main.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import itertools\n",
    "import math\n",
    "\n",
    "import sklearn.datasets\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "import numpy as np\n",
    "from numpy import linalg\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial import distance\n",
    "from Ball_Tree import Ball_Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "CONVENTIONS\n",
    "#* indicates statistical line(s) of code\n",
    "#~ indicates debugging line\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This is a really easy case\n",
    "X, y= sklearn.datasets.make_blobs(n_samples=1000, cluster_std=.3, centers=[(2,2),(4,2)])\n",
    "scaled_X = MinMaxScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f342d72aee0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid()\n",
    "plt.scatter(X[:,0],X[:,1],c=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Clusterer():\n",
    "    \"\"\"\n",
    "    Clusterer Class modeled loosely on SciKit Learn conventions.\n",
    "    hyperparameters are specified in init, and data is passed in during fit.\n",
    "    Data is sorted into ball tree upon fit, but ball tree is not perserved as attribute to save memory space.\n",
    "    ATTRUBUTES:\n",
    "        int gridsize=10: the number of grid rows per dimension\n",
    "        int n_elements=1: the number of elements in the ball tree at which to  perform a brute search\n",
    "        float eps=.1: the radius for calculating local density\n",
    "          should be modified to 'auto' default that picks value based on gridsize\n",
    "    METHODS:\n",
    "        fit(X): fits model params\n",
    "    \"\"\"\n",
    "    def __init__(self, gridsize=10, n_elements=1, eps=.1):\n",
    "        self.gridsize = gridsize\n",
    "        self.eps = eps\n",
    "        self.n_elements = n_elements\n",
    "        \n",
    "    def fit(self, X):\n",
    "        tree = Ball_Tree(X, self.n_elements)\n",
    "        self.grid = self._initialize_grid(X, tree) # self is temp for debug\n",
    "        \n",
    "    def _initialize_grid(self, X, tree):\n",
    "        #creates a grid of gradients at each point\n",
    "        #params:\n",
    "            #np.array X: the data\n",
    "            #Ball_Tree tree: the data in tree form for fast density calculations\n",
    "        #returns:\n",
    "            #np.array: it is an n+1 dimensional array with n being the dimensionality of the data\n",
    "              #each dimension has gridsize elements except for the last, which has n+1 elements for each\n",
    "              #normalized partial with the last element being the magnitude\n",
    "        n_dim = X.shape[1]\n",
    "        min_coord = X.min() - self.eps*1.0001 # 1.001 is a fudge factor. so points at edge to have 0 density\n",
    "        max_coord = X.max() + self.eps*1.0001\n",
    "        width = max_coord - min_coord\n",
    "        offset = width / (self.gridsize)\n",
    "        # realy (gridsize - 1 + 1) -1 because we want offset*(gridsize-1)+ min_pts to evaluate to max\n",
    "        #+1 because we actually want gridsize to add padding so we can compute gradient at ends \n",
    "       \n",
    "        density_shape = (self.gridsize+1,)*n_dim\n",
    "        density_grid = np.empty(density_shape)\n",
    "        density_grid_indices = itertools.product(range(self.gridsize+1),repeat=n_dim)\n",
    "        for grid_i in density_grid_indices:\n",
    "            coords = np.array([offset*i+min_coord for i in grid_i])\n",
    "            #coords is a coordinate pair in n_dim space\n",
    "            density_grid[grid_i] = tree.calc_local_density(coords, self.eps)\n",
    "\n",
    "        #desnity grid now contains densities of each point in the grid\n",
    "        gradient_shape = (self.gridsize+1,)*n_dim+(n_dim+1,) \n",
    "        #last dimension is dimensionality of the gradient itself plus one for magnitude\n",
    "        #gridsize+1 allows us to create some padding as was done with the density\n",
    "        #the padding will be left as zeros\n",
    "        gradient_grid = np.zeros(gradient_shape)\n",
    "        gradient_grid_indices = itertools.product(range(self.gridsize),repeat=n_dim) #does not include padding\n",
    "        for grid_i in gradient_grid_indices:\n",
    "            this_density = density_grid[grid_i]\n",
    "            this_gradient = [this_density - density_grid[grid_i[:dim]+((grid_i[dim]+1),)+grid_i[dim+1:]]\n",
    "                             for dim in range(n_dim)]\n",
    "            #note gradient goes towards lower density\n",
    "            magnitude = linalg.norm(this_gradient)\n",
    "            if magnitude > 0:\n",
    "                this_gradient = [partial/magnitude for partial in this_gradient]\n",
    "            this_gradient.append(magnitude)\n",
    "            gradient_grid[grid_i] = this_gradient\n",
    "            \n",
    "            #for debugging only\n",
    "            self.density_grid = density_grid\n",
    "        return gradient_grid\n",
    "    \n",
    "    def _initialize_function_list(self, grid):\n",
    "        '''\n",
    "        ALGORITHM:\n",
    "            For each gradient in the grid, check all adjacent gradients in the 1st orthant\n",
    "            For each gradient that had an angle greater than 90 and points towards the gradient \n",
    "              add those gradients\n",
    "            return a hyperplane maximally perpendicular to the two gradients\n",
    "        '''\n",
    "        func_list = []\n",
    "        #*\n",
    "        self.n_multiple_obtuse_grads = 0\n",
    "        grid_indices = itertools.product(range(self.gridsize),repeat=n_dim) #does not include padding\n",
    "        for grid_i in gradient_grid_indicies:\n",
    "            this_grad = grid[grid_i]\n",
    "            obtuse_grad_u = np.zeros(n_dim+1) #initialize empty gradient that has obtuse angle with grad\n",
    "            #u indicates unit vector\n",
    "            n_obtuse = 0 #count of num of vectors that had obtuse angles between grad\n",
    "            #iterate through all adjacent gradients in 1st orthant looking for obtuse angles\n",
    "            #if obtuse, sum them into obtuse_grad\n",
    "            for dim in range(n_dim):\n",
    "                adj_grad = grid[grid_i[:dim]+((grid_i[dim]+1),)+grid_i[dim+1:]]\n",
    "                cos = this_grad[:-1] @ adj_grad[:-1]\n",
    "                if cos < 0: #the angle between the vectors is greater than 90\n",
    "                    Must also check if are pointed towards eachother!!!!!!!\n",
    "                    n_obtuse += 1\n",
    "                    obtuse_grad += adj_grad[:-1]*adj_grad[-1]\n",
    "            #*\n",
    "            self.n_multiple_obtuse_grads += 1\n",
    "            #if any obtuse angles were found, normalize them\n",
    "            if n_obtuse > 0:\n",
    "                obtuse_grad /= n_obtuse\n",
    "                obtuse_mag = linalg.norm(obtuse_grad)\n",
    "                obtuse_grad /= obtuse_mag\n",
    "                normal = obtuse_grad - this_grad[:-1] #this is the normal vector of the plane between grads\n",
    "LEFT HERE!!!!!!!!!!!!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It becomes essential that we decide how the code to put a point in a boundary is implemented because\n",
    "we need to know what data should be stored\n",
    "I think we probably want a list of objects of a custom class  or named tuples\n",
    "In either case, they should have:\n",
    "    a function/method that is the hyperplane (this might be a regular func, or it may have to be a sympy \n",
    "        function so we can find intersections easier)\n",
    "    a list (probably?) of interior and exterior rectangles (if you're in the interior, you know that function\n",
    "    aplies, if you're not in the exterior you know it doesn't. if you're in neither, you go to next element in\n",
    "    list and check if you're in those rectangles until you get to the base lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_2d_gradient_grid(grid, X, y, eps):\n",
    "    n_dim = 2\n",
    "    gridsize = grid.shape[0]\n",
    "    min_coord = X.min() - eps*1.0001 #the 1.001 is a fudge factor. Want points at edge to have 0 density\n",
    "    max_coord = X.max() +eps*1.0001#drop positive epsilon because no longer in gradient\n",
    "    width = max_coord - min_coord\n",
    "    offset = width / (gridsize - 1) # this is necessary because you want to have points on both ends\n",
    "    max_vector_len = grid[:,...,-1].max()\n",
    "    \n",
    "    #prepare yourself for some array shaping\n",
    "    vectors = grid.reshape(-1, grid.shape[-1]) #this takes the grid and collapses it into an\n",
    "    #array of vectors through numpy array reshape magic\n",
    "    \n",
    "    grid_indices = np.array(list(itertools.product(range(gridsize),repeat=n_dim)))\n",
    "    print(grid_indices.shape)\n",
    "    grid_coords = grid_indices * offset + min_coord\n",
    "    plt.scatter(scaled_X[:,0],scaled_X[:,1],c=y, marker='.')\n",
    "\n",
    "    plt.quiver(grid_coords[:,0], grid_coords[:,1], vectors[:,0]*vectors[:,2], vectors[:,1]*vectors[:,2],\n",
    "              scale=max_vector_len/offset, scale_units='width') \n",
    "\n",
    "def plot_2d_density_values(grid, X, y, eps):\n",
    "    n_dim = 2\n",
    "    min_coord = X.min() - eps*1.0001 #the 1.001 is a fudge factor. Want points at edge to have 0 density\n",
    "    max_coord = X.max() + eps*1.0001\n",
    "    width = max_coord - min_coord\n",
    "    offset = width / (grid.shape[0] - 1) # this is necessary because you want to have points on both ends\n",
    "    max_density = grid.max()\n",
    "    plt.scatter(scaled_X[:,0],scaled_X[:,1],c=y, marker='.')\n",
    "    for grid_i in itertools.product(range(grid.shape[0]),repeat=n_dim):\n",
    "        coords = np.array([offset*i+min_coord for i in grid_i])\n",
    "        #coords is a coordinate pair in n_dim space\n",
    "        plt.scatter(coords[0], coords[1], c='y', alpha=.5,  marker='+')\n",
    "        plt.scatter(coords[0], coords[1], alpha=((grid[grid_i]/max_density)**.3), c='k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(121, 2)\n"
     ]
    }
   ],
   "source": [
    "clusterer = Clusterer(eps=.1)\n",
    "clusterer.fit(scaled_X)\n",
    "plot_2d_density_values(clusterer.density_grid, scaled_X, y, .1)\n",
    "plt.show()\n",
    "plot_2d_gradient_grid(clusterer.grid, scaled_X, y, .1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = np.array([[x[0]*(1/9)-.03,x[1]*(1/9)-.03] for x in itertools.product(range(10),repeat=2)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Debugging Ball Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def naive_density(data_pt, X, epsilon):\n",
    "    return np.nonzero((distance.cdist(data_pt.reshape(1,-1), X) < epsilon)[0])[0].shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare(data_pt, epsilon):\n",
    "    print(f'naive:{naive_density(data_pt, X, epsilon)}\\tball:{tree.calc_local_density(data_pt, epsilon)}')\n",
    "def compare_bool(data_pt, epsilon):\n",
    "    n_d = naive_density(data_pt, X, epsilon)\n",
    "    b_d = tree.calc_local_density(data_pt,epsilon)\n",
    "    if n_d != b_d:\n",
    "        print(f'{n_d}!={b_d}')\n",
    "        print(type(n_d), type(b_d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "a=np.array([0,1])\n",
    "b = np.array([0,0])\n",
    "for x in X:\n",
    "    compare_bool(x, random.random() * 2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tree.root.data_pt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tree.root.radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "distance.euclidean(a,tree.root.data_pt) + tree.root.radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_node(node, color):\n",
    "    plt.scatter(X[:,0],X[:,1],c=y)\n",
    "    plt.scatter(node.data_pt[0], node.data_pt[1], c=color)\n",
    "    plt.axis(\"equal\")\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "\n",
    "left = tree.root\n",
    "right = tree.root\n",
    "while left:\n",
    "    print(left.data_pt, X[left.data_pt_i], left.n_elements, left.radius)\n",
    "    plot_node(left, 'r')\n",
    "    plot_node(right, 'b')\n",
    "    left = left.left\n",
    "    right = right.right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[1,2,3],[4,5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(arr[0] <=2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "type((distance.cdist(np.array([0,0,0]).reshape(1,-1), arr)[0] <= 2).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "#shape of b is 2 by 2 by 3 for 2 spatial and then gradient\n",
    "b = np.array([[[0,1,1],[1,1,2]],[[0,0,0],[1,0,1]]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "a  = b[0,1, :-1]\n",
    "c = np.array([0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "a += c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1],\n",
       "       [1, 1, 2],\n",
       "       [0, 0, 0],\n",
       "       [1, 0, 1]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.reshape(-1, b.shape[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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