{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cumulative Distribution Transform\n", "\n", "This notebook implements the Cumulative Distribution Transform (CDT) and its inverse and showcases an example application of this transformation. \n", "\n", "## CDT Definition: \n", "\n", "Consider two nonzero probability density functions $I_0$ and $I_1$ defined on $X,Y\\subset\\mathbb{R}$. Considering $I_0$ to be a pre-determined 'reference' density, one can use the following relation, \n", "\n", "\$$\n", "\\int_{inf(Y)}^{f(x)} I_1(\\tau) d\\tau = \\int_{inf(X)}^{x}I_0(\\tau)d\\tau ~~~~~~~(1)\n", "\$$\n", "\n", "to uniquely associate $f_1:X\\rightarrow Y$ to the given density $I_1$. We use this relationship to define the Cumulative Distribution Transform (CDT) of $I_1$ (denoted as $\\hat{I}_1: X \\to \\mathbb{R}$), with respect to the reference $I_0$:\n", "\n", "\\begin{align}\n", "\\hat{I}_1(x) = \\left( f_1(x) - x \\right) \\sqrt{I_0(x)}.~~~~~~~(2)\n", "\\end{align}\n", "\n", "Now let $J_0: X \\to [0,1]$ and $J_1: Y \\to [0,1]$ be the corresponding cumulative distribution functions for ${I}_0$ and ${I}_1$, that is: $J_0(x) = \\int_{\\inf(X)}^x I_0(\\tau) d\\tau$, $J_1(y) = \\int_{\\inf(Y)}^y I_1(\\tau) d\\tau$. Equation (1) can then be rewritten as,\n", "\n", "\$$\n", "J_0(x) = J_1(f_1(x)) \\Rightarrow f_1(x)=J_1^{-1}(J_0(x)).~~~~~~~(3)\n", "\$$\n", "\n", "For continuous cumulative distribution functions $J_0$ and $J_1$, $f_1$ is a continuous and monotonic function. If $f_1$ is differentiable, Equation (3) can be rewritten as\n", "\n", "\$$\n", "I_0(x) = f^{\\prime}_1(x) I_1(f_1(x)).~~~~~~~(4)\n", "\$$\n", "\n", "## Inverse-CDT Definition: \n", "\n", "The Inverse-CDT of $\\hat{I}_1$ is defined as: \n", "\$$\n", "I_1(y) = \\frac{d }{dy}J_0(f_1^{-1}(y)) = (f_1^{-1})^{\\prime} I_0(f^{-1}(y))\n", "\$$\n", "where $f_1^{-1}: Y \\to X$ refers to the inverse of $f_1$ (i.e. $f_1^{-1}(f_1(x)) = x$), $f(x) = {\\hat{I}_1(x)}/{\\sqrt{I_0(x)}} + x$, and where $I_1: Y \\to \\mathbb{R}$ as before. Naturally, the equation above holds for points where $J_0$ and $f$ are differentiable. By the construction above, $f$ will be differentiable except for points where $I_0$ and $I_1$ are discontinuous.\n", "\n", "## Now we implement CDT in python" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n", "from scipy import interp\n", "from sklearn.svm import LinearSVC\n", "from matplotlib import colors\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define CDT and its inverse" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def CDT(I0,I1):\n", " assert I0.shape==I1.shape\n", " assert not((1.0*I0<0).sum() and (1.0*I1<0).sum())\n", " I0=I0/I0.sum()\n", " I1=I1/I1.sum()\n", " cI0=np.cumsum(I0)\n", " cI1=np.cumsum(I1)\n", " x=np.asarray(range(len(I0)))\n", " xtilde=np.linspace(0,1,len(I0))\n", " XI0 = interp(xtilde,cI0, x)\n", " XI1 = interp(xtilde,cI1, x)\n", " u = interp(x,XI0,XI0-XI1)\n", " f = x - u\n", " return u,f\n", "def iCDT(u,I0):\n", " x=np.asarray(range(len(I0)))\n", " f=x-u\n", " fprime=np.gradient(f)\n", " I1 = interp(x,f, I0/fprime)\n", " return I1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the template distribution $I_0$ to be a uniform distribution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x=np.asarray(range(100))\n", "I0= np.ones([100])\n", "I0=I0/I0.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define four classes of signals, where Class $i$, for $i\\in\\{1,2,3,4\\}$, consist of translated versions of $i$ Gaussian distributions. Sample signals are shown below." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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csfSB1dq8efMwxnT5baWgvp4vFRRw7eOPc8x5dZ1TlsPYYWO98sBaWVkZ+/fv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\n1u/pGF4bKir44MwZfp6c3Ol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dhrvF7+8ePatWraK+vp677rgLaGbwWgMzZsxARFi3bp1f6qACnwZ+1aHsdjvX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\nqamRhIQEmfDww4LdLi8fO2bpuHvevUe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a0eNstSclJTE2fCw2sdW/jevguXP8+tgx8puYUG7evHnA+Qt1d6PBr9QlxNnt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\nHL/fVPAbY3hm+HBKa2t5pIl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n=200\n", "I1=[]\n", "I2=[]\n", "I3=[]\n", "I4=[]\n", "eps=1e-7\n", "for i in np.linspace(25,75,n):\n", " temp=(1/20.0)*np.exp(-((x-i)**2)/20.0)+eps\n", " I1.append(temp/temp.sum())\n", " temp=(1/20.0)*np.exp(-((x-i+10)**2)/20.0)+eps+(1/20.0)*np.exp(-((x-i-10)**2)/20.0)\n", " I2.append(temp/temp.sum())\n", " temp=(1/20.0)*np.exp(-((x-i+15)**2)/20.0)+eps+(1/20.0)*np.exp(-((x-i-15)**2)/20.0)+(1/20.0)*np.exp(-((x-i)**2)/20.0)\n", " I3.append(temp/temp.sum())\n", " temp=(1/20.0)*np.exp(-((x-i-15)**2)/20.0)+(1/20.0)*np.exp(-((x-i+15)**2)/20.0)+eps+(1/20.0)*np.exp(-((x-i-5)**2)/20.0)+(1/20.0)*np.exp(-((x-i+5)**2)/20.0)\n", " I4.append(temp/temp.sum())\n", "I1=np.asarray(I1)\n", "I2=np.asarray(I2)\n", "I3=np.asarray(I3)\n", "I4=np.asarray(I4)\n", "for i in [0,n/2,n-1]:\n", " plt.plot(I0) #template\n", " plt.plot(I1[i,:],'r')#class 1\n", " plt.plot(I2[i,:],'g')#class 2\n", " plt.plot(I3[i,:],'k')#class 3\n", " plt.plot(I4[i,:],'c')#class 4 \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the CDT of the signals defined above." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UC0mnaF6pEi/UqEHfgADu9fbGycGBvXv38vp77xEWFkZycjK1atXinXfeYezY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VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", "/Users/gr2z/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:29: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", "/Users/gr2z/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:30: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n", "/Users/gr2z/anaconda/lib/python3.6/site-packages/ipykernel/__main__.py:31: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n" ] }, { "data": { "image/png": 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6VHrGysMJh5n661QWHVhETmEOnUO6MOGOyRR6t+Gb1DQm7TuKSWu87e3p5efH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\n43nooYfwatKE1UlJ9D9/nn0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uaGlp9LmL2uM7XZYv/8xpIQT7Q/fTomKLAq2f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hE0JUbSZT+RUyCQ2VGTpR7an8XMxOzpUdhhDias6eNSpW/ve/RsXKAQPgxReh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u1=[]\n", "u2=[]\n", "u3=[]\n", "u4=[]\n", "for i in range(n):\n", " u1_,f1_=CDT(I0,I1[i,:])\n", " u2_,f2_=CDT(I0,I2[i,:])\n", " u3_,f3_=CDT(I0,I3[i,:])\n", " u4_,f4_=CDT(I0,I4[i,:])\n", " u1.append(u1_)\n", " u2.append(u2_)\n", " u3.append(u3_)\n", " u4.append(u4_) \n", "u1=np.asarray(u1)\n", "u2=np.asarray(u2)\n", "u3=np.asarray(u3) \n", "u4=np.asarray(u4) \n", "\n", "\n", "for i in [0,n/2,n-1]:\n", " fig,[ax1,ax2]=plt.subplots(1,2,figsize=(15,3))\n", " ax1.plot(I1[i,:],'r')#class 1\n", " ax1.set_title('Signal Space')\n", " ax2.plot(u1[i,:],'r')#class 1\n", " ax2.set_title('CDT Space')\n", " ax1.plot(I2[i,:],'g')#class 2\n", " ax2.plot(u2[i,:],'g')#class 2\n", " ax1.plot(I3[i,:],'k')#class 3\n", " ax2.plot(u3[i,:],'k')#class 3\n", " ax1.plot(I4[i,:],'c')#class 4\n", " ax2.plot(u4[i,:],'c')#class 4\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we test the inverse CDT: " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PV0UVtNjYnAV0OkKnijkN6LxBbkboTp2ClJSCq5NSxc+zwB6Xz6OAlcaYxsBK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TvmpVDsTGwmWXOVdWA7oKTwM6VTxsNuslo3p158o79qJTqpCMMX8BuW1o2Ks4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Rs2ON9fG/TEmHOG7TtVX0ePHiU7O5uOXbtyuKCgzBEuD5w8gF/9Z33JZfGVlt2gA2h1cStGXT+K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\nQmCC\n", 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upsikSB6b/xh/HfqLmy68iU9u+5TNWf502biRDSdP0tTPjyktWxK6ZQtD+vZl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in [0,n/2,n-1]:\n", " fig,[ax1,ax2,ax3]=plt.subplots(1,3,figsize=(15,3))\n", " ax1.plot(I1[i,:],'r')#class 1\n", " ax1.set_title('Signal')\n", " ax2.plot(u1[i,:],'r')#class 1\n", " ax2.set_title('CDT Space')\n", " ax3.plot(iCDT(u1[i,:],I0),'r')#class 1\n", " ax3.set_title('Inverse')\n", " ax1.plot(I2[i,:],'g')#class 2\n", " ax2.plot(u2[i,:],'g')#class 2\n", " ax3.plot(iCDT(u2[i,:],I0),'g')#class 2\n", " ax1.plot(I3[i,:],'k')#class 3\n", " ax2.plot(u3[i,:],'k')#class 3 \n", " ax3.plot(iCDT(u3[i,:],I0),'k')#class 3\n", " ax1.plot(I4[i,:],'c')#class 4\n", " ax2.plot(u4[i,:],'c')#class 4 \n", " ax3.plot(iCDT(u4[i,:],I0),'c')#class 4\n", "\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we do linear classification in the Signal Space and in the CDT space. We use LDA for visualization. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# \n", "lda=LinearDiscriminantAnalysis(n_components=2)\n", "\n", "X=np.concatenate((I1,I2,I3,I4),0) #Combine the signals into a features vector X\n", "Xhat=np.concatenate((u1,u2,u3,u4),0) #Combine the transformed signals into a features vector Xhat\n", "label=np.concatenate((np.zeros(n,),np.ones(n,),2*np.ones(n,),3*np.ones(n,))) # Define the labels as -1,0,1 for the three classes" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/gr2z/anaconda/lib/python3.6/site-packages/sklearn/discriminant_analysis.py:387: UserWarning: Variables are collinear.\n", " warnings.warn(\"Variables are collinear.\")\n" ] }, { "data": { "image/png": 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4ZnFrxPPeeEsGL75iwmTSG6xHe348+f7VmQwboii+xUrJc2ZW/TuFffuM3tdC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Apply LDA and show classification boundaries in Signal Space\n", "Xlda=lda.fit_transform(X,label)\n", "svm=LinearSVC()\n", "svm.fit(Xlda,label)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.plot(Xlda[:n,0],Xlda[:n,1],'b*')\n", "plt.plot(Xlda[n:2*n,0],Xlda[n:2*n,1],'ro')\n", "plt.plot(Xlda[2*n:,0],Xlda[2*n:,1],'kx')\n", "plt.plot(Xlda[3*n:,0],Xlda[3*n:,1],'cd')\n", "x_min, x_max = plt.xlim()\n", "y_min, y_max = plt.ylim()\n", "nx, ny = 400, 200\n", "xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", "Z = svm.predict(np.c_[xx.ravel(), yy.ravel()])\n", "Z = Z[:].reshape(xx.shape)\n", "plt.pcolormesh(xx, yy, Z,cmap='OrRd')\n", "plt.contour(xx, yy, Z, linewidths=.5, colors='k')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/gr2z/anaconda/lib/python3.6/site-packages/sklearn/discriminant_analysis.py:387: UserWarning: Variables are collinear.\n", " warnings.warn(\"Variables are collinear.\")\n" ] }, { "data": { "image/png": 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JiHi52NgTdO98A/9Xpwqj+3Zwuh23dVWtymz+aCSr3htOrcpRLAkN4qPIMH5s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\nHzkQFECgvx+3HzhOqNMN5oE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Apply LDA and show classification boundaries in the transform Space\n", "Xhatlda=lda.fit_transform(Xhat,label)\n", "svm=LinearSVC()\n", "svm.fit(Xhatlda,label)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.plot(Xhatlda[:n,0],Xhatlda[:n,1],'b*')\n", "plt.plot(Xhatlda[n:2*n,0],Xhatlda[n:2*n,1],'ro')\n", "plt.plot(Xhatlda[2*n:3*n,0],Xhatlda[2*n:3*n,1],'kx')\n", "plt.plot(Xhatlda[3*n:,0],Xhatlda[3*n:,1],'cd')\n", "x_min, x_max = plt.xlim()\n", "y_min, y_max = plt.ylim()\n", "nx, ny = 400, 200\n", "xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n", " np.linspace(y_min, y_max, ny))\n", "Z = svm.predict(np.c_[xx.ravel(), yy.ravel()])\n", "Z = Z[:].reshape(xx.shape)\n", "plt.pcolormesh(xx, yy, Z,cmap='OrRd')\n", "plt.contour(xx, yy, Z, linewidths=.5, colors='k')\n", "plt.show()" ] } ], "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": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 0 }