區域性切空間排列(Local Tangent Space Alignment).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 區域性切空間排列(Local Tangent Space Alignment)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 先引入我們需要的packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os \n",
    "import numpy as np\n",
    "import scipy as sp\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": "84e3b25f54a944c8a96e7cc955d7a9ef",
       "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",
    "k=30\n",
    "neighbors =np.zeros((N,k))\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",
    "    neighbors[i]=Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LTSA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cda2b2f5151c4f77be6b896ee6770202",
       "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": [
    "B=np.zeros((N,N))\n",
    "n_components=2\n",
    "n_neighbors=k\n",
    "neighbors=neighbors.astype(int)\n",
    "for i in tqdm(range(N)):\n",
    "    tensor=X[neighbors[i],:]-np.mean(X[neighbors[i],:],axis=0)\n",
    "    V=sp.linalg.svd(tensor,full_matrices=True)[0]\n",
    "    Gi = np.zeros((n_neighbors, n_components + 1))\n",
    "    Gi[:, 1:] = V[:, :n_components]\n",
    "    Gi[:, 0] = 1.0 / np.sqrt(n_neighbors)\n",
    "    GiGiT = np.dot(Gi, Gi.T)\n",
    "    nbrs_x, nbrs_y = np.meshgrid(neighbors[i], neighbors[i])\n",
    "    B[nbrs_x, nbrs_y] -= GiGiT\n",
    "    B[neighbors[i], neighbors[i]] += 1\n",
    "U,V=sp.linalg.eigh(B)\n",
    "idx=np.argsort(U.real)\n",
    "X_sub=(V[:,idx[1:3]]).real"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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
}