{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Solution to Assignment 1\n", "\n", "**MATH7502 2019, Semester 2**\n", "\n", "[Assignment 1 questions](https://courses.smp.uq.edu.au/MATH7502/2019/ass1.pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) $1'w$ is the number of words in the document\n", "\n", "(b) $w_{282} = 0$ implies that the 282'nd word in the dictionary has $0$ occurences in the document.\n", "\n", "(c)\n", "$\n", "h = \\frac{1}{\\mathbf{1}' w} w.\n", "$\n", "\n", "(d)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5-element Array{Pair{String,Int64},1}:\n", " \"king\" => 1698\n", " \"love\" => 1279\n", " \"man\" => 1033\n", " \"sir\" => 721 \n", " \"god\" => 555 " ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using HTTP, JSON\n", "\n", "data = HTTP.request(\"GET\",\n", "\"https://ocw.mit.edu/ans7870/6/6.006/s08/lecturenotes/files/t8.shakespeare.txt\")\n", "shakespeare = String(data.body)\n", "shakespeareWords = split(shakespeare)\n", "\n", "jsonWords = HTTP.request(\"GET\",\n", "\"https://raw.githubusercontent.com/\"*\n", "\"h-Klok/StatsWithJuliaBook/master/1_chapter/jsonCode.json\")\n", "parsedJsonDict = JSON.parse( String(jsonWords.body))\n", "\n", "keywords = Array{String}(parsedJsonDict[\"words\"])\n", "numberToShow = parsedJsonDict[\"numToShow\"]\n", "wordCount = Dict([(x,count(w -> lowercase(w) == lowercase(x), shakespeareWords))\n", " for x in keywords])\n", "\n", "sortedWordCount = sort(collect(wordCount),by=last,rev=true)\n", "sortedWordCount[1:numberToShow]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(e) Clearly there are multiple answers. One possible answer is to use the countmap() function from StatsBase" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20-element Array{Pair{String,Int64},1}:\n", " \"the\" => 27549\n", " \"and\" => 26037\n", " \"i\" => 19540\n", " \"to\" => 18700\n", " \"of\" => 18010\n", " \"a\" => 14383\n", " \"my\" => 12455\n", " \"in\" => 10671\n", " \"you\" => 10630\n", " \"that\" => 10487\n", " \"is\" => 9145 \n", " \"for\" => 7982 \n", " \"with\" => 7931 \n", " \"not\" => 7643 \n", " \"your\" => 6871 \n", " \"his\" => 6749 \n", " \"be\" => 6700 \n", " \"but\" => 5886 \n", " \"he\" => 5884 \n", " \"as\" => 5882 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using HTTP, JSON, StatsBase\n", "\n", "data = HTTP.request(\"GET\", \"https://ocw.mit.edu/ans7870/6/6.006/s08/lecturenotes/files/t8.shakespeare.txt\")\n", "shakespeare = String(data.body)\n", "shakespeareWords = lowercase.(split(shakespeare))\n", "\n", "numberToShow = 20\n", "wordCount = countmap(shakespeareWords)\n", "sortedWordCount = sort(collect(wordCount),by=last,rev=true)\n", "sortedWordCount[1:numberToShow]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just write $a$ as $a+b-b$. Then:\n", "$$\n", "||a|| = ||a + b +(-b)|| \\le ||a+b|| + ||-b|| = ||a+b|| + ||b||\n", "$$\n", "Hence,\n", "$$\n", "||a|| - ||b|| \\le ||a+b||\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a)\n", "\n", "(i) $\\beta = e_1$: Tommorow's sales prediction is having sales the same as today.\n", "\n", "(ii) $\\beta = 2e_1 - e_2$: Tommorow's sales predition is twice the sales of today take away the sales of yesterday.\n", "\n", "(iii) $\\beta = e_6$: Tommorow's sales prediction is having the same sales as $6$ days ago.\n", "\n", "(iv) $\\beta = \\frac{1}{2} e_1 + \\frac{1}{2} e_2$: Tomorrow's sales prediction is the average of today and yesterday.\n", "\n", "(b)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loss is: 6.397265063244324\n", "Loss is: 6.8827023607315905\n", "Loss is: 6.4291797868524965\n", "Loss is: 8.27291621054637\n", "Loss is: 2.673542339803326\n" ] } ], "source": [ "using Distributions, Random, LinearAlgebra, Statistics\n", "Random.seed!(0)\n", "\n", "T, M, N = 100, 10, 1000\n", "\n", "ee(i) = begin v = zeros(M); v[i] = 1; v end #just a function for e_i\n", "predict(beta,data,t) = data[t-1:-1:t-M]'*beta #notice reverse order\n", "makeData() = [cos(t*2pi/7) + rand(Normal(0,0.2)) for t in 1:T] \n", "loss(data,pred) = norm(data[M+1:T] - pred) #L_2 loss\n", "\n", "betas = [ee(1), \n", " 2ee(1)-ee(2),\n", " ee(6),\n", " (ee(1) + ee(2))/2,\n", " ee(7)] #notice this additional beta not specified in the question\n", "\n", "\n", "for beta in betas\n", " losses = []\n", " for _ in 1:N\n", " data = makeData()\n", " pred = [predict(beta,data,t) for t in M+1:T]\n", " push!(losses,loss(data,pred))\n", " end\n", " println(\"Loss is: \", mean(losses))\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can thus be seen that from the four specified estimators the first one does the best (slightly better than the third). However if we specify another estimator with $\\beta = e_7$ we do much better." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$||x||_1 = |x_1| + \\ldots + |x_n|$\n", "\n", "(i) $||x||_1 = |x_1| + \\ldots + |x_n| \\ge 0$ trivially.\n", "\n", "(ii) $||x+y||_1 \\le ||x||_1 + ||y||_1$:\n", "\n", "$$\n", "||x+y||_1 = \\sum_{i=1}^n |x_i + y_i| \\le \\sum_{i=1}^n |x_i| + |y_i| = ||x||_1 + ||y||_1\n", "$$\n", "This follows from the triangle inequality for real numbers $|a+b| \\le |a| + |b|$\n", "\n", "(iii) $||x||_1 = 0$ if and only if $x=0$. Follows trivially.\n", "\n", "(iv) $||\\beta x ||_1 = |\\beta| ||x||_1$:\n", "\n", "$$\n", "|| \\beta x||_1 = \\sum_{i=1}^n |\\beta x_i| = |\\beta| \\sum_{i=1}^n |x_i| = |\\beta| ||x||_1.\n", "$$\n", "\n", "---\n", "\n", "$||x||_\\infty = \\max\\{|x_1|,\\ldots,|x_n|\\}$\n", "\n", "(i) $||x||_\\infty \\ge |x_i|\\ge 0$ for all $i$. Hence $||x||_\\infty \\ge 0 $.\n", "\n", "(ii) $||x+y||_\\infty \\le ||x||_\\infty + ||y||_\\infty$:\n", "\n", "$||x+y||_\\infty = \\max \\{ |x_1 + y_1|,\\ldots, |x_n + y_n| \\} = |x_i + y_i| \\le |x_i| + |y_i|$ for some $i$.\n", "\n", "And this is $\\le |x_j| + |y_k|$ for the $j$ and $k$ that determine $||x||_\\infty$ and $||y||_\\infty$ respectivly. Hence,\n", "\n", "$$\n", "||x+y||_\\infty \\le ||x||_\\infty + ||y||_\\infty.\n", "$$\n", "\n", "(iii) $||x||_\\infty = 0$ if and only if $x=0$. Follows trivially.\n", "\n", "(iv) $ || \\beta x||_\\infty = |\\beta| ||x||_\\infty.$\n", "\n", "This is by pulling out the constant $|\\beta|$ out of the maximum: $\\max\\{|a|z,|a|u,|a|v\\} = |a| \\max\\{z,u,v\\}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a)\n", "\n", "$$\n", "\\int_\\alpha^\\beta p(x) \\, dx = \\Big[ c_1 x + c_2 \\frac{1}{2} x^2 + c_3 \\frac{1}{3} x^3 + \\ldots + c_n \\frac{1}{n} x^n \\Big|^\\beta_\\alpha\n", "$$\n", "\n", "$$\n", "=c_1 \\beta + c_2 \\frac{1}{2} \\beta^2 + c_3 \\frac{1}{3} \\beta^3 + \\ldots + c_n \\frac{1}{n} \\beta^n - \n", "(c_1 \\alpha + c_2 \\frac{1}{2} \\alpha^2 + c_3 \\frac{1}{3} x^3 + \\ldots + c_n \\frac{1}{n} \\alpha^n)\n", "$$\n", "\n", "$$\n", "= c_1 (\\beta - \\alpha) + c_2\\frac{1}{2}(\\beta^2 - \\alpha^2) + \\ldots + c_n\\frac{1}{n}(\\beta^n - \\alpha^n)= c^T a\n", "$$\n", "\n", "where $c = (c_1,\\ldots,c^n)^T$ and \n", "$$\n", "a = \\Big(\\beta - \\alpha, \\frac{\\beta^2 - \\alpha^2}{2},\\ldots, \\frac{\\beta^n-\\alpha^n}{n}\\Big)^T.\n", "$$\n", "\n", "(b) Since $p(\\alpha) = c_1 + c_2 \\alpha + c_3 \\alpha^2 + \\ldots + c_n x^{n-1}$ we have:\n", "\n", "$$\n", "p'(\\alpha) = c_2 + 2 c_3 \\alpha + 3 c_4 \\alpha^2 + \\ldots + (n-1) c_n \\alpha^{n-2} = b^T (c_1,\\ldots,c_n)^T.\n", "$$\n", "\n", "Hence,\n", "$$\n", "b = \\Big(0,1,2\\alpha,3\\alpha^2, \\ldots, (n-1) \\alpha^{n-2}\\Big)^T.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Testing for homogeniety: $f(\\alpha x) = \\alpha f(x)$:\n", "\n", "$\\phi(-1(-1,1,1)) = (-1) \\phi(-1,1,1)$ implies $\\phi(1,-1,-1) = -1 \\times 1$ but $\\phi(1,-1,1) = 1$. So the test fails. Hence (ii) is the correct answer. $\\phi$ cannot be linear.\n", "\n", "(b) One modifcation can be $\\phi(1,1,1) = 5$, $\\phi(2,2,2) = 10$ and $\\phi(3,3,3) = 15$. In this case denote $a=(1,1,1)$. We now have $\\phi(a+2a) = \\phi(3a)$ and $\\phi(2a) = 2 \\phi(a)$. This function can be linear however it also can be modified as to be non-linear based on other points. So the answer is (ii)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a)\n", "\n", "$$\n", "L(a) = || x - a {\\bf 1} || = \\sqrt{\\sum_{i=1}^n (x_i -a)^2}\n", "$$\n", "\n", "The minimizer of $L(a)$ is also the minimizer of $\\tilde{L}(a) = L(a)^2$.\n", "\n", "$$\n", "\\tilde{L}(a) = \\sum_{i=1}^n (x_i -a)^2 = \\sum_{i=1}^n (x_i^2 -2x_i a + a^2) = n a^2 - 2 (\\sum x_i) a + \\sum x_i^2.\n", "$$\n", "\n", "This can be done via calculus however also observed that $\\tilde{L}(a)$ is an upward facing parabula and is hence minimized at,\n", "$$\n", "a^* = \\frac{- (- 2 \\sum x_i)}{2(n)} = \\overline{x}\n", "$$\n", "where $\\overline{x}$ is the mean of $x_1,\\ldots,x_n$.\n", "\n", "(b) For gradient descent observe that $\\frac{d}{a} \\tilde{L}(a) = 2(n a-\\sum x_i)$. Denote $S = \\sum x_i$ and hence the gradient is $2(n a - S)$.\n", "\n", "Gradient descent then starts at some $a_0$ and implements,\n", "$$\n", "a_{k+1} = a_k - 2 \\eta(n a_k - S) = (1 - 2 \\eta n)a_k + 2 \\eta S\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The sample mean is: 9.973653925527081\n", "Executed 42 steps\n", "The result of gradient descent is 9.977058990472438\n" ] } ], "source": [ "using Statistics, Random\n", "Random.seed!(1)\n", "\n", "n = 100;\n", "data = 9 .+ 2*rand(n);\n", "xbar = mean(data) #sample mean\n", "println(\"The sample mean is: \",xbar)\n", "S = sum(data);\n", "\n", "function gd(a0,eta)\n", " a = a0\n", " aPrev = -a\n", " numSteps = 0 \n", " while abs(a-aPrev) > 10^-3 && numSteps < 1000 \n", " aPrev = a\n", " a = (1-2*eta*n)*a + 2*eta*S\n", " numSteps += 1\n", " end\n", " println(\"Executed \",numSteps, \" steps\")\n", " a\n", "end\n", "aStar = gd(50,0.001)\n", "println(\"The result of gradient descent is \", aStar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(c) We have a recursion of the form $a_{k+1} = \\kappa a_k + \\gamma$ where $\\kappa = 1-2 \\eta n$ and $\\gamma = 2 \\eta S$\n", "\n", "Notice:\n", "\n", "$$\n", "a_1 = \\kappa a_0 + \\gamma\n", "$$\n", "\n", "$$\n", "a_2 = \\kappa^2 a_0 + \\kappa \\gamma + \\gamma\n", "$$\n", "\n", "$$\n", "a_3 = \\kappa^3 a_0 + \\kappa^2\\gamma + \\kappa \\gamma + \\gamma\n", "$$\n", "\n", "and in general,\n", "\n", "$$\n", "a_k = \\kappa^k + \\gamma \\sum_{i=0}^{k-1} \\kappa^i = \\kappa^k + \\gamma \\frac{\\kappa^{k}-1}{\\kappa-1} = \\kappa^k(1 + \\frac{\\gamma}{\\kappa-1}) + \\frac{\\gamma}{1-\\kappa} = \\kappa^k(1 + \\frac{\\gamma}{\\kappa-1}) + \\overline{x}.\n", "$$\n", "\n", "Hence we have that $\\lim_{k \\to \\infty} a_k$ diverges if $|\\kappa| \\ge 1$ and otherwise converges to $\\overline{x}$. So we need $|1-2 \\eta n| < 1$. With $\\eta > 0$ we always have $1-2\\eta n < 1$ so the requirment is $-1 < 1-2 \\eta n$. Hence we need $\\eta < \\frac{1}{n}$" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Executed 1000 steps\n" ] }, { "data": { "text/plain": [ "6.075639453913123e80" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "badEta = 1/n + 0.001\n", "gd(50,badEta)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Executed 52 steps\n" ] }, { "data": { "text/plain": [ "9.974019541591606" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "goodEta = 1/n - 0.001\n", "gd(50,goodEta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(assume for simplicity that $n$ is even)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Define the $n \\times n$ matrices $A_1$, $A_2$ (these are composed of collumns of either $e_i$ or $0$):\n", "\n", "$$\n", "A_1 = [e_1~0~e_3~0~\\ldots~e_{n-1}~0],\n", "\\qquad\n", "A_2 = [0~e_2~0~e_4~\\ldots~0~e_n],\n", "$$\n", "\n", "Then $f(x) = \\Big(f_1(x),~f_2(x)\\Big)$ has components,\n", "$$\n", "f_1(x) = ||A_1 x||^2 + {\\bf 1}^T(A_2 x),\n", "\\qquad\n", "f_2(x) = ||A_2 x||^2 + {\\bf 1}^T(A_1 x).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(b) The $2 \\times n$ Jacobian matrix $D(x)$ can be worked out directly (e.g. assume $n$ is even): \n", "\n", "$$\n", "D(x) =\n", "\\left[\n", "\\begin{matrix}\n", "2x_1 & 1 & 2x_3 & 1 & \\ldots & 2x_{n-1} & 1\\\\\n", "1 & 2x_2 & 1 & 2x_3 & \\ldots & 1 & 2x_n\n", "\\end{matrix}\n", "\\right].\n", "$$\n", "It can also be worked out via vectors. The first row as $\\nabla f_1(x)^T$ and second row as $\\nabla f_2(x)^T$. Observe that $||Bx||^2 = x^T B^T B x$ and that $\\nabla ||Bx||^2 = 2 B^T B x$. Further observe that $A_1^TA_1 = A_1$ and $A_2^T A_2 = A_2$. Also $A_1$ and $A_2$ are symmetric. Hence,\n", "\n", "$$\n", "\\nabla f_1(x) = 2 A_1 x + {\\bf 1}^T A_2,\n", "\\qquad\n", "\\nabla f_2(x) = 2 A_2 x + {\\bf 1}^T A_1.\n", "$$\n", "\n", "Or\n", "\n", "$$\n", "D(x) = \n", "\\left[\n", "\\begin{matrix}\n", "2 x^T A_1 + {\\bf 1}^T A_2 \\\\\n", "2 x^T A_2 + {\\bf 1}^T A_1\n", "\\end{matrix}\n", "\\right].\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(c) and (d) Now take $z={\\bf 1}$ hence \n", "$$\n", "D(z) = \n", "\\left[\n", "\\begin{matrix}\n", "2 {\\bf 1}^T A_1 + {\\bf 1}^T A_2 \\\\\n", "2 {\\bf 1}^T A_2 + {\\bf 1}^T A_1\n", "\\end{matrix}\n", "\\right]\n", "=\n", "\\left[\n", "\\begin{matrix}\n", "{\\bf 1}^T (2 A_1 + A_2) \\\\\n", "{\\bf 1}^T (2 A_2 + A_1)\n", "\\end{matrix}\n", "\\right]\n", "=\n", "\\left[\n", "\\begin{matrix}\n", "2 & 1 & 2 & 1 & \\ldots &2 &1 \\\\\n", "1 & 2 & 1 & 2 & \\ldots &1 &2\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×6 Array{Float64,2}:\n", " 2.0 1.0 2.0 1.0 2.0 1.0\n", " 1.0 2.0 1.0 2.0 1.0 2.0" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 6;\n", "A1 = [isodd(i) && i == j ? 1 : 0 for i in 1:n, j in 1:n ];\n", "A2 = [iseven(i) && i == j ? 1 : 0 for i in 1:n, j in 1:n ];\n", "D = [ones(n)'*(2A1+A2)\n", " ones(n)'*(2A2+A1)]" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [], "source": [ "using LinearAlgebra" ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2-element Array{Float64,1}:\n", " 6.0\n", " 6.0" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = [norm(A1*x)^2 + ones(n)'*A2*x, norm(A2*x)^2 + ones(n)'*A1*x]\n", "f1 = f(ones(n))" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fApprox (generic function with 1 method)" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fApprox(x) = f1 + D*(x-ones(n))" ] }, { "cell_type": "code", "execution_count": 145, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "After trying 100000 random vectors within raidus 0.5, the worst has is 0.2499577140111187\n", "After trying 100000 random vectors within raidus 0.25, the worst has is 0.0624535565900629\n", "After trying 100000 random vectors within raidus 1.0, the worst has is 0.99943513971916\n" ] } ], "source": [ "#This function takes random vectors of radius r around z=ones(n) and looks for the worst one\n", "function randomWorst(r)\n", " N = 10^5\n", " worst = -Inf\n", " for _ in 1:N\n", " v = rand(n)\n", " v = r*v/norm(v)\n", " x = ones(n) + v\n", " err = norm(f(x) - fApprox(x))\n", " if err > worst\n", " worst = err\n", " end\n", " end\n", " println(\"After trying $(N) random vectors within raidus $(r), the worst has is $(worst)\")\n", "end\n", "randomWorst(0.5)\n", "randomWorst(0.25)\n", "randomWorst(1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Note: There is also an analytical solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Listing 9.9 from SWJ](https://github.com/h-Klok/StatsWithJuliaBook/blob/master/9_chapter/kMeansManual.jl)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Counts of clusters (manual implementation): [899, 952, 1149]\n" ] } ], "source": [ "using RDatasets, Distributions, Random\n", "Random.seed!(1)\n", "\n", "k = 3\n", "\n", "xclara = dataset(\"cluster\", \"xclara\")\n", "n,_ = size(xclara)\n", "dataPoints = [convert(Array{Float64,1},xclara[i,:]) for i in 1:n]\n", "shuffle!(dataPoints)\n", "\n", "xMin,xMax = minimum(first.(dataPoints)),maximum(first.(dataPoints))\n", "yMin,yMax = minimum(last.(dataPoints)),maximum(last.(dataPoints))\n", "\n", "means = [[rand(Uniform(xMin,xMax)),rand(Uniform(yMin,yMax))] for _ in 1:k]\n", "labels = rand([1,k],n)\n", "prevMeans = -means\n", "\n", "while norm(prevMeans - means) > 0.001\n", " prevMeans = means\n", " labels = [findmin([norm(means[i]-x) for i in 1:k])[2] for x in dataPoints]\n", " means = [sum(dataPoints[labels .== i])/sum(labels .==i) for i in 1:k]\n", "end\n", "\n", "cnts = [sum(labels .== i) for i in 1:k]\n", "\n", "println(\"Counts of clusters (manual implementation): \", cnts)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots; pyplot()\n", "scatter(first.(dataPoints[labels .== 1]),last.(dataPoints[labels .== 1]),c = :yellow,legend=false)\n", "scatter!(first.(dataPoints[labels .== 2]),last.(dataPoints[labels .== 2]),c = :red)\n", "scatter!(first.(dataPoints[labels .== 3]),last.(dataPoints[labels .== 3]),c = :blue)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now fix some labels... See lines 12-14 for fixing lables and lines 26-28 for enforcing it in the algorithm" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Counts of clusters (manual implementation): [1024, 1004, 972]\n" ] }, { "data": { "text/plain": [ "3-element Array{Array{Int64,1},1}:\n", " [15, 21, 65, 73, 87, 110, 116, 119, 136, 144 … 2678, 2733, 2814, 2839, 2883, 2900, 2915, 2955, 2995, 3000] \n", " [29, 57, 95, 160, 198, 228, 237, 298, 330, 338 … 2863, 2892, 2896, 2925, 2929, 2930, 2945, 2948, 2958, 2990]\n", " [279, 890, 991, 1044, 1105, 1121, 1272, 1377, 1945, 1961, 2170, 2394, 2525, 2855] " ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using RDatasets, Plots, Distributions, Random, LinearAlgebra\n", "Random.seed!(1)\n", "\n", "k = 3\n", "\n", "xclara = dataset(\"cluster\", \"xclara\")\n", "n,_ = size(xclara)\n", "dataPoints = [convert(Array{Float64,1},xclara[i,:]) for i in 1:n]\n", "shuffle!(dataPoints)\n", "\n", "#Say these are the fixed labels - they are based on the location\n", "fixedLabels = [ filter((k)->norm(dataPoints[k] - [70,70]) < 20,1:n),\n", " filter((k)->norm(dataPoints[k] - [50,50]) < 5,1:n),\n", " filter((k)->norm(dataPoints[k] - [90,-5]) < 5,1:n)]\n", "\n", "xMin,xMax = minimum(first.(dataPoints)),maximum(first.(dataPoints))\n", "yMin,yMax = minimum(last.(dataPoints)),maximum(last.(dataPoints))\n", "\n", "means = [[rand(Uniform(xMin,xMax)),rand(Uniform(yMin,yMax))] for _ in 1:k]\n", "labels = rand([1,k],n)\n", "prevMeans = -means\n", "\n", "while norm(prevMeans - means) > 0.001\n", " prevMeans = means\n", " labels = [findmin([norm(means[i]-x) for i in 1:k])[2] for x in dataPoints]\n", " for k in 1:3\n", " labels[fixedLabels[k]] .= k\n", " end\n", " means = [sum(dataPoints[labels .== i])/sum(labels .==i) for i in 1:k]\n", "end\n", "\n", "cnts = [sum(labels .== i) for i in 1:k]\n", "\n", "println(\"Counts of clusters (manual implementation): \", cnts)\n", "fixedLabels" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots; pyplot()\n", "scatter(first.(dataPoints[labels .== 1]),last.(dataPoints[labels .== 1]),c = :yellow,legend=false)\n", "scatter!(first.(dataPoints[labels .== 2]),last.(dataPoints[labels .== 2]),c = :red)\n", "scatter!(first.(dataPoints[labels .== 3]),last.(dataPoints[labels .== 3]),c = :blue)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution to Question 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have that for $i=1,\\ldots,k$: $b_i = \\sum_{j=1}^m \\alpha_j a_j$. Further, $c = \\sum_{i=1}^k \\beta_i b_i$.\n", "\n", "Hence \n", "$$\n", "c = \\sum_{i=1}^k \\beta_i \\sum_{j=1}^m \\alpha_j a_j = \\sum_{i=1}^k \\sum_{j=1}^m \\beta_i a_j = \\sum_{j=1}^m \\sum_{i=1}^k\\beta_i \\alpha_j a_j = \\sum_{j=1}^m a_j\\sum_{i=1}^k\\beta_i \\alpha_j = \\sum_{j=1}^m a_j \\gamma_j\n", "$$\n", "where $\\gamma_{j} = \\sum_{i=1}^k\\beta_i \\alpha_j$. Then $c$ is a linear combination of $a_1,\\ldots,a_m$." ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.1.1", "language": "julia", "name": "julia-1.1" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.1.1" } }, "nbformat": 4, "nbformat_minor": 2 }