lrr_subspace_segmentation.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "lrr_subspace_segmentation",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "CP8fygQHVfl2"
      },
      "source": [
        "import numpy as np\n",
        "from scipy.linalg import orth"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gCwx9AXuSmnA"
      },
      "source": [
        "def lrr(X, lamda, itr_max, norm_choice=0):\n",
        "  # returns the LRR\n",
        "  # norm choices:\n",
        "  # 0 : max element in X\n",
        "  # 1 : infinity norm\n",
        "  # 2 : l2 norm\n",
        "  # 3 : l1 norm\n",
        "  # 4 : l-2 norm (smallest singular value)\n",
        "  # 5 : l-1 norm (smallest  absolute row sum)\n",
        "\n",
        "  A = X\n",
        "  P = orth(A.T)\n",
        "  B = np.dot(A, P)\n",
        "  d, n = X.shape\n",
        "  m = B.shape[1]\n",
        "\n",
        "  # initial values\n",
        "  Z = np.zeros((m,n), dtype=np.float32)\n",
        "  J = np.zeros((m,n), dtype=np.float32)\n",
        "  E = np.zeros((d,n), dtype=np.float32)\n",
        "  Y1 = np.zeros((d,n), dtype=np.float32)\n",
        "  Y2 = np.zeros((m,n), dtype=np.float32)\n",
        "  mu = 1.0E-6\n",
        "  mu_max = 1.0E+10\n",
        "  rho = 1.1\n",
        "  epsilon = 1.0E-8\n",
        "\n",
        "  itr = 0\n",
        "\n",
        "  params = []\n",
        "  while itr < itr_max:\n",
        "    itr = itr + 1\n",
        "    # if itr % 100 == 0:\n",
        "    #   print('LRR itr=',itr)\n",
        "    #   print('Convergence:', max(norm_eq1,norm_eq2))\n",
        "\n",
        "    # optimizing over J (Step 1)\n",
        "    Y = Z + Y2/mu\n",
        "    U, sdiag, Vh = np.linalg.svd(Y, full_matrices=False)\n",
        "    V = Vh.T\n",
        "    r = sum(sdiag > 1.0/mu)\n",
        "    if r == 0:\n",
        "      sigma_thres = [0]\n",
        "    else:\n",
        "      sigma_thres = sdiag[0:r+1] - 1.0/mu\n",
        "    Usigma = np.dot( U[:,0:r+1], np.diag(sigma_thres) )\n",
        "    J = np.dot( Usigma, V[:,0:r+1].T );\n",
        "\n",
        "    # optimizing over Z (Step 2)\n",
        "    factor1 = np.linalg.inv( np.identity(m) + np.dot(B.T,B) )\n",
        "    factor2 = np.dot( B.T,(X-E) ) + J + ( np.dot(B.T,Y1)-Y2 )/mu\n",
        "    Z = np.dot( factor1, factor2 )\n",
        "    rank_Z = np.linalg.matrix_rank(Z)\n",
        "\n",
        "    # optimizing over E (Step 3)\n",
        "    alpha = lamda/mu\n",
        "    Q = X - np.dot(B,Z) + Y1/mu\n",
        "    for i in range( Q.shape[1] ):\n",
        "      q = Q[:,[i]]\n",
        "      q_norm = np.linalg.norm( q,2 )\n",
        "      if q_norm > alpha:\n",
        "        scalar = (q_norm - alpha) / q_norm\n",
        "        E[:,[i]] = scalar * q\n",
        "      else:\n",
        "        E[:,[i]] = np.zeros((d,1))\n",
        "\n",
        "    # updating multipliers (Step 4)\n",
        "    eq1 = X - np.dot(B,Z) - E\n",
        "    eq2 = Z - J\n",
        "    Y1 = Y1 + mu*eq1\n",
        "    Y2 = Y2 + mu*eq2\n",
        "\n",
        "    # updating mu (Step 5)\n",
        "    mu = min( rho*mu, mu_max )\n",
        "\n",
        "    # convergence conditions (Step 6)\n",
        "    norm_eq1 = 0\n",
        "    norm_eq2 = 0\n",
        "    if(norm_choice==0): # paper inf\n",
        "      norm_eq1 = np.amax( np.abs(eq1) )\n",
        "      norm_eq2 = np.amax( np.abs(eq2) )\n",
        "    elif (norm_choice==1): # actual inf\n",
        "      norm_eq1 = np.linalg.norm(eq1, np.inf)\n",
        "      norm_eq2 = np.linalg.norm(eq2, np.inf)\n",
        "    elif (norm_choice==2): # l2\n",
        "      norm_eq1 = np.linalg.norm(eq1, 2)\n",
        "      norm_eq2 = np.linalg.norm(eq2, 2)\n",
        "    elif (norm_choice==3): # l1\n",
        "      norm_eq1 = np.linalg.norm(eq1, 1)\n",
        "      norm_eq2 = np.linalg.norm(eq2, 1)\n",
        "    elif (norm_choice==4): # l-2\n",
        "      norm_eq1 = np.linalg.norm(eq1, -2)\n",
        "      norm_eq2 = np.linalg.norm(eq2, -2)\n",
        "    elif (norm_choice==5): # l-1\n",
        "      norm_eq1 = np.linalg.norm(eq1, -1)\n",
        "      norm_eq2 = np.linalg.norm(eq2, -1)\n",
        "\n",
        "    params.append( {'mu':mu, 'max_norm_eq':max(norm_eq1,norm_eq2), 'r':r, 'rank_Z':rank_Z, 'iter':itr} )\n",
        "\n",
        "    if norm_eq1 < epsilon and norm_eq2 < epsilon:\n",
        "      break\n",
        "\n",
        "  return np.dot(P,Z), E, params\n",
        "  # returns Z_star, E_star, dictionary of parameter values at each iteration"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bk3O_XzbQ1Uo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c045bd8c-8919-4f20-f6c2-3195270a57fc"
      },
      "source": [
        "!rm -r /content/subspace-segmentation-via-low-rank-representation/\n",
        "!git clone https://github.com/kaushal-k/subspace-segmentation-via-low-rank-representation.git"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "rm: cannot remove '/content/subspace-segmentation-via-low-rank-representation/': No such file or directory\n",
            "Cloning into 'subspace-segmentation-via-low-rank-representation'...\n",
            "remote: Enumerating objects: 520, done.\u001b[K\n",
            "remote: Counting objects: 100% (520/520), done.\u001b[K\n",
            "remote: Compressing objects: 100% (436/436), done.\u001b[K\n",
            "remote: Total 520 (delta 79), reused 520 (delta 79), pack-reused 0\u001b[K\n",
            "Receiving objects: 100% (520/520), 31.63 MiB | 35.83 MiB/s, done.\n",
            "Resolving deltas: 100% (79/79), done.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Eap1HNy7Vjh"
      },
      "source": [
        "import os\n",
        "from scipy.io import loadmat\n",
        "from sklearn.cluster import KMeans\n",
        "from itertools import permutations"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MZ5F7FvYGJKW"
      },
      "source": [
        "def affinity_matrix(Z_star):\n",
        "  # Z_star : LRR\n",
        "  # returns the affinity matrix\n",
        "\n",
        "  # Step 2\n",
        "  U, sdiag, Vh = np.linalg.svd(Z_star, full_matrices=False)\n",
        "  V = Vh.T\n",
        "  zero_thres = 0.0001 * sdiag[0]\n",
        "  r = sum( sdiag > zero_thres )\n",
        "  U = U[:,0:r+1]\n",
        "  sdiag = sdiag[0:r+1]\n",
        "\n",
        "  # Step 3\n",
        "  U_tilda_inter = np.dot( U, np.diag(np.sqrt(sdiag)) )\n",
        "  U_tilda = U_tilda_inter / np.linalg.norm(U_tilda_inter, ord=2, axis=1, keepdims=True)\n",
        "  W = np.square( np.dot(U_tilda,U_tilda.T) )\n",
        "  W = np.square( W )\n",
        "\n",
        "  return W"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fh92b877IiUE"
      },
      "source": [
        "def spectral_clustering(W,K):\n",
        "  # W : affinity matrix\n",
        "  # K : no. of subspace clusters\n",
        "  # NCut clustering\n",
        "\n",
        "  # Step 4 (Spectral Clustering)\n",
        "  Ddiag = 1.0 / np.sqrt( W.sum(axis=1, dtype=np.float) )\n",
        "  D = np.diag(Ddiag)\n",
        "  L = np.dot( D, np.dot(W,D) )\n",
        "  U, s, Vh = np.linalg.svd(L)\n",
        "  V = U[:,0:K]\n",
        "  V = np.dot( D,V )\n",
        "  res = KMeans(n_clusters=K, init='k-means++', random_state=1).fit_predict(V)\n",
        "  res = res + 1\n",
        "\n",
        "  return res"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hBMLikMnCqL2"
      },
      "source": [
        "def motion_seg(lamda, lrr_itr_max, norm_choice):  \n",
        "  # motion segmentation on Hopkins155 datset\n",
        "  dataset = []\n",
        "  error = []\n",
        "  params = []\n",
        "  last_exec = ''\n",
        "\n",
        "  # hopkins155_path = '/content/ee609_data/Hopkins155/'\n",
        "  hopkins155_path = '/content/subspace-segmentation-via-low-rank-representation/Data/Hopkins155/'\n",
        "  for dir in os.listdir(hopkins155_path):\n",
        "    if os.path.isdir(hopkins155_path+dir):\n",
        "      data = loadmat(hopkins155_path+dir+'/'+dir+'_truth.mat')\n",
        "      # frames x points (a tracked point is one sample in this one motion sequnce)\n",
        "      X = np.concatenate([ data['x'][0,:,:].T, data['x'][1,:,:].T ])\n",
        "      row_ones = np.ones( (1,X.shape[1]), dtype=np.float32 )\n",
        "      X = np.concatenate( [X, row_ones] )\n",
        "      S = data['s']\n",
        "      dataset.append( {'name':dir, 'X':X, 'seg_ids':S} )\n",
        "\n",
        "  for data in dataset:\n",
        "    print('Working on: ', data['name'])\n",
        "\n",
        "    last_exec = data['name']\n",
        "\n",
        "    # given number of subspace segments\n",
        "    K = np.amax( data['seg_ids'] )\n",
        "\n",
        "    # Step 1 (Low-Rank Representation)\n",
        "    Z_star, E_star, params = lrr(data['X'], lamda, lrr_itr_max, norm_choice)\n",
        "\n",
        "    # Steps 2 & 3 (Affinity Matrix)\n",
        "    W = affinity_matrix(Z_star)\n",
        "\n",
        "    res = spectral_clustering(W,K)\n",
        "\n",
        "    # errors\n",
        "    rng = [*range(1,K+1,1)]\n",
        "    perms = list( permutations(rng) )\n",
        "    perms = np.array(perms)\n",
        "    perms = np.flip(perms, axis=0)\n",
        "    perms_dim = perms.shape[0]\n",
        "    miss = np.zeros( (perms_dim,1), dtype=np.float32 )\n",
        "    for i in range(perms_dim):\n",
        "      absol = np.abs( res[:] - perms[ i, data['seg_ids'].T-1 ] )\n",
        "      absol = absol > 0.1\n",
        "      miss[i,0] = np.sum(absol)\n",
        "    seg_err = 1.0*np.amin(miss) / res.shape[0]\n",
        "    error.append(seg_err)\n",
        "\n",
        "  return error, params, last_exec\n",
        "  # last_exec: file name of last data that was worked upon\n",
        "  # params: list of dictionary with keys mu, r, max_norm_eq, and iter, depicting evolution over iterations (corresponding to last_exec)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GQTBAtHSh-Hd",
        "outputId": "ef125351-42a6-40dc-ac9b-ccf8737e9b2d"
      },
      "source": [
        "# Run this and the next 2 cells for norm_choice = 0, but different values of lamda_motion = 1, 2, 3, 3.6, 4, 4.6, 6, 7 to obtain plots and error results\n",
        "# Run this and the next 2 cells for lamda_motion=4.6, but different values of norm_choice = 0, 1, 2, 3, 4, 5\n",
        "# (One run of this cell will take about 25-30 mins)\n",
        "\n",
        "lamda_motion = 4.6\n",
        "max_iter_motion = 500\n",
        "norm_choice = 0\n",
        "error, params, last_exec = motion_seg(lamda_motion, max_iter_motion, norm_choice)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Working on:  2T3RCR_g13\n",
            "Working on:  1R2RC\n",
            "Working on:  cars5\n",
            "Working on:  cars2_07_g12\n",
            "Working on:  cars2B_g23\n",
            "Working on:  2T3RCRT_g12\n",
            "Working on:  cars10\n",
            "Working on:  cars5_g13\n",
            "Working on:  two_cranes_g23\n",
            "Working on:  2R3RTCRT\n",
            "Working on:  cars2_06_g13\n",
            "Working on:  people1\n",
            "Working on:  people2\n",
            "Working on:  cars2_06_g12\n",
            "Working on:  cars8\n",
            "Working on:  2R3RTC_g13\n",
            "Working on:  cars1\n",
            "Working on:  2RT3RTCRT\n",
            "Working on:  1RT2TC_g13\n",
            "Working on:  1R2RC_g12\n",
            "Working on:  2T3RCRTP\n",
            "Working on:  2T3RCRT_g23\n",
            "Working on:  cars10_g23\n",
            "Working on:  2RT3RCR_g23\n",
            "Working on:  2RT3RCT_B_g12\n",
            "Working on:  2RT3RCT_A_g12\n",
            "Working on:  1R2RCT_A_g13\n",
            "Working on:  1R2RCT_B_g13\n",
            "Working on:  cars4\n",
            "Working on:  1RT2RCR_g13\n",
            "Working on:  2R3RTCRT_g12\n",
            "Working on:  1R2RCT_B\n",
            "Working on:  2RT3RCT_A_g23\n",
            "Working on:  1R2RCR\n",
            "Working on:  1RT2RCR\n",
            "Working on:  2T3RCRTP_g23\n",
            "Working on:  cars3\n",
            "Working on:  cars2_07_g23\n",
            "Working on:  cars3_g23\n",
            "Working on:  1RT2TC\n",
            "Working on:  1RT2TC_g23\n",
            "Working on:  2RT3RCR\n",
            "Working on:  2RT3RC_g12\n",
            "Working on:  1R2TCR_g13\n",
            "Working on:  cars6\n",
            "Working on:  1R2RCR_g23\n",
            "Working on:  1R2RCT_A_g23\n",
            "Working on:  2R3RTC\n",
            "Working on:  2T3RCRTP_g13\n",
            "Working on:  cars9_g13\n",
            "Working on:  three-cars_g12\n",
            "Working on:  2RT3RCT_B_g13\n",
            "Working on:  1R2RCT_B_g23\n",
            "Working on:  2RT3RTCRT_g23\n",
            "Working on:  cars5_g23\n",
            "Working on:  1RT2TCRT_A_g23\n",
            "Working on:  2RT3RTCRT_g12\n",
            "Working on:  cars2_07\n",
            "Working on:  cars2B\n",
            "Working on:  1RT2RTCRT_A_g23\n",
            "Working on:  2T3RCR_g23\n",
            "Working on:  1RT2RCRT_g12\n",
            "Working on:  1RT2TCRT_B_g13\n",
            "Working on:  articulated_g23\n",
            "Working on:  1R2RC_g23\n",
            "Working on:  2T3RTCR_g23\n",
            "Working on:  2RT3RCT_B_g23\n",
            "Working on:  1R2RCT_B_g12\n",
            "Working on:  cars2B_g13\n",
            "Working on:  1R2TCRT\n",
            "Working on:  2T3RTCR_g12\n",
            "Working on:  1R2TCRT_g23\n",
            "Working on:  1R2RCR_g12\n",
            "Working on:  2R3RTCRT_g23\n",
            "Working on:  2RT3RCT_A_g13\n",
            "Working on:  1RT2TCRT_B\n",
            "Working on:  1R2TCR_g12\n",
            "Working on:  cars3_g12\n",
            "Working on:  cars9\n",
            "Working on:  2RT3RTCRT_g13\n",
            "Working on:  1RT2TC_g12\n",
            "Working on:  truck2\n",
            "Working on:  head\n",
            "Working on:  2T3RTCR\n",
            "Working on:  kanatani3\n",
            "Working on:  1R2TCRT_g13\n",
            "Working on:  1RT2RTCRT_A_g12\n",
            "Working on:  cars9_g23\n",
            "Working on:  2RT3RCR_g13\n",
            "Working on:  2RT3RCT_B\n",
            "Working on:  three-cars_g13\n",
            "Working on:  arm\n",
            "Working on:  cars5_g12\n",
            "Working on:  1RT2RTCRT_B_g13\n",
            "Working on:  2T3RCR\n",
            "Working on:  2T3RCTP\n",
            "Working on:  1RT2RCRT\n",
            "Working on:  1R2RCR_g13\n",
            "Working on:  1RT2TCRT_A_g13\n",
            "Working on:  2RT3RC_g23\n",
            "Working on:  2RT3RCT_A\n",
            "Working on:  1RT2RCR_g12\n",
            "Working on:  1R2TCR\n",
            "Working on:  cars2_06_g23\n",
            "Working on:  1RT2RTCRT_B_g12\n",
            "Working on:  dancing\n",
            "Working on:  two_cranes_g12\n",
            "Working on:  2T3RCTP_g12\n",
            "Working on:  2T3RTCR_g13\n",
            "Working on:  articulated\n",
            "Working on:  1R2RC_g13\n",
            "Working on:  two_cranes_g13\n",
            "Working on:  articulated_g12\n",
            "Working on:  1RT2RCR_g23\n",
            "Working on:  2RT3RC_g13\n",
            "Working on:  cars9_g12\n",
            "Working on:  articulated_g13\n",
            "Working on:  cars2_07_g13\n",
            "Working on:  2RT3RCR_g12\n",
            "Working on:  cars3_g13\n",
            "Working on:  two_cranes\n",
            "Working on:  cars2_06\n",
            "Working on:  three-cars\n",
            "Working on:  cars7\n",
            "Working on:  2T3RCRT\n",
            "Working on:  1RT2TCRT_B_g23\n",
            "Working on:  2R3RTC_g23\n",
            "Working on:  kanatani2\n",
            "Working on:  kanatani1\n",
            "Working on:  1RT2RCRT_g23\n",
            "Working on:  1R2TCR_g23\n",
            "Working on:  2T3RCTP_g13\n",
            "Working on:  cars10_g12\n",
            "Working on:  2RT3RC\n",
            "Working on:  cars2\n",
            "Working on:  1R2RCT_A_g12\n",
            "Working on:  1RT2TCRT_A\n",
            "Working on:  2T3RCTP_g23\n",
            "Working on:  cars2B_g12\n",
            "Working on:  truck1\n",
            "Working on:  1RT2RTCRT_A_g13\n",
            "Working on:  1RT2RTCRT_B_g23\n",
            "Working on:  1R2TCRT_g12\n",
            "Working on:  cars10_g13\n",
            "Working on:  1RT2TCRT_A_g12\n",
            "Working on:  2T3RCRT_g13\n",
            "Working on:  1RT2RCRT_g13\n",
            "Working on:  1RT2RTCRT_B\n",
            "Working on:  three-cars_g23\n",
            "Working on:  1R2RCT_A\n",
            "Working on:  2T3RCRTP_g12\n",
            "Working on:  2R3RTCRT_g13\n",
            "Working on:  1RT2TCRT_B_g12\n",
            "Working on:  1RT2RTCRT_A\n",
            "Working on:  2T3RCR_g12\n",
            "Working on:  2R3RTC_g12\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YH1xZRVhBQ89",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5cb07f0f-cc55-49e3-b4f6-5e3497abdaf0"
      },
      "source": [
        "# to calulcate errors\n",
        "from statistics import mean, stdev\n",
        "print('motion segmentation error statistics on hopkins155')\n",
        "print('lamda=',lamda_motion)\n",
        "print('max_iter=',max_iter_motion)\n",
        "print('norm_choice=', norm_choice)\n",
        "print('mean error',mean(error))\n",
        "print('stdev error', stdev(error))\n",
        "print('max error', max(error))\n",
        "print('min error', min(error))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "motion segmentation error statistics on hopkins155\n",
            "lamda= 4.6\n",
            "max_iter= 500\n",
            "norm_choice= 0\n",
            "mean error 0.017213136077969312\n",
            "stdev error 0.048956981307033985\n",
            "max error 0.3333333333333333\n",
            "min error 0.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "HHKGYaPTrKR8",
        "outputId": "737828c6-5c77-478f-ebb7-0b67935acd58"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "print('lamda=',lamda_motion)\n",
        "print('max_iter=',max_iter_motion)\n",
        "print('norm_choice=', norm_choice)\n",
        "\n",
        "print('Parameter Evolution with iterations for motion_seg in file:', last_exec)\n",
        "iters = []\n",
        "mus = []\n",
        "rs = []\n",
        "rank_Zs = []\n",
        "max_norm_eqs = []\n",
        "for d in params:\n",
        "  iters.append(d['iter'])\n",
        "  mus.append(d['mu'])\n",
        "  rs.append(d['r'])\n",
        "  rank_Zs.append(d['rank_Z'])\n",
        "  max_norm_eqs.append(d['max_norm_eq'])\n",
        "\n",
        "print('Final values:')\n",
        "print('mu:',mus[-1], ' r:',rs[-1], ' max_norm_eq:',max_norm_eqs[-1], 'rank_Z:',rank_Zs[-1], ' iters:',iters[-1], '\\n')\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,mus)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('\\u03BC')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z+Y2/\\u03BC)')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,max_norm_eqs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('convergence error')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rank_Zs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z)')\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "lamda= 4.6\n",
            "max_iter= 500\n",
            "norm_choice= 0\n",
            "Parameter Evolution with iterations for motion_seg in file: 2R3RTC_g12\n",
            "Final values:\n",
            "mu: 112680.02566852688  r: 9  max_norm_eq: 9.976372075670703e-09 rank_Z: 59  iters: 267 \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V9pbaBGuzP9M"
      },
      "source": [
        "def face_seg(lamda, lrr_itr_max, norm_choice):\n",
        "  # face segmentation on yaleb10 dataset\n",
        "  # yaleb_path = '/content/ee609_data/yaleb10.mat'\n",
        "  yaleb_path = '/content/subspace-segmentation-via-low-rank-representation/Data/yaleb10.mat'\n",
        "  data = loadmat(yaleb_path)\n",
        "  X = data['obj'][0,0][0]\n",
        "  seg_ids = data['obj'][0,0][1].T\n",
        "\n",
        "  # given number of subspace segments\n",
        "  K = np.amax(seg_ids)\n",
        "\n",
        "  # Step 1 (Low-Rank Representation)\n",
        "  Z_star, E_star, lrr_params = lrr(X,lamda,lrr_itr_max, norm_choice)\n",
        "\n",
        "  # Steps 2 & 3 (Affinity Matrix)\n",
        "  W = affinity_matrix(Z_star)\n",
        "\n",
        "  # Step 4 (NCut Spectral Clustering)\n",
        "  res = spectral_clustering(W,K)\n",
        "  copy_res = res\n",
        "\n",
        "  # calculating accuracy\n",
        "  unique_segs_exp = np.unique(res)\n",
        "  for unique_seg_exp in unique_segs_exp:\n",
        "    filter = (res == unique_seg_exp)\n",
        "    gnd_filter = seg_ids[ filter ]\n",
        "    unique_gnd = np.unique( gnd_filter )\n",
        "    max_cnt = 0\n",
        "    majority_label = 0\n",
        "    for ug in unique_gnd:\n",
        "      cnt = np.sum( gnd_filter==ug )\n",
        "      if cnt > max_cnt:\n",
        "        max_cnt = cnt\n",
        "        majority_label = ug\n",
        "    res[ filter ] = majority_label\n",
        "  res = np.reshape( res, (res.shape[0],1) )\n",
        "  acc = np.sum( res==seg_ids ) / res.shape[0]\n",
        "\n",
        "  return copy_res, res, acc, lrr_params"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qoeDPwB2FaKY"
      },
      "source": [
        "# Run this and the next 1 cell for norm_choice=0, but different lamda_face = 0.06, 0.1, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22\n",
        "# Run this and the next 1 cell for lamda_face = 0.16, but different norm_choice = 0, 1, 2, 3, 4, 5\n",
        "# (This cell will take about 7 mins)\n",
        "\n",
        "lamda_face = 0.16\n",
        "max_iters_face = 500\n",
        "norm_choice = 0\n",
        "copy_res, res, acc, lrr_params = face_seg(lamda_face,max_iters_face, norm_choice)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h32e19Q9zNdE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "d39edba5-b78a-4099-d970-50018bf90776"
      },
      "source": [
        "print('Face Segmentation')\n",
        "print('lamda=', lamda_face)\n",
        "print(\"max_iter=\", max_iters_face)\n",
        "print(\"norm_choice=\", norm_choice)\n",
        "print('accuracy=', acc)\n",
        "\n",
        "print('Parameter Evolution with iterations for face_seg')\n",
        "iters = []\n",
        "mus = []\n",
        "rs = []\n",
        "rank_Zs = []\n",
        "max_norm_eqs = []\n",
        "for d in lrr_params:\n",
        "  iters.append(d['iter'])\n",
        "  mus.append(d['mu'])\n",
        "  rs.append(d['r'])\n",
        "  rank_Zs.append(d['rank_Z'])\n",
        "  max_norm_eqs.append(d['max_norm_eq'])\n",
        "\n",
        "print('Final values:')\n",
        "print('mu:',mus[-1], ' r:',rs[-1], ' max_norm_eq:',max_norm_eqs[-1], 'rank_Z:',rank_Zs[-1], ' iters:',iters[-1], '\\n')\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,mus)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('\\u03BC')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z+Y2/\\u03BC)')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,max_norm_eqs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('convergence error')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rank_Zs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z)')\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Face Segmentation\n",
            "lamda= 0.16\n",
            "max_iter= 500\n",
            "norm_choice= 0\n",
            "accuracy= 0.634375\n",
            "Parameter Evolution with iterations for face_seg\n",
            "Final values:\n",
            "mu: 10000000000.0  r: 638  max_norm_eq: 3.8425021164911755e-08 rank_Z: 640  iters: 500 \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pvw8L2C2aQhg"
      },
      "source": [
        "def soft_thres(s, t):\n",
        "  res = np.zeros( s.shape, dtype=np.float32 )\n",
        "  res[ s>=t ] = 1.0\n",
        "  res[ s<t ] = np.log( 1.0 + np.square(s[s<t]/t) )\n",
        "  return res"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C5bGBv8b26Eg"
      },
      "source": [
        "def motion_seg_k(lamda, lrr_itr_max, t, norm_choice=0):\n",
        "  # Estimating number of subspace segments\n",
        "  dataset = []\n",
        "  error1 = []\n",
        "  params = []\n",
        "  last_exec = ''\n",
        "  num_pred = 0\n",
        "\n",
        "  # hopkins155_path = '/content/ee609_data/Hopkins155/'\n",
        "  hopkins155_path = '/content/subspace-segmentation-via-low-rank-representation/Data/Hopkins155/'\n",
        "  for dir in os.listdir(hopkins155_path):\n",
        "    if os.path.isdir(hopkins155_path+dir):\n",
        "      data = loadmat(hopkins155_path+dir+'/'+dir+'_truth.mat')\n",
        "      # frames x points (a tracked point is one sample in this one motion sequnce)\n",
        "      X = np.concatenate([ data['x'][0,:,:].T, data['x'][1,:,:].T ])\n",
        "      row_ones = np.ones( (1,X.shape[1]), dtype=np.float32 )\n",
        "      X = np.concatenate( [X, row_ones] )\n",
        "      S = data['s']\n",
        "      dataset.append( {'name':dir, 'X':X, 'seg_ids':S} )\n",
        "  \n",
        "  for data in dataset:\n",
        "    print('Working on file: ', data['name'])\n",
        "\n",
        "    K = np.amax( data['seg_ids'] )\n",
        "\n",
        "    last_exec = data['name']\n",
        "    Z_star, E_star, params = lrr(data['X'], lamda, lrr_itr_max, norm_choice)\n",
        "    W = affinity_matrix(Z_star)\n",
        "    Ddiag = 1.0 / np.sqrt( W.sum(axis=1, dtype=np.float) )\n",
        "    D = np.diag(Ddiag)\n",
        "    DWD = np.dot( D, np.dot(W,D) )\n",
        "    L = np.identity( DWD.shape[0] ) - DWD\n",
        "    n = data['X'].shape[1]\n",
        "    U,s,Vh = np.linalg.svd(L)\n",
        "    soft_thres_s = soft_thres(s,t)\n",
        "    k = int( n - np.sum(soft_thres_s) )\n",
        "    err1 = 1.0*np.abs(K-k) / K\n",
        "    error1.append( err1 )\n",
        "    if(k == K):\n",
        "      num_pred = num_pred + 1\n",
        "\n",
        "  return error1, params, last_exec, num_pred\n"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kqWsr3ptbonX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ae71b547-348a-42f7-cca9-76b75e134d39"
      },
      "source": [
        "# Run this and the next 2 cells for lambda_k = 4, but different values of t_k = 0.06, 0.07, 0.08, 0.09, 0.10, 0.11\n",
        "# One run of this cell will take about 25-30 mins\n",
        "\n",
        "lamda_k = 4\n",
        "lrr_itr_max_k = 500\n",
        "t_k = 0.11\n",
        "norm_choice = 0\n",
        "error1, params, last_exec, num_pred = motion_seg_k(lamda_k, lrr_itr_max_k, t_k, norm_choice)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Working on file:  2T3RCR_g13\n",
            "Working on file:  1R2RC\n",
            "Working on file:  cars5\n",
            "Working on file:  cars2_07_g12\n",
            "Working on file:  cars2B_g23\n",
            "Working on file:  2T3RCRT_g12\n",
            "Working on file:  cars10\n",
            "Working on file:  cars5_g13\n",
            "Working on file:  two_cranes_g23\n",
            "Working on file:  2R3RTCRT\n",
            "Working on file:  cars2_06_g13\n",
            "Working on file:  people1\n",
            "Working on file:  people2\n",
            "Working on file:  cars2_06_g12\n",
            "Working on file:  cars8\n",
            "Working on file:  2R3RTC_g13\n",
            "Working on file:  cars1\n",
            "Working on file:  2RT3RTCRT\n",
            "Working on file:  1RT2TC_g13\n",
            "Working on file:  1R2RC_g12\n",
            "Working on file:  2T3RCRTP\n",
            "Working on file:  2T3RCRT_g23\n",
            "Working on file:  cars10_g23\n",
            "Working on file:  2RT3RCR_g23\n",
            "Working on file:  2RT3RCT_B_g12\n",
            "Working on file:  2RT3RCT_A_g12\n",
            "Working on file:  1R2RCT_A_g13\n",
            "Working on file:  1R2RCT_B_g13\n",
            "Working on file:  cars4\n",
            "Working on file:  1RT2RCR_g13\n",
            "Working on file:  2R3RTCRT_g12\n",
            "Working on file:  1R2RCT_B\n",
            "Working on file:  2RT3RCT_A_g23\n",
            "Working on file:  1R2RCR\n",
            "Working on file:  1RT2RCR\n",
            "Working on file:  2T3RCRTP_g23\n",
            "Working on file:  cars3\n",
            "Working on file:  cars2_07_g23\n",
            "Working on file:  cars3_g23\n",
            "Working on file:  1RT2TC\n",
            "Working on file:  1RT2TC_g23\n",
            "Working on file:  2RT3RCR\n",
            "Working on file:  2RT3RC_g12\n",
            "Working on file:  1R2TCR_g13\n",
            "Working on file:  cars6\n",
            "Working on file:  1R2RCR_g23\n",
            "Working on file:  1R2RCT_A_g23\n",
            "Working on file:  2R3RTC\n",
            "Working on file:  2T3RCRTP_g13\n",
            "Working on file:  cars9_g13\n",
            "Working on file:  three-cars_g12\n",
            "Working on file:  2RT3RCT_B_g13\n",
            "Working on file:  1R2RCT_B_g23\n",
            "Working on file:  2RT3RTCRT_g23\n",
            "Working on file:  cars5_g23\n",
            "Working on file:  1RT2TCRT_A_g23\n",
            "Working on file:  2RT3RTCRT_g12\n",
            "Working on file:  cars2_07\n",
            "Working on file:  cars2B\n",
            "Working on file:  1RT2RTCRT_A_g23\n",
            "Working on file:  2T3RCR_g23\n",
            "Working on file:  1RT2RCRT_g12\n",
            "Working on file:  1RT2TCRT_B_g13\n",
            "Working on file:  articulated_g23\n",
            "Working on file:  1R2RC_g23\n",
            "Working on file:  2T3RTCR_g23\n",
            "Working on file:  2RT3RCT_B_g23\n",
            "Working on file:  1R2RCT_B_g12\n",
            "Working on file:  cars2B_g13\n",
            "Working on file:  1R2TCRT\n",
            "Working on file:  2T3RTCR_g12\n",
            "Working on file:  1R2TCRT_g23\n",
            "Working on file:  1R2RCR_g12\n",
            "Working on file:  2R3RTCRT_g23\n",
            "Working on file:  2RT3RCT_A_g13\n",
            "Working on file:  1RT2TCRT_B\n",
            "Working on file:  1R2TCR_g12\n",
            "Working on file:  cars3_g12\n",
            "Working on file:  cars9\n",
            "Working on file:  2RT3RTCRT_g13\n",
            "Working on file:  1RT2TC_g12\n",
            "Working on file:  truck2\n",
            "Working on file:  head\n",
            "Working on file:  2T3RTCR\n",
            "Working on file:  kanatani3\n",
            "Working on file:  1R2TCRT_g13\n",
            "Working on file:  1RT2RTCRT_A_g12\n",
            "Working on file:  cars9_g23\n",
            "Working on file:  2RT3RCR_g13\n",
            "Working on file:  2RT3RCT_B\n",
            "Working on file:  three-cars_g13\n",
            "Working on file:  arm\n",
            "Working on file:  cars5_g12\n",
            "Working on file:  1RT2RTCRT_B_g13\n",
            "Working on file:  2T3RCR\n",
            "Working on file:  2T3RCTP\n",
            "Working on file:  1RT2RCRT\n",
            "Working on file:  1R2RCR_g13\n",
            "Working on file:  1RT2TCRT_A_g13\n",
            "Working on file:  2RT3RC_g23\n",
            "Working on file:  2RT3RCT_A\n",
            "Working on file:  1RT2RCR_g12\n",
            "Working on file:  1R2TCR\n",
            "Working on file:  cars2_06_g23\n",
            "Working on file:  1RT2RTCRT_B_g12\n",
            "Working on file:  dancing\n",
            "Working on file:  two_cranes_g12\n",
            "Working on file:  2T3RCTP_g12\n",
            "Working on file:  2T3RTCR_g13\n",
            "Working on file:  articulated\n",
            "Working on file:  1R2RC_g13\n",
            "Working on file:  two_cranes_g13\n",
            "Working on file:  articulated_g12\n",
            "Working on file:  1RT2RCR_g23\n",
            "Working on file:  2RT3RC_g13\n",
            "Working on file:  cars9_g12\n",
            "Working on file:  articulated_g13\n",
            "Working on file:  cars2_07_g13\n",
            "Working on file:  2RT3RCR_g12\n",
            "Working on file:  cars3_g13\n",
            "Working on file:  two_cranes\n",
            "Working on file:  cars2_06\n",
            "Working on file:  three-cars\n",
            "Working on file:  cars7\n",
            "Working on file:  2T3RCRT\n",
            "Working on file:  1RT2TCRT_B_g23\n",
            "Working on file:  2R3RTC_g23\n",
            "Working on file:  kanatani2\n",
            "Working on file:  kanatani1\n",
            "Working on file:  1RT2RCRT_g23\n",
            "Working on file:  1R2TCR_g23\n",
            "Working on file:  2T3RCTP_g13\n",
            "Working on file:  cars10_g12\n",
            "Working on file:  2RT3RC\n",
            "Working on file:  cars2\n",
            "Working on file:  1R2RCT_A_g12\n",
            "Working on file:  1RT2TCRT_A\n",
            "Working on file:  2T3RCTP_g23\n",
            "Working on file:  cars2B_g12\n",
            "Working on file:  truck1\n",
            "Working on file:  1RT2RTCRT_A_g13\n",
            "Working on file:  1RT2RTCRT_B_g23\n",
            "Working on file:  1R2TCRT_g12\n",
            "Working on file:  cars10_g13\n",
            "Working on file:  1RT2TCRT_A_g12\n",
            "Working on file:  2T3RCRT_g13\n",
            "Working on file:  1RT2RCRT_g13\n",
            "Working on file:  1RT2RTCRT_B\n",
            "Working on file:  three-cars_g23\n",
            "Working on file:  1R2RCT_A\n",
            "Working on file:  2T3RCRTP_g12\n",
            "Working on file:  2R3RTCRT_g13\n",
            "Working on file:  1RT2TCRT_B_g12\n",
            "Working on file:  1RT2RTCRT_A\n",
            "Working on file:  2T3RCR_g12\n",
            "Working on file:  2R3RTC_g12\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rmr0GbzHdM6l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "54cfc591-2481-43fd-b221-33ed96c88db3"
      },
      "source": [
        "from statistics import mean, stdev\n",
        "print('error statistics on hopkins155 - K estimation')\n",
        "print('lamda=',lamda_k)\n",
        "print('tau=',t_k)\n",
        "print('norm_choice=', norm_choice)\n",
        "print('mean error1',mean(error1))\n",
        "print('stdev error1', stdev(error1))\n",
        "print('max error1', max(error1))\n",
        "print('min error1', min(error1))\n",
        "print('No. of predicted:', num_pred)\n"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "error statistics on hopkins155 - K estimation\n",
            "lamda= 4\n",
            "tau= 0.11\n",
            "norm_choice= 0\n",
            "mean error1 0.27286324786324784\n",
            "stdev error1 0.2732468913189618\n",
            "max error1 1.5\n",
            "min error1 0.0\n",
            "No. of predicted: 69\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "llogR9NSdpo3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "6c9f9302-1c53-4287-fd87-0e651514ffbb"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "print('\\nParameter Evolution on file:', last_exec)\n",
        "iters = []\n",
        "mus = []\n",
        "rs = []\n",
        "rank_Zs = []\n",
        "max_norm_eqs = []\n",
        "for d in params:\n",
        "  iters.append(d['iter'])\n",
        "  mus.append(d['mu'])\n",
        "  rs.append(d['r'])\n",
        "  rank_Zs.append(d['rank_Z'])\n",
        "  max_norm_eqs.append(d['max_norm_eq'])\n",
        "\n",
        "print('Final values:')\n",
        "print('mu:',mus[-1], ' r:',rs[-1], ' max_norm_eq:',max_norm_eqs[-1], 'rank_Z:',rank_Zs[-1], ' iters:',iters[-1])\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,mus)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('\\u03BC')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z+Y2/\\u03BC)')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,max_norm_eqs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('convergence error')\n",
        "plt.show()\n",
        "\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(iters,rank_Zs)\n",
        "plt.xlabel('# iteration')\n",
        "plt.ylabel('rank(Z)')\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Parameter Evolution on file: 2R3RTC_g12\n",
            "Final values:\n",
            "mu: 123948.02823537958  r: 9  max_norm_eq: 9.711357579211821e-09 rank_Z: 59  iters: 268\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l0PdXr1DhQKC"
      },
      "source": [
        ""
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lPOuWXFYmS6d"
      },
      "source": [
        ""
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RweH6wrOmTWi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "8c61e858-20e8-4780-aad5-c7ed0584be4e"
      },
      "source": [
        "# motion_segmentation (mean error vs lamda plot)\n",
        "# norm_choice = 0\n",
        "lamda = np.array([1.0, 2.0, 3.0, 3.6, 4.0, 4.6, 6.0, 7.0])\n",
        "mean_error = np.array([ 0.026637113764302226,  0.023475780703100305, 0.02016318489349344,  0.01779393939225322, 0.017418053639225082, 0.017213136077969312, 0.028186935117254917, 0.031127707291906805])\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(lamda,mean_error,'-o')\n",
        "plt.xlabel('\\u03BB')\n",
        "plt.ylabel('Mean Error')\n",
        "plt.show()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eBxMWjiCoagI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "outputId": "a535c829-4e94-4519-d564-e5b96d6a57ef"
      },
      "source": [
        "# face segmentation (yaleb10) (accuracy vs lambda plot)\n",
        "# norm_choice = 0\n",
        "lamda = np.array([0.06, 0.1, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22])\n",
        "acc = np.array([0.584375, 0.5203125, 0.44375, 0.534375, 0.634375, 0.459375, 0.5453125, 0.5328125])\n",
        "plt.figure(figsize=(6,4))\n",
        "plt.rcParams.update({'font.size': 14})\n",
        "plt.plot(lamda,acc,'-o')\n",
        "plt.xlabel('\\u03BB')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LBPFE003sITo"
      },
      "source": [
        ""
      ],
      "execution_count": 20,
      "outputs": []
    }
  ]
}