test_hnsw_mips.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import pickle\n",
    "from hnsw.hnsw import HNSW\n",
    "import numpy as np\n",
    "from typing import Tuple\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(\n",
    "    num_atoms: int = 10**3,\n",
    "    len_signal: int = 10**4,\n",
    "    num_signals: int = 1,\n",
    "    num_best_atoms: int =5,\n",
    "    seed: int = 0,\n",
    ") -> Tuple[np.ndarray, np.ndarray]:\n",
    "\n",
    "\t\n",
    "    rng = np.random.default_rng(seed)\n",
    "    atoms_array = np.empty((num_atoms, len_signal))\n",
    "    means = rng.normal(size=num_atoms)\n",
    "    atoms_array = np.empty((num_atoms, len_signal))\n",
    "    for idx in range(num_atoms):\n",
    "      atoms_array[idx] = rng.normal(loc=means[idx], size=len_signal)\n",
    "    signal = rng.normal(loc=rng.normal(), size=(num_signals, len_signal))\n",
    "    if num_signals == 1:\n",
    "        signal = signal.reshape(1,-1)\n",
    "\n",
    "    return atoms_array, signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_complexity(dimension):\n",
    "    \n",
    "    top_k = 50\n",
    "\n",
    "    atoms, signal = generate_data(num_atoms=1000, len_signal=dimension, num_best_atoms=top_k)\n",
    "    \n",
    "    hnsw = HNSW('cosine', m0=16, ef=128)\n",
    "    for i in range(len(atoms)):\n",
    "        hnsw.add(atoms[i])\n",
    "\n",
    "\n",
    "    # save index\n",
    "    with open('glove.ind', 'wb') as f:\n",
    "        picklestring = pickle.dump(hnsw, f, pickle.HIGHEST_PROTOCOL)\n",
    "\n",
    "    # load index\n",
    "    fr = open('glove.ind','rb')\n",
    "    hnsw_n = pickle.load(fr)\n",
    "\n",
    "    add_point_time = time.time()\n",
    "    idx = hnsw_n.search(signal, top_k)\n",
    "    search_time = time.time() - add_point_time\n",
    "\n",
    "    \n",
    "    \n",
    "    return search_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Searchtime: 0.006575\n",
      "top 10 from hnsw:[691, 190, 51, 69, 616, 176, 12, 478, 775, 98]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "dim = 200\n",
    "num_elements = 100\n",
    "top_k = 10\n",
    "\n",
    "atoms, signal = generate_data(num_atoms=1000, len_signal=200)\n",
    "\n",
    "\n",
    "hnsw = HNSW('cosine', m0=16, ef=128)\n",
    "\n",
    "for i in range(len(atoms)):\n",
    "    hnsw.add(atoms[i])\n",
    "\n",
    "\n",
    "# save index\n",
    "with open('glove.ind', 'wb') as f:\n",
    "    picklestring = pickle.dump(hnsw, f, pickle.HIGHEST_PROTOCOL)\n",
    "\n",
    "# load index\n",
    "fr = open('glove.ind','rb')\n",
    "hnsw_n = pickle.load(fr)\n",
    "\n",
    "add_point_time = time.time()\n",
    "idx = hnsw_n.search(signal, top_k)\n",
    "search_time = time.time() - add_point_time\n",
    "candidates = [k[0] for k in idx]\n",
    "print(\"Searchtime: %f\" % (search_time ))\n",
    "print(f\"top {top_k} from hnsw:{candidates}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[478 303 616  69 948 413 284 238  12 982]]\n",
      "time taken by naive search:0.010150909423828125\n",
      "precision=40.0 percent\n",
      "speedup over naive search = 1.5437833133906234\n"
     ]
    }
   ],
   "source": [
    "num_best_atoms =10\n",
    "\n",
    "begin = time.time()\n",
    "naive_candidates_array = (\n",
    "                np.matmul(atoms, signal.transpose())\n",
    "                .argsort(axis=0)[:num_best_atoms]\n",
    "                .transpose()\n",
    "            )\n",
    "naive_time = time.time() - begin \n",
    "\n",
    "print(naive_candidates_array)\n",
    "\n",
    "print(f\"time taken by naive search:{naive_time}\")\n",
    "\n",
    "intersection = np.intersect1d(candidates, naive_candidates_array[0])\n",
    "precision = len(intersection)\n",
    "speedup = naive_time/search_time\n",
    "print(f\"precision={precision*100/top_k} percent\\nspeedup over naive search = {speedup}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting sample complexity plot\n",
    "\n",
    "dimensions = [2**i for i in range(4,15)]\n",
    "sample_comp  = []\n",
    "for dimension in dimensions:\n",
    "    sample_comp.append(sample_complexity(dimension))\n",
    "\n",
    "plt.plot(dimensions,sample_comp)\n",
    "plt.xlabel(\"Dimension of vectors\")\n",
    "plt.ylabel(\"Sample complexity\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Movie Lens Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 10 candidates (indices):\n",
      "[2831, 3524, 3667, 3179, 3485, 3504, 3604, 3679, 3666, 3436]\n",
      "search time: 0.008379697799682617\n",
      "Top 10 candidates using naive approach (indices): [3666 3426 3524 ...   75  851  183]\n",
      "Accuracy compared to naive method: 50.00%\n",
      "Speedup ratio: 10.81 times faster than naive computation.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "from surprise import Dataset, Reader\n",
    "from surprise.model_selection import train_test_split\n",
    "\n",
    "# Load the MovieLens dataset (100k version for simplicity)\n",
    "reader = Reader(line_format='user item rating timestamp', sep='\\t')\n",
    "data = Dataset.load_builtin('ml-1m')\n",
    "trainset, testset = train_test_split(data, test_size=0.2)\n",
    "\n",
    "# Build a user-item matrix\n",
    "user_item_matrix = np.zeros((trainset.n_users, trainset.n_items))\n",
    "for uid, iid, rating in trainset.all_ratings():\n",
    "    user_item_matrix[int(uid), int(iid)] = rating\n",
    "\n",
    "# Use SVD to reduce dimensionality\n",
    "svd = TruncatedSVD(n_components=50)\n",
    "atoms = svd.fit_transform(user_item_matrix.T)  # Transpose to get item embeddings\n",
    "\n",
    "# Create a signal (simulate a user's preference vector)\n",
    "user_id = 0  # Choose a user ID from the dataset\n",
    "user_ratings = user_item_matrix[user_id]\n",
    "signal = np.dot(user_ratings, atoms)  # Weighted average of rated item embeddings\n",
    "signals = signal[np.newaxis, :]  # Ensure signal has 2D shape for batch processing\n",
    "\n",
    "\n",
    "num_best_atoms = 10  # Top-k items to retrieve\n",
    "\n",
    "# Run hnsw MIPS\n",
    "hnsw = HNSW('cosine', m0=24, ef=200)\n",
    "\n",
    "for i in range(len(atoms)):\n",
    "    hnsw.add(atoms[i])\n",
    "\n",
    "\n",
    "# save index\n",
    "with open('glove.ind', 'wb') as f:\n",
    "    picklestring = pickle.dump(hnsw, f, pickle.HIGHEST_PROTOCOL)\n",
    "\n",
    "# load index\n",
    "fr = open('glove.ind','rb')\n",
    "hnsw_n = pickle.load(fr)\n",
    "\n",
    "add_point_time = time.time()\n",
    "idx = hnsw_n.search(signal, top_k)\n",
    "search_time = time.time() - add_point_time\n",
    "candidates = [k[0] for k in idx]\n",
    "\n",
    "# Output results\n",
    "print(f\"Top {num_best_atoms} candidates (indices):\\n{candidates}\")\n",
    "print(f\"search time: {search_time}\")\n",
    "\n",
    "# Naive approach for validation\n",
    "begin = time.time()\n",
    "inner_products = np.dot(atoms, signal)\n",
    "top_k_naive = np.argsort(inner_products)[num_best_atoms:]\n",
    "naive_time = time.time()-begin\n",
    "print(f\"Top {num_best_atoms} candidates using naive approach (indices): {top_k_naive}\")\n",
    "\n",
    "# Compare results\n",
    "accuracy = len(np.intersect1d(candidates, top_k_naive)) / num_best_atoms\n",
    "print(f\"Accuracy compared to naive method: {accuracy * 100:.2f}%\")\n",
    "\n",
    "# Compute speedup ratio\n",
    "speedup_ratio = search_time / naive_time\n",
    "print(f\"Speedup ratio: {speedup_ratio:.2f} times faster than naive computation.\")"
   ]
  }
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