拉普拉斯特徵映射(Laplacian Eigenmaps).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 拉普拉斯特徵映射(Laplacian Eigenmaps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 先引入我們需要的packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import random\n",
    "from tqdm.notebook import tqdm\n",
    "from random import choices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "X=digits.data/16\n",
    "y=digits.target\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "plt.gray() \n",
    "for i in range(100):\n",
    "    plt.subplot(20, 20, i + 1)\n",
    "    plt.imshow(digits.images[i], cmap=plt.cm.gray, vmax=16, interpolation='nearest')\n",
    "    plt.xticks(())\n",
    "    plt.yticks(())\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ball Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BuildSubtree(root,points,index,leaf_size,depth):\n",
    "    if(depth==0):\n",
    "        return\n",
    "    centroid=np.mean(points[index,:],axis=0)\n",
    "    root.centroid=centroid\n",
    "    root.radius=np.max(np.sum((points[index,:]-centroid)**2,axis=1))**0.5\n",
    "    farthest_point_1=np.argmax(np.sum((points[index,:]-centroid)**2,axis=1))\n",
    "    real_index_1=index[farthest_point_1]\n",
    "    distance_array_1=np.sum((points[index,:]-points[real_index_1,:])**2,axis=1)\n",
    "    farthest_point_2=np.argmax(np.sum((points[index,:]-points[real_index_1,:])**2,axis=1))\n",
    "    real_index_2=index[farthest_point_2]\n",
    "    distance_array_2=np.sum((points[index,:]-points[real_index_2,:])**2,axis=1)\n",
    "    BOOL=(distance_array_1<=distance_array_2)\n",
    "    child1_index,child2_index=index[BOOL],index[~BOOL]\n",
    "    root.index1,root.index2=real_index_1,real_index_2\n",
    "    if(len(child1_index)<=leaf_size and len(child2_index)<=leaf_size):\n",
    "        if(depth==1):\n",
    "            print(\"tree is not complete\")\n",
    "        root.child1=\"end\"\n",
    "        root.child2=\"end\"\n",
    "    elif(len(child1_index)<=leaf_size):\n",
    "        root.child1=\"end\"\n",
    "        root.child2=Tree()\n",
    "        BuildSubtree(root.child2,points,child2_index,leaf_size,depth-1)\n",
    "    elif(len(child2_index)<=leaf_size):\n",
    "        root.child2=\"end\"\n",
    "        root.child1=Tree()\n",
    "        BuildSubtree(root.child1,points,child1_index,leaf_size,depth-1)\n",
    "    else:\n",
    "        root.child1=Tree()\n",
    "        BuildSubtree(root.child1,points,child1_index,leaf_size,depth-1)\n",
    "        root.child2=Tree()\n",
    "        BuildSubtree(root.child2,points,child2_index,leaf_size,depth-1)\n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Nearest Neighbor Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check(X,p,k,Q,index):\n",
    "    if(np.sum((p-X[index,:])**2)<np.sum((p-X[Q[0],:])**2)):\n",
    "        Q.append(index)\n",
    "        Q=np.array(Q)\n",
    "        Q=list(Q[np.argsort(-1*np.sum((p-X[Q,:])**2,axis=1))])\n",
    "        if(len(Q)>k):    \n",
    "            del Q[0]\n",
    "    return Q\n",
    "\n",
    "def kNN_search(X,p,k,Q,root):\n",
    "    if(np.sqrt(np.sum((p-root.centroid)**2))-root.radius>=np.sqrt(np.sum((p-X[Q[0],:])**2))):\n",
    "        return Q\n",
    "    elif(root.child1==\"end\" and root.child2==\"end\"):\n",
    "        Q=check(X,p,k,Q,root.index1)\n",
    "        Q=check(X,p,k,Q,root.index2)\n",
    "    elif(root.child1==\"end\"):\n",
    "        Q=check(X,p,k,Q,root.index1)\n",
    "        Q=kNN_search(X,p,k,Q,root.child2)\n",
    "    elif(root.child2==\"end\"):\n",
    "        Q=check(X,p,k,Q,root.index2)\n",
    "        Q=kNN_search(X,p,k,Q,root.child1)\n",
    "    else:\n",
    "        Q=kNN_search(X,p,k,Q,root.child1)\n",
    "        Q=kNN_search(X,p,k,Q,root.child2)\n",
    "    return Q    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Building Tree and Nearest Neighbor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7a81a9a0d61b4390ac2574629db30901",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=1797), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "class Tree:\n",
    "    def __init__(self):\n",
    "        self.child1=None\n",
    "        self.child2=None\n",
    "        self.radius=None\n",
    "        self.centroid=None\n",
    "        self.index1=None\n",
    "        self.index2=None\n",
    "root=Tree()\n",
    "N,M=X.shape\n",
    "Index=np.array(range(0,N))\n",
    "BuildSubtree(root,X,Index,1,30)\n",
    "W=np.zeros((N,N))\n",
    "k=3\n",
    "for i in tqdm(range(0,N)):\n",
    "    Q=[]\n",
    "    while(len(Q)!=k+1):\n",
    "        Q=list(np.random.randint(N,size=1))\n",
    "        Q=kNN_search(X,X[i,:],k+1,Q,root)\n",
    "    del Q[k]\n",
    "    W[i,Q]=np.exp(-np.sqrt(np.sum((X[Q,:]-X[i,:])**2,axis=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Laplacian Eigenmaps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sym_W=np.maximum(W,W.T)\n",
    "D=np.diag(np.sum(Sym_W,axis=1))\n",
    "Arr=np.dot(np.linalg.inv(D),D-Sym_W)\n",
    "U,V=np.linalg.eig(Arr)\n",
    "X_sub=V[:,:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "color=[\"#FF0000\",\"#FFFF00\",\"#00FF00\",\"#00FFFF\",\"#0000FF\",\n",
    "       \"#FF00FF\",\"#FF0088\",\"#FF8800\",\"#00FF99\",\"#7700FF\"]\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "for i in range(0,10):\n",
    "    BOOL=(y==i)\n",
    "    plt.scatter(X_sub[BOOL,0],X_sub[BOOL,1],c=color[i],label=i)\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "plt.legend(fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}