From 89437dea68fb5e301d525981a68605e1575feec7 Mon Sep 17 00:00:00 2001 From: ilyavasilev Date: Thu, 5 Oct 2023 00:27:43 +0300 Subject: [PATCH] Make homework 1 V0.1 --- HW1/Problem_6_sol.ipynb | 438 +++++++++++++++++++++++++ HW1/Solutions_HW1.ipynb | 153 +++++++++ HW1/kmeans_solution.ipynb | 668 ++++++++++++++++++++++++++++++++++++++ 3 files changed, 1259 insertions(+) create mode 100755 HW1/Problem_6_sol.ipynb create mode 100755 HW1/Solutions_HW1.ipynb create mode 100755 HW1/kmeans_solution.ipynb diff --git a/HW1/Problem_6_sol.ipynb b/HW1/Problem_6_sol.ipynb new file mode 100755 index 0000000..0807c6a --- /dev/null +++ b/HW1/Problem_6_sol.ipynb @@ -0,0 +1,438 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "from numba import njit\n", + "import time" + ], + "metadata": { + "id": "Qaq--qm2_Qfm" + }, + "execution_count": 19, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## The Hofstadter-Conway sequence $a(n)$: \n", + "\n", + "$a(1) = 1, a(2) = 1, ... , a(n) = a(a(n-1)) + a(n - a(n - 1))$" + ], + "metadata": { + "id": "9A0VfT5yePm5" + } + }, + { + "cell_type": "code", + "source": [ + "n = int(1e3)\n", + "a = np.ones(n, dtype = int)" + ], + "metadata": { + "id": "l_UpCyuqQBwt" + }, + "execution_count": 20, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## **First implemination:** pre-allocating `numpy` array and filling it using `for` loop." + ], + "metadata": { + "id": "GkeqAQzceyOD" + } + }, + { + "cell_type": "code", + "source": [ + "def HC_func1(array, n):\n", + " if n < 1:\n", + " raise Exception(\"n must be positive\")\n", + " elif n == 1:\n", + " array[0] = 1\n", + " else:\n", + " array[0], array[1] = 1, 1\n", + "\n", + " for idx in range(2, n):\n", + " array[idx] = array[array[idx - 1] - 1] + array[idx - array[idx - 1]]" + ], + "metadata": { + "id": "i1B9t7PwPrB-" + }, + "execution_count": 21, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "%time HC_func1(a, n)\n", + "%time HC_func1(a, n)\n", + "%time HC_func1(a, n)" + ], + "metadata": { + "id": "MlymyYQDPscK", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "c7f93f12-16f3-4b18-af01-b7c85ebcc5c9" + }, + "execution_count": 22, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 1.73 ms, sys: 0 ns, total: 1.73 ms\n", + "Wall time: 1.74 ms\n", + "CPU times: user 1.62 ms, sys: 104 µs, total: 1.73 ms\n", + "Wall time: 1.73 ms\n", + "CPU times: user 1.72 ms, sys: 0 ns, total: 1.72 ms\n", + "Wall time: 1.73 ms\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Second implemination:** cumulatively appending `python` list and converting it to `numpy` array." + ], + "metadata": { + "id": "mtt236qrfDnI" + } + }, + { + "cell_type": "code", + "source": [ + "def HC_func2(n):\n", + " if n < 1:\n", + " raise Exception(\"n must be positive\")\n", + " elif n == 1:\n", + " result = [1]\n", + " else:\n", + " result = [1, 1]\n", + " for idx in range(2, n):\n", + " elem = result[result[idx - 1] - 1] + result[idx - result[idx - 1]]\n", + " result.append(elem)\n", + " return np.array(result)" + ], + "metadata": { + "id": "LY9YUjFFNIs2" + }, + "execution_count": 23, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "%time HC_func2(n)\n", + "%time HC_func2(n)\n", + "%time HC_func2(n)\n", + "\"\"" + ], + "metadata": { + "id": "9X9tMCeYVYhm", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 140 + }, + "outputId": "957c3a66-7e73-4997-8f7c-aead3217beab" + }, + "execution_count": 24, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 779 µs, sys: 0 ns, total: 779 µs\n", + "Wall time: 785 µs\n", + "CPU times: user 720 µs, sys: 13 µs, total: 733 µs\n", + "Wall time: 737 µs\n", + "CPU times: user 736 µs, sys: 0 ns, total: 736 µs\n", + "Wall time: 740 µs\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "''" + ], + "application/vnd.google.colaboratory.intrinsic+json": { + "type": "string" + } + }, + "metadata": {}, + "execution_count": 24 + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Second implemination:** compiled (`jit`) version." + ], + "metadata": { + "id": "tKz26-9RfUex" + } + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "id": "7h5Woys4-Z3S" + }, + "outputs": [], + "source": [ + "@njit\n", + "def HC_func3(array, n):\n", + " if n < 1:\n", + " raise Exception(\"n must be positive\")\n", + " elif n == 1:\n", + " array[0] = 1\n", + " else:\n", + " array[0], array[1] = 1, 1\n", + "\n", + " for idx in range(2, n):\n", + " array[idx] = array[array[idx - 1] - 1] + array[idx - array[idx - 1]]" + ] + }, + { + "cell_type": "code", + "source": [ + "%time HC_func3(a, n)\n", + "%time HC_func3(a, n)\n", + "%time HC_func3(a, n)" + ], + "metadata": { + "id": "6rhqO950CzUg", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "06e1ac2d-11f2-49a2-e3a9-7b8b165e42b0" + }, + "execution_count": 26, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 235 ms, sys: 19.7 ms, total: 255 ms\n", + "Wall time: 298 ms\n", + "CPU times: user 23 µs, sys: 0 ns, total: 23 µs\n", + "Wall time: 26.7 µs\n", + "CPU times: user 19 µs, sys: 0 ns, total: 19 µs\n", + "Wall time: 22.6 µs\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Let's compare execution time" + ], + "metadata": { + "id": "6WubSLEUfcLW" + } + }, + { + "cell_type": "code", + "source": [ + "def comp_time_res():\n", + " res1, res2, res3 = np.array([]), np.array([]), np.array([])\n", + " for k in list(map(int, [1e1, 1e2, 1e3, 1e4, 1e5])):\n", + " data = np.ones(k, dtype = int)\n", + "\n", + " start_time = time.time()\n", + " HC_func1(data, k)\n", + " end_time = time.time()\n", + " res1 = np.append(res1, end_time - start_time)\n", + "\n", + " start_time = time.time()\n", + " HC_func2(k)\n", + " end_time = time.time()\n", + " res2 = np.append(res2, end_time - start_time)\n", + "\n", + " start_time = time.time()\n", + " HC_func3(data, k)\n", + " end_time = time.time()\n", + " res3 = np.append(res3, end_time - start_time)\n", + " return (res1, res2, res3)" + ], + "metadata": { + "id": "LELxb0HRoWvh" + }, + "execution_count": 27, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "import matplotlib.pyplot as plt\n", + "first_func, second_func, third_func = comp_time_res()\n", + "x = np.array([1e1, 1e2, 1e3, 1e4, 1e5], dtype=int)\n", + "\n", + "plt.plot(x, first_func)\n", + "plt.plot(x, second_func)\n", + "plt.plot(x, third_func)\n", + "\n", + "plt.xlabel(\"n\", fontsize=14)\n", + "plt.ylabel(\"comp time\", fontsize=14)\n", + "plt.legend([\"HC_func_1\", \"HC_func_2\", \"HC_func_3\"]);" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 455 + }, + "id": "4MPOWTsXtZhU", + "outputId": "7299eddf-166f-4e26-9058-716eaefe6168" + }, + "execution_count": 28, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## The option with a `jit` compiler turned out to be the fastest. Let's use it to calculate $a(10^8)$:" + ], + "metadata": { + "id": "KDEaQcaifhfn" + } + }, + { + "cell_type": "code", + "source": [ + "n = int(1e8)\n", + "a = np.ones(n, dtype = int)\n", + "\n", + "%time HC_func3(a, n)\n", + "%time HC_func3(a, n)\n", + "%time HC_func3(a, n)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "dhgtJB8X0fkO", + "outputId": "e01fe169-8137-4a64-88f9-e08d57600fcd" + }, + "execution_count": 29, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 586 ms, sys: 4.05 ms, total: 590 ms\n", + "Wall time: 588 ms\n", + "CPU times: user 586 ms, sys: 4.75 ms, total: 590 ms\n", + "Wall time: 586 ms\n", + "CPU times: user 587 ms, sys: 2.11 ms, total: 589 ms\n", + "Wall time: 584 ms\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "x = np.arange(1, n + 1, 1, dtype=int)\n", + "plt.plot(x, a);\n", + "plt.title(\"$a(10^8)$\", fontsize=14);" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 476 + }, + "id": "fggJi6PlgQOv", + "outputId": "7a4d3f18-b3d8-4002-d4b5-38cae766af9f" + }, + "execution_count": 30, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Finally we display the graph $f(n) = a(n)/n$ for $n = 1, 2, ..., 2000$" + ], + "metadata": { + "id": "pH6dsdzmhBmv" + } + }, + { + "cell_type": "code", + "source": [ + "n = int(2000)\n", + "a = np.ones(n, dtype = int)\n", + "HC_func3(a, n)\n", + "\n", + "x = np.arange(1, n + 1, 1, dtype=int)\n", + "y = a * np.array([1 / (i + 1) for i in range(n)])\n", + "plt.plot(x, y);\n", + "plt.title(\"a(n)/n\", fontsize=14);" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 453 + }, + "id": "tm9UvLrD9wfW", + "outputId": "e0b72afe-3cd1-444b-8849-744c827a7f75" + }, + "execution_count": 31, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file diff --git a/HW1/Solutions_HW1.ipynb b/HW1/Solutions_HW1.ipynb new file mode 100755 index 0000000..1a96017 --- /dev/null +++ b/HW1/Solutions_HW1.ipynb @@ -0,0 +1,153 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "### **Problem 1(5)**:\n", + "\n", + "Consider the matrix $H(v) = \\hat{1} - 2vv^T$, where $v$ is a unit column vector. What is the rank of the matrix $H(v)$? Prove that it is orthogonal.\n" + ], + "metadata": { + "id": "8rZACDYdX9AU" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Solution:**\n", + "\n", + "Let we have a vector $v = (v_{1} v_{2} ... v_{n})^T$ that, by condition, is unit, i.e. $v^Tv=1$.Then the matrix $\\underset{n\\times{}n}H$ has the following form:\n", + "\n", + "$H(v) = \\hat{1} - 2vv^T = (h_{ij}), 1\\leq{i,j}\\leq{n}$, where $h_{ij} = \\begin{equation}\n", + " \\begin{cases}\n", + " 1-2v_{i}^2, i = j\\\\\n", + " -2v_{i}v_{j}, i \\ne j\n", + " \\end{cases}.\n", + "\\end{equation}$\n", + "\n", + "It can be seen that the matrix $H$ is symmetrical. Let us prove that it is orthogonal, which also means that the equality $HH^T = \\hat{1}$. On the other hand, due to symmetry:\n", + "\n", + "$HH^T = H^2 = (\\hat{1} - 2vv^T)^2 = \\hat{1} - 4vv^T + 4(vv^T)(vv^T) \\overset{v^Tv=1} = \\hat{1} - 4vv^T + 4vv^T = \\hat{1}$.\n", + "\n", + "It follows that the matrix is orthoganal. It also follows that the $rk(H) = n$.\n", + "\n" + ], + "metadata": { + "id": "QLstl0WUan2w" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Problem 2(10)** \n", + "Prove the following inequalities and provide examples of x and A when they turn into equalities:\n", + "\n", + "* $∥x∥_{2} ≤ \\sqrt{m}∥x∥_{∞}$\n", + "* $∥A∥_{∞} ≤ \\sqrt{n}∥A∥_{2}$\n", + "\n", + "where $x$ is a vector of $m$ components and $A$ is $m × n$ matrix.\n", + "\n" + ], + "metadata": { + "id": "imeyAc5D93on" + } + }, + { + "cell_type": "markdown", + "source": [ + "**1)** By definition we have: \n", + "$\\parallel x∥_{2} = \\sqrt{\\sum_{n=1}^{m} x_i^2}$ and $\\parallel x∥_{∞} = \\underset{1 ≤ i ≤ m}\\max{|x_i|}$ \n", + "Then the original inequality can be rewritten in the form: \n", + "$\\sqrt{\\sum_{n=1}^{m} x_i^2} ≤ \\sqrt{m}\\underset{1 ≤ i ≤ m}\\max{|x_i|}$ \n", + "Let's square both sides: \n", + "$\\sum_{n=1}^{m} x_i^2 ≤ m (\\underset{1 ≤ i ≤ m}\\max{|x_i|})^2 ⇒ \\sum_{n=1}^{m} x_i^2 ≤ m \\underset{1 ≤ i ≤ m}\\max{x_i^2} ⇔ \\sum_{n=1}^{m} x_i^2 ≤ \\sum_{n=1}^{m} \\underset{1 ≤ i ≤ m}\\max{x_i^2}$ \n", + "Hence its validity is obvious and it is clear that equality is achieved for arbitrary $m ∈ ℕ$ if $x_{1} = x_{2} = ... = x_{m}$, otherwise if $m = 1$." + ], + "metadata": { + "id": "qP9zP8Da-uZf" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Problem 3(5)**:\n", + "\n", + "Assuming $u$ and $v$ are $m$-vectors, consider the matrix $A = 1 + uv^T$ which is a rank-one perturbation of identity. Can it be singular? Assuming it is not, compute its inverse. You may look for it in a form of $A^{-1} = 1 + \\alpha{}uv^T$ for some scalar $\\alpha$ and evaluate $\\alpha$.\n" + ], + "metadata": { + "id": "H9RDz5NmqXcx" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Solution:** \n", + "**1)** Matrix $A$ is singular if there is a $m$-vector $x \\ne 0$ such that: \n", + "$(1 + uv^T)x = 0 ⇔ x + uv^Tx = 0 ⇔ uv^Tx = -x.$\n", + "Note that $v^Tx$ is a scalar, so the matrix $A$ is singular if $x = \\beta{}u$, $\\beta{} \\ne 0$. \n", + "From here we can see: \n", + "$uv^Tx = -x ⇔ \\beta{}uv^Tu = -\\beta{}u ⇔ v^Tu = -1$. \n", + "Thus, matrix $A$ is singular if $v^Tu = -1$ \n", + "\n", + "**2)** Assume that matrix $A$ has an inverse of the form $A^{-1} = 1 + αuv^T$. \n", + "$AA^{-1} = 1 ⇔ (1 + uv^T)(1 + αuv^T) = 1 ⇔ αuv^T + uv^T + αuv^Tuv^T = O$. \n", + "Since $v^Tu$ is a scalar, we denote it as $γ \\ne -1$ (otherwise the matrix will be singular). Then the resulting equality will be written in the form: \n", + "$αuv^T + uv^T + αuv^Tuv^T = O ⇔ αuv^T + uv^T + αγuv^T = O ⇔ (α + 1 + αγ)uv^T = O ⇔ α + 1 + αγ = 0 ⇔ α = -\\frac{1}{1 + γ} = -\\frac{1}{1 + v^Tu}$. \n", + "Thus, the matrix $A$ has the inverse of the form $A^{-1} = 1 + αuv^T$ and $α = -\\frac{1}{1 + v^Tu}, v^Tu \\ne -1$" + ], + "metadata": { + "id": "R_uvoqagr0td" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Problem 4(5)**:\n", + "\n", + "Prove that for any unitary matrix $U$ one has $\\parallel UA \\parallel_{F} = \\parallel AU\\parallel_{F} = \\parallel A \\parallel_{F}$." + ], + "metadata": { + "id": "WwlMFp33i0PH" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Solution:** \n", + "Let's write down the expression by definition:\n", + "\n", + "$\\parallel UA \\parallel_{F} = \\sqrt{tr[(UA)^*(UA)]} = \\sqrt{tr[A^*U^*UA]}$.\n", + "\n", + "Let us take advantage of the fact that $U$ is unitary, i.e. $U^*U = I$. That:\n", + "\n", + "$\\parallel UA \\parallel_{F} = \\sqrt{tr[A^*U^*UA]} = \\sqrt{tr[A^*A]} = \\parallel A \\parallel_{F}$\n", + "\n", + "Similarly for $AU$ we get:\n", + "\n", + "$\\parallel AU \\parallel_{F} = \\sqrt{tr[(AU)^*(AU)]} = \\sqrt{tr[U^*A^*AU]}$.\n", + "\n", + "Let's use the trace property $tr(AB) = tr(BA)$. So:\n", + "$\\parallel AU \\parallel_{F} = \\sqrt{tr[U^*A^*AU]} = \\sqrt{tr[A^*AUU^*]} = \\sqrt{tr[A^*A]} = \\parallel A \\parallel_{F}$.\n", + "\n", + "Thus $\\parallel UA \\parallel_{F} = \\parallel AU\\parallel_{F} = \\parallel A \\parallel_{F}$." + ], + "metadata": { + "id": "Tvy4TARzl_Rc" + } + } + ] +} \ No newline at end of file diff --git a/HW1/kmeans_solution.ipynb b/HW1/kmeans_solution.ipynb new file mode 100755 index 0000000..b162969 --- /dev/null +++ b/HW1/kmeans_solution.ipynb @@ -0,0 +1,668 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 182, + "metadata": { + "id": "dfXNsL1pva-M" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 183, + "metadata": { + "id": "z-2z3kejva-O" + }, + "outputs": [], + "source": [ + "def scatter_plot(data, col=None):\n", + " from mpl_toolkits.mplot3d import Axes3D\n", + " %matplotlib inline\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111, projection='3d')\n", + " ax.scatter(data[:,0], data[:,1], data[:,2], s = 0.5, color=col)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 184, + "metadata": { + "id": "aOHWooBTva-O" + }, + "outputs": [], + "source": [ + "N = 1000\n", + "K = 3\n", + "d = 3\n", + "L = 10" + ] + }, + { + "cell_type": "code", + "execution_count": 185, + "metadata": { + "id": "cobkrTwrva-O" + }, + "outputs": [], + "source": [ + "# Generate some data\n", + "np.random.seed(42)\n", + "mu_true = np.random.uniform(-L, L, size = (K, d))\n", + "data = np.random.normal(mu_true, size = (N, K, d))\n", + "data = np.vstack(data)\n", + "np.random.shuffle(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 186, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 413 + }, + "id": "fN4RBXksva-O", + "outputId": "bf587173-2253-4552-ceed-9a0e29275fd1" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "if d == 3:\n", + " scatter_plot(data, None)" + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "metadata": { + "id": "kSd05Udfva-P" + }, + "outputs": [], + "source": [ + "mu = data[np.random.choice(range(data.shape[0]), K, replace=False)]" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Slow implementation**" + ], + "metadata": { + "id": "WZN75AXlwLgL" + } + }, + { + "cell_type": "code", + "execution_count": 188, + "metadata": { + "id": "-bQpVYXWva-P" + }, + "outputs": [], + "source": [ + "def dist_i(x, mu):\n", + " # x: N datapoints, mu: N cluster centers\n", + " # returns: D_{i}, squared distances from x[i] to mu[i]\n", + " dist = np.zeros(x.shape[0])\n", + " for i in range(x.shape[0]):\n", + " dist[i] = np.sum((x[i] - mu[i])**2)\n", + " return dist\n", + "def dist_ij(x, mu):\n", + " # x: N datapoints, mu: K cluster centers\n", + " # returns: D_{ij}, squared distances from x[i] to mu[j]\n", + " dist = np.zeros((x.shape[0], mu.shape[0]))\n", + " for i in range(x.shape[0]):\n", + " for j in range(mu.shape[0]):\n", + " dist[i, j] += np.sum((x[i] - mu[j])**2)\n", + " return dist" + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "metadata": { + "id": "uGu5-pGYva-P" + }, + "outputs": [], + "source": [ + "def kmeans(data, mu):\n", + " ss_list = []\n", + " for n in range(10):\n", + " c = np.argmin(dist_ij(data, mu), axis = 1)\n", + " ss = np.mean(dist_i(data, mu[c]))\n", + " ss_list.append(ss)\n", + " for i in range(K):\n", + " cluster_members = data[c == i]\n", + " cluster_members = cluster_members.mean(axis = 0)\n", + " mu[i] = cluster_members\n", + " return ss_list, c" + ] + }, + { + "cell_type": "code", + "execution_count": 190, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "N5fihPeqva-P", + "outputId": "e99820af-847e-43cd-c9f5-bd989f945880" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + 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\n" + }, + "metadata": {} + } + ], + "source": [ + "res, c = kmeans(data, mu)\n", + "plt.plot(res);" + ] + }, + { + "cell_type": "code", + "source": [ + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "\"\"" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 140 + }, + "id": "PtEqaxIDSzv9", + "outputId": "07677ae5-6edd-4239-b0fb-91c8984a281a" + }, + "execution_count": 191, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 1.41 s, sys: 963 µs, total: 1.41 s\n", + "Wall time: 1.46 s\n", + "CPU times: user 908 ms, sys: 223 µs, total: 908 ms\n", + "Wall time: 917 ms\n", + "CPU times: user 760 ms, sys: 2.65 ms, total: 763 ms\n", + "Wall time: 765 ms\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "''" + ], + "application/vnd.google.colaboratory.intrinsic+json": { + "type": "string" + } + }, + "metadata": {}, + "execution_count": 191 + } + ] + }, + { + "cell_type": "code", + "execution_count": 192, + "metadata": { + "id": "mt_AmTnRva-P" + }, + "outputs": [], + "source": [ + "colors = np.array([plt.cm.cool(i/(K-1)) for i in range(K)])" + ] + }, + { + "cell_type": "code", + "execution_count": 193, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 413 + }, + "id": "w9EG7ndhva-Q", + "outputId": "3cd8f596-c60d-480d-ccee-3f5bec578424" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "if d == 3:\n", + " scatter_plot(data, colors[c])" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Fast implementation** \n", + "To speed up `dist_i` we will simply use `numpy` vectorization. \n", + "For `dist_iо` we will note that the $ij$-element of the output matrix $C$ has the form: \n", + "\n", + "$c_{ij} = \\sum_{k=1}^{n}(x_{ik} + mu_{jk})^2 = \\sum_{k=1}^{n}x_{ik}^2 - 2\\sum_{k=1}^{n}x_{ik}mu_{jk} + \\sum_{k=1}^{n}mu_{jk}^2$. \n", + "\n", + "Using vectorization of `numpy`, you can represent the terms as: \n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "$(\\sum_{k=1}^{n}x_{1k}^2 \\sum_{k=1}^{n}x_{2k}^2 ... \\sum_{k=1}^{n}x_{mk}^2)^T =$ `np.sum(x**2, axis=1).reshape((x.shape[0], 1))` \n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "$\\underset{1 ≤ i ≤ m\\\\1 ≤ j ≤ n}{(-2\\sum_{k=1}^{n}x_{ik}mu_{jk})} = $ `-2*(x @ mu.T)` \n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "$(\\sum_{k=1}^{n}mu_{1k}^2 \\sum_{k=1}^{n}mu_{2k}^2 ... \\sum_{k=1}^{n}mu_{nk}^2)^T = $ `np.sum(mu**2, axis = 1).reshape((1, mu.shape[0]))`\n", + "\n", + "\n", + "---\n", + "\n", + "Using `numpy` broadcasting we can add these terms and get the desired matrix." + ], + "metadata": { + "id": "74HbN5R2wRCu" + } + }, + { + "cell_type": "code", + "source": [ + "# Generate some data\n", + "np.random.seed(42)\n", + "mu_true = np.random.uniform(-L, L, size = (K, d))\n", + "data = np.random.normal(mu_true, size = (N, K, d))\n", + "data = np.vstack(data)\n", + "np.random.shuffle(data)" + ], + "metadata": { + "id": "d1qp6tO4U6cz" + }, + "execution_count": 194, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "mu = data[np.random.choice(range(data.shape[0]), K, replace=False)]" + ], + "metadata": { + "id": "RdcERcHHUtpe" + }, + "execution_count": 195, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "def dist_i(x, mu):\n", + " # x: N datapoints, mu: N cluster centers\n", + " # returns: D_{i}, squared distances from x[i] to mu[i]\n", + " dist = np.sum((x - mu)**2, axis=1)\n", + " return dist\n", + "def dist_ij(x, mu):\n", + " # x: N datapoints, mu: K cluster centers\n", + " # returns: D_{ij}, squared distances from x[i] to mu[j]\n", + " sum_xij = np.sum(x**2, axis = 1).reshape((x.shape[0], 1))\n", + " sum_muij = np.sum(mu**2, axis = 1).reshape((1, mu.shape[0]))\n", + " sum_xij_muij = -2 * (x @ mu.T)\n", + " dist = sum_xij + sum_xij_muij + sum_muij\n", + " return dist" + ], + "metadata": { + "id": "NsVoKN2mwQiG" + }, + "execution_count": 196, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "res, c = kmeans(data, mu)\n", + "plt.plot(res);" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "id": "E4OAApKsS9L1", + "outputId": "8e2dd22a-7e2c-40ce-cacf-c9cfc0f880d0" + }, + "execution_count": 197, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "\"\"" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 140 + }, + "outputId": "85e0c979-2082-49b1-f572-4c4c880a47c3", + "id": "k450H4hjZkpo" + }, + "execution_count": 198, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 11.5 ms, sys: 0 ns, total: 11.5 ms\n", + "Wall time: 12.5 ms\n", + "CPU times: user 7.45 ms, sys: 0 ns, total: 7.45 ms\n", + "Wall time: 7.46 ms\n", + "CPU times: user 7.05 ms, sys: 0 ns, total: 7.05 ms\n", + "Wall time: 7.06 ms\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "''" + ], + "application/vnd.google.colaboratory.intrinsic+json": { + "type": "string" + } + }, + "metadata": {}, + "execution_count": 198 + } + ] + }, + { + "cell_type": "code", + "source": [ + "colors = np.array([plt.cm.cool(i/(K-1)) for i in range(K)])" + ], + "metadata": { + "id": "38N1euNRTKBq" + }, + "execution_count": 199, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "if d == 3:\n", + " scatter_plot(data, colors[c])" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 413 + }, + "id": "N5kLSOWgTLDg", + "outputId": "d58fa579-3fb6-44ee-ba3c-3308b7357402" + }, + "execution_count": 200, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Now let's run a faster algorithm for $H = 10000$" + ], + "metadata": { + "id": "-SU0tN1AdKCt" + } + }, + { + "cell_type": "code", + "execution_count": 201, + "metadata": { + "id": "Rv5bbq9cdbOU" + }, + "outputs": [], + "source": [ + "N = 10000\n", + "K = 3\n", + "d = 3\n", + "L = 10" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "metadata": { + "id": "v9Ix7FhfdbOV" + }, + "outputs": [], + "source": [ + "# Generate some data\n", + "np.random.seed(42)\n", + "mu_true = np.random.uniform(-L, L, size = (K, d))\n", + "data = np.random.normal(mu_true, size = (N, K, d))\n", + "data = np.vstack(data)\n", + "np.random.shuffle(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 203, + "metadata": { + "id": "XWNOXpG1dbOV" + }, + "outputs": [], + "source": [ + "mu = data[np.random.choice(range(data.shape[0]), K, replace=False)]" + ] + }, + { + "cell_type": "code", + "source": [ + "res, c = kmeans(data, mu)\n", + "plt.plot(res);" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "outputId": "851de315-4b00-4437-dba2-7af188f4c4d5", + "id": "TEHtJrspdgtz" + }, + "execution_count": 204, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "%time kmeans(data, mu)\n", + "\"\"" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 140 + }, + "outputId": "9096e0e8-7c69-47a5-c87c-379c7c8084d9", + "id": "6Mhrk1gDdgt0" + }, + "execution_count": 205, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CPU times: user 88.5 ms, sys: 69.7 ms, total: 158 ms\n", + "Wall time: 83.9 ms\n", + "CPU times: user 95.6 ms, sys: 68.2 ms, total: 164 ms\n", + "Wall time: 85.1 ms\n", + "CPU times: user 87.7 ms, sys: 62 ms, total: 150 ms\n", + "Wall time: 84.5 ms\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "''" + ], + "application/vnd.google.colaboratory.intrinsic+json": { + "type": "string" + } + }, + "metadata": {}, + "execution_count": 205 + } + ] + }, + { + "cell_type": "code", + "source": [ + "colors = np.array([plt.cm.cool(i/(K-1)) for i in range(K)])" + ], + "metadata": { + "id": "QM15hXyPdgt0" + }, + "execution_count": 206, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "if d == 3:\n", + " scatter_plot(data, colors[c])" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 414 + }, + "outputId": "76097871-351f-49b5-d56c-fdcc39e34eea", + "id": "GPB2uN_udgt0" + }, + "execution_count": 207, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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