{ "metadata": { "name": "", "signature": "sha256:f3cb96fd327ea1eedfd4c23aba072f67fce1d64a7484ddb7b8ef143de2d42bc3" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Inverse Projection\n", "-------------------------------------------------\n", "\n", "In our [previous discussion](http://python-for-signal-processing.blogspot.com/2012/11/projection-in-multiple-dimensions-in.html), we developed a powerful intuitive sense for projections and their relationships to minimum mean squared error problems. Here, we continue to extract yet another powerful result from the same concept. Recall that we learned to minimize\n", "\n", "$$J = || \\mathbf{y} - \\mathbf{V}\\boldsymbol{\\alpha} ||^2$$\n", "\n", "by projecting $\\mathbf{y}$ onto the space characterized by $\\mathbf{V}$ as follows:\n", "\n", "$$\\mathbf{\\hat{y}} = \\mathbf{P}_V \\mathbf{y}$$\n", "\n", "where\n", "\n", "$$\\mathbf{P}_V = \\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1} \\mathbf{V}^T$$\n", "\n", "where the corresponding error ($\\boldsymbol{\\epsilon}$) comes directly from the Pythagorean theorem:\n", "\n", "$$||\\mathbf{y}||^2 = ||\\mathbf{\\hat{y}}||^2 + ||\\boldsymbol{\\epsilon}||^2$$\n", "\n", "Now, let's consider the inverse problem: given $\\mathbf{\\hat{y}}$, what is the corresponding $\\mathbf{y}$? The first impulse in this situation is to re-visit \n", "\n", "$$\\mathbf{\\hat{y}} = \\mathbf{P}_V \\mathbf{y}$$\n", "\n", "and see if you can somehow compute the inverse of $\\mathbf{P}_V$. This will not work because the projection matrix does not possess a unique inverse. In the following figure, the vertical sheet represents all vectors in the space that have exactly the same projection, $\\mathbf{\\hat{y}}$. Thus, there is no unique solution to the inverse problem which is to say that it is \"ill-posed\"." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#http://stackoverflow.com/questions/10374930/matplotlib-annotating-a-3d-scatter-plot\n", "\n", "from mpl_toolkits.mplot3d import proj3d\n", "import matplotlib.patches as patches\n", "import mpl_toolkits.mplot3d.art3d as art3d\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "fig = plt.figure()\n", "fig.set_size_inches([8,8])\n", "\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "ax.set_aspect(1)\n", "ax.set_xlim([0,2])\n", "ax.set_ylim([0,2])\n", "ax.set_zlim([0,2])\n", "ax.set_aspect(1)\n", "ax.set_xlabel('x-axis',fontsize=16)\n", "ax.set_ylabel('y-axis',fontsize=16)\n", "ax.set_zlabel('z-axis',fontsize=16)\n", "\n", "y = matrix([1,1,1]).T \n", "V = matrix([[1,0.25], # columns are v_1, v_2\n", " [0,0.50],\n", " [0,0.00]])\n", "\n", "alpha=inv(V.T*V)*V.T*y # optimal coefficients\n", "P = V*inv(V.T*V)*V.T\n", "yhat = P*y # approximant\n", "\n", "\n", "u = np.linspace(0, 2*np.pi, 100)\n", "v = np.linspace(0, np.pi, 100)\n", "\n", "xx = np.outer(np.cos(u), np.sin(v))\n", "yy = np.outer(np.sin(u), np.sin(v))\n", "zz = np.outer(np.ones(np.size(u)), np.cos(v))\n", "\n", "sphere=ax.plot_surface(xx+y[0,0], yy+y[1,0], zz+y[2,0], \n", " rstride=4, cstride=4, color='gray',alpha=0.3,lw=0.25)\n", "\n", "ax.plot3D([y[0,0],0],[y[1,0],0],[y[2,0],0],'r-',lw=3)\n", "ax.plot3D([y[0,0]],[y[1,0]],[y[2,0]],'ro')\n", "\n", "ax.plot3D([V[0,0],0],[V[1,0],0],[V[2,0],0],'b-',lw=3)\n", "ax.plot3D([V[0,0]],[V[1,0]],[V[2,0]],'bo')\n", "ax.plot3D([V[0,1],0],[V[1,1],0],[V[2,1],0],'b-',lw=3)\n", "ax.plot3D([V[0,1]],[V[1,1]],[V[2,1]],'bo')\n", "\n", "ax.plot3D([yhat[0,0],0],[yhat[1,0],0],[yhat[2,0],0],'g--',lw=3)\n", "ax.plot3D([yhat[0,0]],[yhat[1,0]],[yhat[2,0]],'go')\n", "\n", "\n", "x2, y2, _ = proj3d.proj_transform(y[0,0],y[1,0],y[2,0], ax.get_proj())\n", "ax.annotate(\n", " \"$\\mathbf{y}$\", \n", " xy = (x2, y2), xytext = (40, 20), fontsize=24,\n", " textcoords = 'offset points', ha = 'right', va = 'bottom',\n", " bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))\n", "\n", "x2, y2, _ = proj3d.proj_transform(yhat[0,0],yhat[1,0],yhat[2,0], ax.get_proj())\n", "ax.annotate(\n", " \"$\\hat{\\mathbf{y}}$\", \n", " xy = (x2, y2), xytext = (40, 10), fontsize=24,\n", " textcoords = 'offset points', ha = 'right', va = 'bottom',\n", " bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))\n", "\n", "x2, y2, _ = proj3d.proj_transform(V[0,0],V[1,0],V[2,0], ax.get_proj())\n", "ax.annotate(\n", " \"$\\mathbf{v}_1$\", \n", " xy = (x2, y2), xytext = (120, 10), fontsize=24,\n", " textcoords = 'offset points', ha = 'right', va = 'bottom',\n", " bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))\n", "\n", "x2, y2, _ = proj3d.proj_transform(V[0,1],V[1,1],V[2,1], ax.get_proj())\n", "ax.annotate(\n", " \"$\\mathbf{v}_2$\", \n", " xy = (x2, y2), xytext = (-30, 30), fontsize=24,\n", " textcoords = 'offset points', ha = 'right', va = 'bottom',\n", " bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),\n", " arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0'))\n", "\n", "xx = array([0,yhat[0],yhat[0]])\n", "yy = array([0,yhat[1],yhat[1]])\n", "zz = array([0,0,2])\n", "\n", "ax.add_collection3d( art3d.Poly3DCollection([zip(xx,yy,zz)],alpha=0.15,color='m') )\n", "ax.set_title(r'The magenta sheet contains vectors with the same projection, $\\mathbf{\\hat{y}}$')\n", "\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IWVlZ8PPzQ3Z2NtauXTsnx9pMYjY/pI4Vg8EwZpfsTIYKppdwl1vJW01KpZIs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\ndC2OHTvmw5riPSHIzD1qtRqTycSTTz5JU1MT//iP/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bf/xte+9rWASLO5uZmXXnpJ9fFz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\nhYUFGo2G/Px87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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, since the unique inverse does not exist, we can impose constraints on the solution to enforce a unique solution. For example, since there are many $\\mathbf{y}$ that correspond to the same $\\mathbf{\\hat{y}}$, we can pick the one that has the shortest length, $||\\mathbf{y} ||$. Thus, we can solve this inverse projection problem by enforcing additional constraints. \n", "\n", "Consider the following constrained minimization problem:\n", "\n", "$$\\min_y \\mathbf{y}^T \\mathbf{y}$$\n", "\n", "subject to:\n", "\n", "$$\\mathbf{v_1}^T \\mathbf{y} = c_1$$\n", "$$\\mathbf{v_2}^T \\mathbf{y} = c_2$$\n", "\n", "Here, we have the same setup as before: we want to minimize something with a set of constraints. We can re-write the constraints in a more familiar form as\n", "\n", "$$\\mathbf{V}^T \\mathbf{y} = \\mathbf{c}$$\n", "\n", "We can multiply both sides to obtain the even more familiar form:\n", "\n", "$$\\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1} \\mathbf{V}^T \\mathbf{y} = \\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1}\\mathbf{c}$$\n", "\n", "which by cleaning up the notation gives,\n", "\n", "$$\\mathbf{P}_V \\mathbf{y} = \\mathbf{\\hat{y}}$$\n", "\n", "where\n", "\n", "$$\\mathbf{\\hat{y}} = \\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1}\\mathbf{c}$$\n", "\n", "and\n", "\n", "$$\\mathbf{P}_V=\\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1} \\mathbf{V}^T$$\n", "\n", "So far, nothing has really happened yet. We've just rewritten the constraints as a projection, but we still don't know how to find the $\\mathbf{y}$ of minimum length. To do that, we turn to the Pythagorean relationship we pointed out earlier,\n", "\n", "$$||\\mathbf{y}||^2 = ||\\mathbf{\\hat{y}}||^2 + ||\\boldsymbol{\\epsilon}||^2$$\n", "\n", "where $\\boldsymbol{\\epsilon} = \\mathbf{y} - \\mathbf{\\hat{y}}$. So, we have\n", "\n", "$$||\\mathbf{y}||^2 = ||\\mathbf{\\hat{y}}||^2 + || \\mathbf{y} - \\mathbf{\\hat{y}}||^2 \\ge 0$$\n", "\n", "and since this is always non-negative, the only way to minimize $||\\mathbf{y}||^2$ is to set \n", "\n", "$$\\mathbf{y} = \\mathbf{\\hat{y}} = \\mathbf{V} (\\mathbf{V}^T \\mathbf{V})^{-1}\\mathbf{c}$$\n", "\n", "which is the solution to our constrained minimization problem.\n", "\n", "If that seems shockingly easy, remember that we have already done all the heavy lifting by solving the projection problem. Here, all we have done is re-phrased the same problem.\n", "\n", "Let's see this in action using scipy.optimize for comparison. Here's the problem\n", "\n", "$$\\min_y \\mathbf{y}^T \\mathbf{y}$$\n", "\n", "subject to:\n", "\n", "$$\\mathbf{e_1}^T \\mathbf{y} = 1$$\n", "$$\\mathbf{e_2}^T \\mathbf{y} = 1$$\n", "\n", "where $\\mathbf{e}_i$ is the coordinate vector that is zero everywhere except for the $i^{th}$ entry.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "# constraints formatted for scipy.optimize.minimize\n", "cons = [{'type':'eq','fun':lambda x: x[0]-1,'jac':None},\n", " {'type':'eq','fun':lambda x: x[1]-1,'jac':None},\n", " ]\n", "\n", "init_point = np.array([1,2,3,0]) # initial guess\n", "ysol= minimize(lambda x: np.dot(x,x),init_point,constraints=cons,method='SLSQP')\n", "\n", "# using projection method\n", "c = np.matrix([[1,1,0,0]]).T # RHS constraint vector\n", "V = np.matrix(np.eye(4)[:,0:2])\n", "ysol_p = V*np.linalg.inv(V.T*V)*V.T*c\n", "\n", "print 'scipy optimize solution:',\n", "print ysol['x']\n", "print 'projection solution:',\n", "print np.array(ysol_p).flatten()\n", "\n", "print np.allclose(np.array(ysol_p).flat,ysol['x'],atol=1e-6)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "scipy optimize solution: [ 1.00000000e+00 1.00000000e+00 -2.17476398e-08 -2.93995881e-08]\n", "projection solution: [ 1. 1. 0. 0.]\n", "True\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Weighted Constrained Minimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can again pursue a more general problem using the same technique:\n", "\n", "$$\\min_y \\mathbf{y}^T \\mathbf{Q} \\mathbf{y}$$\n", "\n", "subject to:\n", "\n", "$$\\mathbf{V}^T \\mathbf{y} = \\mathbf{c}$$\n", "\n", "where $\\mathbf{Q}$ is a positive definite matrix. In this case, we can define $\\eta$ such that:\n", "\n", "$$\\mathbf{y} = \\mathbf{Q}^{-1} \\boldsymbol{\\eta}$$\n", "\n", "and re-write the constraint as\n", "\n", "$$\\mathbf{V}^T \\mathbf{Q}^{-1} \\boldsymbol{\\eta} = \\mathbf{c}$$ \n", "\n", "and multiply both sides,\n", "\n", "$$\\mathbf{P}_V \\boldsymbol{\\eta}=\\mathbf{V} ( \\mathbf{V}^T \\mathbf{Q^{-1} V})^{-1} \\mathbf{c}$$\n", "\n", "where\n", "\n", "$$\\mathbf{P}_V=\\mathbf{V} ( \\mathbf{V}^T \\mathbf{Q^{-1} V})^{-1} \\mathbf{V}^T \\mathbf{Q}^{-1}$$\n", "\n", "To sum up, the minimal $\\mathbf{y}$ that solves this constrained minimization problem is\n", "\n", "$$\\mathbf{y}_o = \\mathbf{V} ( \\mathbf{V}^T \\mathbf{Q^{-1} V})^{-1} \\mathbf{c}$$\n", "\n", "Once again, let's illustrate this using scipy.optimize in the following" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from scipy.optimize import minimize\n", "\n", "# constraints formatted for scipy.optimize.minimize\n", "cons = [{'type':'eq','fun':lambda x: x[0]-1,'jac':None},\n", " {'type':'eq','fun':lambda x: x[1]-1,'jac':None},\n", " ]\n", "\n", "Q = np.diag ([1,2,3,4])\n", "\n", "\n", "init_point = np.array([1,2,3,0]) # initial guess\n", "ysol= minimize(lambda x: np.dot(x,np.dot(Q,x)),init_point,constraints=cons,method='SLSQP')\n", "\n", "# using projection method\n", "Qinv = np.linalg.inv(Q)\n", "c = np.matrix([[1,1,0,0]]).T # RHS constraint vector\n", "V = np.matrix(np.eye(4)[:,0:2])\n", "ysol_p = V*np.linalg.inv(V.T*Qinv*V)*V.T*Qinv*c\n", "print 'scipy optimize solution:',\n", "print ysol['x']\n", "print 'projection solution:',\n", "print np.array(ysol_p).flatten()\n", "print np.allclose(np.array(ysol_p).flat,ysol['x'],atol=1e-5)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "scipy optimize solution: [ 1.00000000e+00 1.00000000e+00 -9.93437889e-09 -2.31626259e-06]\n", "projection solution: [ 1. 1. 0. 0.]\n", "True\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we pulled yet another powerful result from the projection concept we developed previously. We showed how \"inverse projection\" can lead to the solution of the classic constrained minimization problem. Although there are many approaches to the same problem, by once again appealing to the power projection method, we can maintain our intuitive geometric intuition. " ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This post was created using the [nbconvert](https://github.com/ipython/nbconvert) utility from the source [IPython Notebook](www.ipython.org) which is available for [download](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Inverse_Projection_Constrained_Optimization.ipynb) from the main github [site](https://github.com/unpingco/Python-for-Signal-Processing) for this blog. The projection concept is masterfully discussed in the classic Strang, G. (2003). *Introduction to linear algebra*. Wellesley Cambridge Pr. Also, some of Dr. Strang's excellent lectures are available on [MIT Courseware](http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/). I highly recommend these as well as the book." ] } ], "metadata": {} } ] }