3. Embeddings.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "507f97c2",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=150px> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Generative AI with OpenAI API</h1>\n",
    "<h1>Embeddings</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "22ea4375",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from ipywidgets import interact\n",
    "import tiktoken\n",
    "from openai import OpenAI\n",
    "\n",
    "import nltk\n",
    "from nltk.corpus import reuters\n",
    "from nltk import bigrams, trigrams\n",
    "\n",
    "import scipy\n",
    "from scipy.spatial.distance import cosine as cosine_similarity\n",
    "\n",
    "import os\n",
    "import gzip\n",
    "\n",
    "import tqdm as tq\n",
    "from tqdm.notebook import tqdm\n",
    "tqdm.pandas()\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08ff8650",
   "metadata": {},
   "source": [
    "We start by printing out the versions of the libraries we're using for future reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "72778f4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.11.7\n",
      "IPython version      : 8.12.3\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 23.4.0\n",
      "Machine     : arm64\n",
      "Processor   : arm\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 5217868ae783ab0315a9d79f2e1ac0fb25095003\n",
      "\n",
      "numpy    : 1.26.4\n",
      "pandas   : 2.1.4\n",
      "tiktoken : 0.6.0\n",
      "tqdm     : 4.66.2\n",
      "scipy    : 1.11.4\n",
      "nltk     : 3.8.1\n",
      "watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95305d0c",
   "metadata": {},
   "source": [
    "Get the API key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c22118eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "client = OpenAI()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01443066",
   "metadata": {},
   "source": [
    "# Extract embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8e482d6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "response = client.embeddings.create(\n",
    "    model=\"text-embedding-ada-002\",\n",
    "    input=\"Your text goes here\",\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "703b3f8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CreateEmbeddingResponse(data=[Embedding(embedding=[-0.013014387339353561, -0.013467525132000446, 0.009609189815819263, -0.021537378430366516, -0.02504253387451172, 0.044007688760757446, -0.01971150003373623, -0.01577986218035221, -0.010795344598591328, -0.023349929600954056, 0.005287719890475273, 0.016606172546744347, -0.009849085472524166, -0.0010128965368494391, 0.003032025881111622, -0.006457215175032616, 0.02437615394592285, -0.004034926649183035, 0.014460430480539799, -0.012201405130326748, -0.0046146768145263195, 0.01326761208474636, 0.013207637704908848, 0.01222139596939087, -0.004747952334582806, 0.0010237251408398151, 0.01196150854229927, -0.017259223386645317, 0.015926465392112732, 0.009502568282186985, 0.005900788586586714, -0.006327271461486816, -0.020177964121103287, -0.006793736945837736, -0.017872292548418045, -0.009056094102561474, 0.0024939244613051414, -0.015926465392112732, 0.027987930923700333, -0.005111129023134708, 0.011328447610139847, 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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "response"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f48e6cb",
   "metadata": {},
   "source": [
    "The embedding itself is a high dimensional vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f4391e77",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 0.02780134417116642,\n",
       " ...]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "response.data[0].embedding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d5808e9",
   "metadata": {},
   "source": [
    "And the similarity between vectors represents the similarity between the texts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53b4155f",
   "metadata": {},
   "outputs": [],
   "source": [
    "emb1 = client.embeddings.create(\n",
    "    model=\"text-embedding-ada-002\",\n",
    "    input=\"love\",\n",
    "    ).data[0].embedding\n",
    "\n",
    "emb2 = client.embeddings.create(\n",
    "    model=\"text-embedding-ada-002\",\n",
    "    input=\"kindness\",\n",
    "    ).data[0].embedding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c123847e",
   "metadata": {},
   "source": [
    "Cosine similarity is a quick and dirty way to measure how similar two vectors are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4f533ab6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.162337414711768"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosine_similarity(emb1, emb2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dfdadc1",
   "metadata": {},
   "source": [
    "Naturally, unrelated words have much lower degree of similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7c6ebf27",
   "metadata": {},
   "outputs": [],
   "source": [
    "emb3 = client.embeddings.create(\n",
    "    model=\"text-embedding-ada-002\",\n",
    "    input=\"airplane\",\n",
    "    ).data[0].embedding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fec66047",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22999315123592778"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cosine_similarity(emb2, emb3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c3e7a53",
   "metadata": {},
   "source": [
    "# Generate embeddings for the Reuters sentences dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0206f42",
   "metadata": {},
   "source": [
    "We're going to use Reuters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a87107b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "sentences = [\" \".join(word for word in sent) for sent in reuters.sents()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f552f222",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "54716"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sentences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aa9c7281",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[\"ASIAN EXPORTERS FEAR DAMAGE FROM U . S .- JAPAN RIFT Mounting trade friction between the U . S . And Japan has raised fears among many of Asia ' s exporting nations that the row could inflict far - reaching economic damage , businessmen and officials said .\",\n",
       " 'They told Reuter correspondents in Asian capitals a U . S . Move against Japan might boost protectionist sentiment in the U . S . And lead to curbs on American imports of their products .',\n",
       " \"But some exporters said that while the conflict would hurt them in the long - run , in the short - term Tokyo ' s loss might be their gain .\",\n",
       " \"The U . S . Has said it will impose 300 mln dlrs of tariffs on imports of Japanese electronics goods on April 17 , in retaliation for Japan ' s alleged failure to stick to a pact not to sell semiconductors on world markets at below cost .\",\n",
       " 'Unofficial Japanese estimates put the impact of the tariffs at 10 billion dlrs and spokesmen for major electronics firms said they would virtually halt exports of products hit by the new taxes .',\n",
       " '\" We wouldn \\' t be able to do business ,\" said a spokesman for leading Japanese electronics firm Matsushita Electric Industrial Co Ltd & lt ; MC . T >.',\n",
       " '\" If the tariffs remain in place for any length of time beyond a few months it will mean the complete erosion of exports ( of goods subject to tariffs ) to the U . S .,\" said Tom Murtha , a stock analyst at the Tokyo office of broker & lt ; James Capel and Co >.',\n",
       " 'In Taiwan , businessmen and officials are also worried .',\n",
       " '\" We are aware of the seriousness of the U . S .',\n",
       " 'Threat against Japan because it serves as a warning to us ,\" said a senior Taiwanese trade official who asked not to be named .']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sentences[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb439504",
   "metadata": {},
   "source": [
    "Let us build a DataFrame of 1000 sentences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b8c826fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(sentences[:1000], columns=[\"text\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4506607b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>They told Reuter correspondents in Asian capit...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>But some exporters said that while the conflic...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>The U . S . Has said it will impose 300 mln dl...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Unofficial Japanese estimates put the impact o...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>The decision to cut deposits was taken by the ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>The cuts were likely to attract more business ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>ELECTRO RENT CORP &amp; lt ; ELRC &gt; 3RD QTR FEB 28...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                  text\n",
       "0    ASIAN EXPORTERS FEAR DAMAGE FROM U . S .- JAPA...\n",
       "1    They told Reuter correspondents in Asian capit...\n",
       "2    But some exporters said that while the conflic...\n",
       "3    The U . S . Has said it will impose 300 mln dl...\n",
       "4    Unofficial Japanese estimates put the impact o...\n",
       "..                                                 ...\n",
       "995  The decision to cut deposits was taken by the ...\n",
       "996  The cuts were likely to attract more business ...\n",
       "997  ELECTRO RENT CORP & lt ; ELRC > 3RD QTR FEB 28...\n",
       "998           WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS\n",
       "999           WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS\n",
       "\n",
       "[1000 rows x 1 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "941c527a",
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding_model = \"text-embedding-ada-002\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0c3833f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "encoding = tiktoken.encoding_for_model(embedding_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39065f42",
   "metadata": {},
   "source": [
    "# Compute the embeddings for each sentence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "52d61eab-5a61-4c9c-b993-f03ec1f73355",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_embedding(text, engine):\n",
    "    text = text.replace(\"\\n\", \" \")\n",
    "    \n",
    "    return client.embeddings.create(input=[text], model=engine).data[0].embedding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0ddf3098",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b629bfef7e4c4a049f3cfbfe60369914",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[\"embedding\"] = data.text.progress_apply(lambda x: get_embedding(x, engine=embedding_model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "181910bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>text</th>\n",
       "      <th>embedding</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ASIAN EXPORTERS FEAR DAMAGE FROM U . S .- JAPA...</td>\n",
       "      <td>[-0.016322532668709755, -0.028255142271518707,...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>They told Reuter correspondents in Asian capit...</td>\n",
       "      <td>[-0.021973947063088417, -0.016387123614549637,...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>But some exporters said that while the conflic...</td>\n",
       "      <td>[-0.020723218098282814, -0.018283598124980927,...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>The U . S . Has said it will impose 300 mln dl...</td>\n",
       "      <td>[-0.02001209929585457, -0.01670563593506813, 0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Unofficial Japanese estimates put the impact o...</td>\n",
       "      <td>[-0.02122245542705059, -0.03379626199603081, 0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>The decision to cut deposits was taken by the ...</td>\n",
       "      <td>[0.003845407161861658, -0.014886741526424885, ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>The cuts were likely to attract more business ...</td>\n",
       "      <td>[-0.02035561017692089, -0.02054610475897789, 0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>ELECTRO RENT CORP &amp; lt ; ELRC &gt; 3RD QTR FEB 28...</td>\n",
       "      <td>[0.0014210807858034968, -0.012158041819930077,...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS</td>\n",
       "      <td>[0.002370386151596904, 0.00641195522621274, 0....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS</td>\n",
       "      <td>[0.002370386151596904, 0.00641195522621274, 0....</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                  text  \\\n",
       "0    ASIAN EXPORTERS FEAR DAMAGE FROM U . S .- JAPA...   \n",
       "1    They told Reuter correspondents in Asian capit...   \n",
       "2    But some exporters said that while the conflic...   \n",
       "3    The U . S . Has said it will impose 300 mln dl...   \n",
       "4    Unofficial Japanese estimates put the impact o...   \n",
       "..                                                 ...   \n",
       "995  The decision to cut deposits was taken by the ...   \n",
       "996  The cuts were likely to attract more business ...   \n",
       "997  ELECTRO RENT CORP & lt ; ELRC > 3RD QTR FEB 28...   \n",
       "998           WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS   \n",
       "999           WALGREEN CO 2ND QTR SHR 62 CTS VS 58 CTS   \n",
       "\n",
       "                                             embedding  \n",
       "0    [-0.016322532668709755, -0.028255142271518707,...  \n",
       "1    [-0.021973947063088417, -0.016387123614549637,...  \n",
       "2    [-0.020723218098282814, -0.018283598124980927,...  \n",
       "3    [-0.02001209929585457, -0.01670563593506813, 0...  \n",
       "4    [-0.02122245542705059, -0.03379626199603081, 0...  \n",
       "..                                                 ...  \n",
       "995  [0.003845407161861658, -0.014886741526424885, ...  \n",
       "996  [-0.02035561017692089, -0.02054610475897789, 0...  \n",
       "997  [0.0014210807858034968, -0.012158041819930077,...  \n",
       "998  [0.002370386151596904, 0.00641195522621274, 0....  \n",
       "999  [0.002370386151596904, 0.00641195522621274, 0....  \n",
       "\n",
       "[1000 rows x 2 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f662177b",
   "metadata": {},
   "source": [
    "# Generate Recommendations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2b3075ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_recommendations(data, pos, k_nearest_neighbors=3):\n",
    "    embeddings = np.array(data[\"embedding\"].to_list())\n",
    "    strings = data[\"text\"].to_list()\n",
    "\n",
    "    query_embedding = embeddings[pos]\n",
    "\n",
    "    distances = [ cosine_similarity(query_embedding, embedding) for embedding in tqdm(embeddings, total=len(embeddings)) ]\n",
    "\n",
    "    indices_of_nearest_neighbors = np.argsort(distances)\n",
    "\n",
    "    query_string = strings[pos]\n",
    "    print(f\"Query: {query_string}\\n\\n\")\n",
    "\n",
    "    for pos, i in enumerate(indices_of_nearest_neighbors[1:k_nearest_neighbors+1]):\n",
    "        print(\"-- Nearest neighbor %u of %u (%u)---\\n%s\\n\\n\" % (pos, k_nearest_neighbors, i, strings[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cb5ff9f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "61ad338e17724894a55e0372a3f4f267",
       "version_major": 2,
       "version_minor": 0
      },
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       "  0%|          | 0/1000 [00:00<?, ?it/s]"
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     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Query: It will be the next decade before we see if the strategy is right or wrong .\"\n",
      "\n",
      "\n",
      "-- Nearest neighbor 0 of 5 (94)---\n",
      "But financial analysts are divided on whether and how quickly the gamble will pay off .\n",
      "\n",
      "\n",
      "-- Nearest neighbor 1 of 5 (118)---\n",
      "We expect this will be allowed in two or three years ,\" he said .\n",
      "\n",
      "\n",
      "-- Nearest neighbor 2 of 5 (106)---\n",
      "We only have to wait two or three years , not until the 21st century ,\" Komatsu said .\n",
      "\n",
      "\n",
      "-- Nearest neighbor 3 of 5 (321)---\n",
      "Bankers say it is too early to venture a forecast for economic growth this year or next .\n",
      "\n",
      "\n",
      "-- Nearest neighbor 4 of 5 (580)---\n",
      "\" And we will have to see if the United States is able to do what they promised in Paris on reducing the budget deficit -- and get it through Congress ,\" he added .\n",
      "\n",
      "\n",
      "CPU times: user 41.8 ms, sys: 4.39 ms, total: 46.2 ms\n",
      "Wall time: 45.2 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "get_recommendations(data, 123, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "532d4ba5",
   "metadata": {},
   "source": [
    "<center>\n",
    "     <img src=\"https://raw.githubusercontent.com/DataForScience/Networks/master/data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</center>"
   ]
  }
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