notebooks/ppm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using MatrixNetworks\n",
    "using Distributions\n",
    "using Gadfly\n",
    "using Clustering\n",
    "using BenchmarkTools, Compat\n",
    "using DelimitedFiles\n",
    "using SparseArrays\n",
    "using LinearAlgebra\n",
    "using EllipsoidalGraphEmbedding\n",
    "using Random\n",
    "using Plots\n",
    "using LaTeXStrings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading data\n",
    "m = readdlm(\"Data/PowerEU/ElistPowerEU.txt\");\n",
    "dim = size(m,1);\n",
    "\n",
    "M_int = zeros(Int64,dim,2);\n",
    "for i =1:dim\n",
    "\tfor j=1:2\n",
    "\t\tM_int[i,j] = Int64(m[i,j]);\n",
    "\tend\n",
    "end\n",
    "\n",
    "N = maximum([maximum(M_int[:,1]),maximum(M_int[:,2])]);\n",
    "\n",
    "A0 =spzeros(N,N);\n",
    "A0 = sparse(M_int[:,1],M_int[:,2],vec(ones(Int64,dim,1)),N,N);\n",
    "A0 = A0+A0';\n",
    "A,p = largest_component(A0);\n",
    "\n",
    "A0=0;p=0;m =0;\n",
    "\n",
    "# nb iterations projected power method\n",
    "n_it_PPM = 30000;\n",
    "\n",
    "# relative objective variation\n",
    "t = 1e-8;\n",
    "\n",
    "r0 = 10\n",
    "\n",
    "N = size(A, 1)\n",
    "d = sum(A, dims=2)\n",
    "s = sum(d)\n",
    "\n",
    "# ROW NORMALIZATION \n",
    "index = sample(1:N, r0; replace=false, ordered=true)\n",
    "H0 = A[:, index] - (1 / s) * d * d[index]'\n",
    "\n",
    "# Project on the sphere\n",
    "H0 = H0./sqrt.(sum(abs2, H0, dims=2));\n",
    "X = H0\n",
    "\n",
    "# GPMM\n",
    "# Initialization\n",
    "f = vec(1 .+ 2 * d - (d .^ 2) / s)\n",
    "\n",
    "i = 1\n",
    "diff = 10.0\n",
    "\n",
    "Y0 = zeros(size(X))\n",
    "Y = zeros(size(X))\n",
    "\n",
    "obj_0 = 1.0\n",
    "obj = 1.0\n",
    "r = 0.0\n",
    "\n",
    "n_it = 50\n",
    "objective_GPMM = zeros(n_it,1)\n",
    "\n",
    "while (i <= n_it) \n",
    "\n",
    "    # Matrix product\n",
    "    Y = A * X - (d / s) * (d' * X) + Diagonal(f) * X\n",
    "    # In order to avoid calculating twice the same products\n",
    "    # Since X is feasible, we calculate the objective value AFTER the first matrix product.\n",
    "    obj = (tr(X' * Y)) / s\n",
    "    objective_GPMM[i] = obj\n",
    "    #Difference between consecutive objectives\n",
    "    diff = abs.(obj - obj_0) / obj_0\n",
    "\n",
    "    #Update with momentum\n",
    "    r = (i - 1.0) / (i + 2.0)\n",
    "    X = (1 + r) * Y\n",
    "    X = X - r * Y0\n",
    "\n",
    "    #Project on the sphere\n",
    "    X = X ./ sqrt.(sum(abs2, X, dims=2))\n",
    "\n",
    "    #Update objective and momentum\n",
    "    obj_0 = obj\n",
    "\n",
    "    Y0 = Y\n",
    "    i += 1\n",
    "end\n",
    "\n",
    "\n",
    "\n",
    "X = H0\n",
    "# GPM\n",
    "# Initialization\n",
    "# Initialization\n",
    "i = 1\n",
    "diff = 10.0\n",
    "\n",
    "Y0 = zeros(size(X))\n",
    "Y = zeros(size(X))\n",
    "\n",
    "obj_0 = 1.0\n",
    "obj = 1.0\n",
    "r = 0.0\n",
    "\n",
    "n_it = 50\n",
    "objective_GPM = zeros(n_it,1)\n",
    "\n",
    "while (i <= n_it) \n",
    "\n",
    "    # Matrix product\n",
    "    Y = A * X - (d / s) * (d' * X) + Diagonal(f) * X\n",
    "    # In order to avoid calculating twice the same products\n",
    "    # Since X is feasible, we calculate the objective value AFTER the first matrix product.\n",
    "    obj = (tr(X' * Y)) / s\n",
    "    objective_GPM[i] = obj\n",
    "    #Difference between consecutive objectives\n",
    "    diff = abs.(obj - obj_0) / obj_0\n",
    "\n",
    "    #Update with momentum HERE CHANGE\n",
    "    r = 0\n",
    "    X = (1 + r) * Y\n",
    "    X = X - r * Y0\n",
    "\n",
    "    #Project on the sphere\n",
    "    X = X ./ sqrt.(sum(abs2, X, dims=2))\n",
    "\n",
    "    #Update objective and momentum\n",
    "    obj_0 = obj\n",
    "\n",
    "    Y0 = Y\n",
    "    i += 1\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
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   ],
   "source": [
    "gr()\n",
    "p2 = Plots.plot(1:length(objective_GPMM),objective_GPMM, label = \"GPMM\" ,seriestype=:scatter)\n",
    "Plots.plot!(1:length(objective_GPM),objective_GPM, label = \"GPM\",seriestype=:scatter,legend=:bottomright,xtickfontsize=10,ytickfontsize=10, xguidefontsize=15, yguidefontsize=15)\n",
    "xlabel!(L\"n\")\n",
    "ylabel!(L\"f(x_n)\")\n",
    "savefig(\"figures/PPM_momentum_PowerEU.pdf\")\n",
    "display(p2)\n",
    "\n",
    "# nicer plots\n",
    "pgfplotsx()\n",
    "p2 = Plots.plot(1:length(objective_GPMM),objective_GPMM, label = \"GPMM\" ,seriestype=:scatter)\n",
    "Plots.plot!(1:length(objective_GPM),objective_GPM, label = \"GPM\",seriestype=:scatter,legend=:bottomright,xtickfontsize=10,ytickfontsize=10, xguidefontsize=15, yguidefontsize=15)\n",
    "xlabel!(L\"n\")\n",
    "ylabel!(L\"f(x_n)\")\n",
    "savefig(\"figures/PPM_momentum_PowerEU.pdf\")\n",
    "display(p2)\n"
   ]
  }
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