{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "2D Data Plots and Analysis\n", "===\n", "\n", "## Unit 7, Lecture 4\n", "\n", "*Numerical Methods and Statistics*\n", "\n", "----\n", "\n", "#### Prof. Andrew White, Feburary 27th 2018" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import random\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from math import sqrt, pi\n", "import scipy\n", "import scipy.stats\n", "\n", "plt.style.use('seaborn-whitegrid')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Working with 2D data\n", "===\n", "\n", "Now we'll consider 2D numeric data. Recall that we're taking two measurements simultaneously so that their should be an equal number of data points for each dimension. Furthermore, they should be paired. For example, measuring people's weight and height is valid. Measuring one group of people's height and then a different group of people's weight is not valid." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Our example for this lecture will be one of the most famous datasets of all time: the Iris dataset. It's a commonly used dataset in education and describes measurements in centimeters of 150 Iris flowers. The measured data are the columns and each row is an iris flower. They are sepal length, sepal width, pedal length, pedal width, and species. We'll ignore species for our example." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Flower Anatomy\n", "---\n", "" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "import pydataset\n", "\n", "data = pydataset.data('iris').values\n", "#remove species column\n", "data = data[:,:4].astype(float)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Sample Covariance\n", "===\n", "\n", "Let's begin by computing sample covariance. The syntax for covariance is similar to the `std` syntax for standard deviation. We'll compute the sample covariance between petal width and sepal width." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.18997942, -0.12163937],\n", " [-0.12163937, 0.58100626]])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.cov(data[:,1], data[:,3], ddof=1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "This is called a **covariance matrix**:\n", "\n", "$$\\left[\\begin{array}{lr}\n", "\\sigma_{xx} & \\sigma_{xy}\\\\\n", "\\sigma_{yx} & \\sigma_{yy}\\\\\n", "\\end{array}\\right]$$\n", "\n", "The diagonals are the sample variances and the off-diagonal elements are the sample covariances. It is symmetric, since $\\sigma_{xy} = \\sigma_{yx}$. The value we observed for sample covariance is negative covariance the measurements. That means as one increases, the other decreases. The `ddof` was set to 1, meaning that the divosor for sample covariance is $N - 1$. Remember that $N$ is the number of *pairs* of $x$ and $y$ values. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The covariance matrix can be any size. So we can explore all possible covariances simultaneously. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.68569351, -0.042434 , 1.27431544, 0.51627069],\n", " [-0.042434 , 0.18997942, -0.32965638, -0.12163937],\n", " [ 1.27431544, -0.32965638, 3.11627785, 1.2956094 ],\n", " [ 0.51627069, -0.12163937, 1.2956094 , 0.58100626]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#add rowvar = False to indicate we want cov\n", "#over our columns and not rows\n", "np.cov(data, rowvar=False, ddof=1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To read this larger matrix, recall the column descriptions: sepal length (0), sepal width (1), pedal length (2), pedal width (3). Then use the row and column index to identify which sample covariance is being computed. The row and column indices are interchangable because it is symmetric. For example, the sample covariance of sepal length with sepal width is $-0.042$ centimeters." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Scatter Plot\n", "----\n", "\n", "To get a better sense of this data, we can use a scatter plot. Let's see a high positive sample covariance and a low positive sample covariance. Sepal length and pedal length have a high positive sample covariance and sepal width with pedal width has a low positive sample covariance." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(data[:,0], data[:,2])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "What happened? It turns out, our data are not sorted according to sepal length, so the lines go from value to value. There is no reason that our data should be ordered by sepal length, so we need to use dot markers to get rid of the lines." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title('Sample Covariance: 1.27 cm')\n", "plt.plot(data[:,0], data[:,2], 'o')\n", "plt.xlabel('Sepal Length [cm]')\n", "plt.ylabel('Pedal Length [cm]')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now the other plot" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title('Sample Covariance: 0.52 cm')\n", "plt.plot(data[:,0], data[:,3], 'o')\n", "plt.xlabel('Sepal Length [cm]')\n", "plt.ylabel('Pedal Width [cm]')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "That is suprising! The \"low\" sample variance plot looks like it has as much correlation as the \"high\" sample covariance. That's because sample variance measures both the underlying variance of both dimensions and their correlation. The reason this is a low sample covariance is that the y-values change less than in the first plot." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Sample Correlation\n", "====\n", "\n", "Since the covariance includes the correlation between variables and the variance of the two variables, sample correlation tries to remove the variacne so we can view only correlation.\n", "\n", "$$r_{xy} = \\frac{\\sigma_{xy}}{\\sigma_x \\sigma_y}$$\n", "\n", "Similar to the covariance, there is something called the **correlation matrix** or **the normalized covariance matrix**." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , -0.11756978, 0.87175378, 0.81794113],\n", " [-0.11756978, 1. , -0.4284401 , -0.36612593],\n", " [ 0.87175378, -0.4284401 , 1. , 0.96286543],\n", " [ 0.81794113, -0.36612593, 0.96286543, 1. ]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.corrcoef(data, rowvar=False)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Note that we don't have to pass in `ddof` because it cancels in the correlation coefficient expression. Now we also see that the two plots from above have similar correlations as we saw visually." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Caveats of Correlation\n", "====" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Let's try creating some *synthetic* data to observe properties of correlation. I'm using the `rvs` function to sample data from distributions using `scipy.stats.`" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = scipy.stats.norm.rvs(size=15, scale=4)\n", "y = scipy.stats.norm.rvs(size=15, scale=4)\n", "cor = np.corrcoef(x,y)[0,1]\n", "plt.title('r = {}'.format(cor))\n", "plt.plot(x, y, 'o')\n", "plt.xlabel('x')\n", "plt.ylabel('$y$')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = scipy.stats.norm.rvs(size=100, scale=4)\n", "y = x ** 2\n", "cor = np.corrcoef(x,y)[0,1]\n", "plt.title('r = {}'.format(cor))\n", "plt.plot(x, y, 'o')\n", "plt.xlabel('x')\n", "plt.ylabel('$x^2$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "See that $x^2$ is an analytic function of $x$, but it has a lower correlation than two independent random numbers. That's because correlation coefficients are unreliable for non-linear behavior. Another example:" ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }