",
    "colors = [\"k\", \"orange\", \"blue\"]\n",
    "linestyles = [\"--\", \"-\", \"-\"]\n",
    "\n",
    "x = np.linspace(-1, 1, 201)\n",
    "\n",
    "yvals = [np.polyval(c, x) for c in example_coeffs]\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, sharex=True)\n",
    "\n",
    "for y, label, color, ls in zip(yvals, poly_labels, colors, linestyles):\n",
    "    axes[0].plot(x, y, lw=3, label=\"$y=\"+label+\"$\", c=color, linestyle=ls, alpha=0.9)\n",
    "    axes[1].plot(x, y-yvals[0], lw=3, label=\"y=$\"+label+\"$\", c=color, linestyle=ls, alpha=0.9)\n",
    "\n",
    "    \n",
    "legend = plt.legend(fontsize=22, bbox_to_anchor=(0.3, 1.5), framealpha=1.0)\n",
    "axes[0].set_ylabel(\"Y value\")\n",
    "axes[1].set_xlabel(\"X value\")\n",
    "axes[1].set_ylabel(\"Residual Magnitude\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By looking at the curves I think most people would say that the cubic is much more similar to the line than the quadratic curve is. But the quadratic is significantly closer in coefficient space (a distance of $\\sqrt{6}$ versus $\\sqrt{13}$). \n",
    "\n",
    "You might think that I am cherry picking a special example and that in general the difference in coefficients will be a good predictor of the differences between the curves. Although the example above was chosen to be iullustrative it is in no way unusual. The distance in coefficient space is actually fairly loosely related to the distances between the associated curves. Lets pick a large set of polynomials with randomly distributed coefficients and compare the distances between the associated curves and the distances between the coefficient vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f040bbe6c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_polys = 3.0*np.random.normal(size=(500, 4))\n",
    "rand_yvals = np.array([np.polyval(c, x) for c in random_polys])\n",
    "\n",
    "for i in range(10):\n",
    "    plt.plot(x, rand_yvals[i])\n",
    "    \n",
    "plt.xlabel(\"X value\")\n",
    "plt.ylabel(\"Y value\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "dx = np.mean(scipy.gradient(x))\n",
    "curve_dists = dx*scipy.spatial.distance_matrix(rand_yvals, rand_yvals)\n",
    "coeff_dists = scipy.spatial.distance_matrix(random_polys, random_polys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f040bc0bcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist2d(curve_dists.ravel(), coeff_dists.ravel(), 101)\n",
    "plt.xlabel(\"Curve Distance\")\n",
    "plt.ylabel(\"Coefficient Distance\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although it is clear that there is at least a fairly strong correlation between the distance in coefficient space and the distance in curve space there is an awful lot of leeway. In most situations it is the difference between the curves that really matters not the difference in coefficients. I think that the moral is clear, don't use the distance between the raw polynomial coefficients as a measure of similarity between the associated curves.\n",
    "\n",
    "\n",
    "## A Little Linear Algebra\n",
    "\n",
    "The problem with calculating distances in the polynomial coefficient space is that changes in different coefficients can have very similar looking effects on the shape of the curves. It isn't hard to tell the difference between $x$ and $x^2$ but if you squint $x^2$ and $x^4$ can look an awful lot alike. But it is possible to use a different sort of representation for our polynomials in which no two curves look too similar.\n",
    "\n",
    "Lets come back to the concept of representing the polynomials as points in $R^N$. The polynomials of order $K$ will be a linear subspace of $R^N$. This true since any linear combination of polynomials is a polynomial (thus they are restricted to a linear subspace) and any polynomial can be expressed in the usual form.\n",
    "\n",
    "$$\n",
    "y(x) = \\sum_{k=0}^{k=K} c_k x^k\n",
    "$$ \n",
    "\n",
    "\n",
    "To use the language of linear algebra the monomials $x^k$ form a basis for the linear subspace of $R^{N}$ spanned by polynomial curves. If you are none too familiar with linear algebra, that may sound fancy but it is just a restatement of the fact that all polynomials can be expressed in the form above.\n",
    "\n",
    "The observation that $x^2$ and $x^4$ \"kinda look alike\" can be made rigorous by considering the dot product of their corresponding sampled curves interpreted as points in $R^N$. It should be clear to see that the dot product in this case corresponds directly to the integral of the product of the two polynomials. The fact that these integrals don't tend to come out to 0 means that the usual polynomial basis functions $x^k$ aren't orthogonal to each other. \n",
    "\n",
    "This is exactly analogous to using a coordinate system in which the axes aren't at right angles to each other. In the usual case we pick a coordinate system in which each axis is orthonormal to all the others. If the coordinate basis is orthonormal then the distance between the coordinates is proportional to the distance between the corresponding points, which is rather handy. But this is true only if the coordinate axes are orthonormal to each other. If the coordinate axes aren't all at right angles to each other there is still always a unique coordinate label for any point, but, the distance between the labeled points is not necessarily equal (or even proportional) to the distance between the coordinate labels.\n",
    "\n",
    "In this particular situation the polynomial coefficients are a set of \"coordinates\" which allow us to locate a polynomial within the subspace of all possible polynomials of a certain order. The coordinate axes are the basis functions $x^k$. But if you measure the angle in $R^n$ between these axes you often find that they are not quite perpendicular and this is what is causing us our distance based troubles. There is not really any reason why we must use the regular basis functions $x^k$ to express our polynomials. If we choose a set of basis functions which were all orthogonal to each other then distances in our coefficient space would correspond to the differences between the curves, success!\n",
    "\n",
    "## Legendre Polynomials\n",
    "\n",
    "It is one thing to say \"just use an orthogonal polynomial basis!\" but it is quite another to know how to go about doing that in practice. The first detail which must be dealt with is that it isn't possible to orthogonalize polynomials over every interval simultaneously. We need first to fix an interval in x and then we can set about finding a set of polynomials which are orthogonal to each other on that interval. \n",
    "\n",
    "As you might imagine this is a very old and well studied problem. Instead of needing to solve the orthogonalization problem afresh for each and every possible interval it is much more convenient to simply map whatever interval we desire onto the range $[-1, 1]$ and then always use the same set of orthogonal polynomials. \n",
    "\n",
    "Although there are a potentially infinite number of possible orthogonal polynomial bases one might choose. It is nice to pick the basis polynomials so that the order of the first polynomial is 0 the order of the second polynomial is 1, the order of the next is 2 and so on. With this additional constraint there turns out to be just one unique set of functions (up to a normalization constant) and those are the <a href=https://en.wikipedia.org/wiki/Legendre_polynomials>Legendre Polynomials</a>.\n",
    "\n",
    "Conveniently there is a helper function in the numpy.polynomial module which will convert the coefficients of our polynomials from the usual coefficient space into a set of coefficients in an expansion over Legendre polynomials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "leg_coeffs = np.array([np.polynomial.legendre.poly2leg(c[::-1]) for c in random_polys])\n",
    "leg_dists = scipy.spatial.distance_matrix(leg_coeffs, leg_coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f040ba03b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist2d(curve_dists.ravel(), leg_dists.ravel(), 101)\n",
    "plt.xlabel(\"Curve Distance\")\n",
    "plt.ylabel(\"Legendre Coefficient Distance\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hey what gives! I said that if the basis functions were orthonormal then the distance between the coefficients should be proportional to the distance between the curves. The distribution above may be a little better but it is still a far cry from exactly 1 to 1. \n",
    "\n",
    "One thing you might note in the code above is that when I do the conversion from the normal polynomial coefficients to the Legendre coefficients I flip the ordering of the coefficients first. This is because the polyval function which I use above comes from the old np.poly1d module which orders coefficients highest order first but the newer np.polynomial module (including the legendre routines) uses the opposite convention of ordering coefficients lowest order first. Blithely combinging functions from the poly1d module with the newer polynomial module expecting them to play nice is a bug which has bitten me on no small number of occaisions, be warned!\n",
    "\n",
    "But the reason that the distances don't match up exactly is that the legendre polynomials as they have been implemented in numpy.polynomial are not actually orthonormal, only orthogonal. For reasons relating to other important properties of Legendre polynomials like recurrence relations etc, the polynomials all have different norms from each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38369392722802725"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(np.polynomial.Legendre([0, 0, 0, 1])(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correcting for this problem is relatively straight forward we simply have to make sure that each Legendre coefficient gets a weight which is proportional to its norm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate the norms of each legendre polynomial\n",
    "def rms(x):\n",
    "    return np.sqrt(np.mean(x**2))\n",
    "\n",
    "leg_norms = np.array([rms(np.polynomial.Legendre(v)(x)) for v in np.eye(4)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.58022984,  0.45169663,  0.38369393])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leg_norms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rescale the coefficients by the corresponding basis norms\n",
    "scaled_leg = leg_coeffs*leg_norms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_dists = scipy.spatial.distance_matrix(scaled_leg, scaled_leg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f040bb66278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist2d(curve_dists.ravel(), scaled_dists.ravel(), 101)\n",
    "plt.xlabel(\"Curve Distance\")\n",
    "plt.ylabel(\"Scaled Legendre Coefficient Distance\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tada! a proper exact 1-1 relationship. "
   ]
  }
 ],
 "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": "3.6.3"
  },
  "nikola": {
   "author": "Tim Anderton",
   "category": "",
   "date": "2018-07-11 13:40:06 UTC-06:00",
   "description": "",
   "link": "",
   "slug": "a-simple-similarity-function-for-polynomial-curves",
   "tags": "",
   "title": "A simple similarity function for polynomial curves",
   "type": "text"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
