Created
August 1, 2019 15:41
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import faiss" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "nq = 100\n", | |
| "nb = 1000\n", | |
| "d = 32\n", | |
| "\n", | |
| "xq = faiss.randn((nq, d))\n", | |
| "xb = faiss.randn((nb, d))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# reference IP search\n", | |
| "k = 10\n", | |
| "index = faiss.IndexFlatIP(d)\n", | |
| "index.add(xb)\n", | |
| "Dref, Iref = index.search(xq, k)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# see http://ulrichpaquet.com/Papers/SpeedUp.pdf theorem 5\n", | |
| "\n", | |
| "def get_phi(xb): \n", | |
| " return (xb ** 2).sum(1).max()\n", | |
| "\n", | |
| "def augment_xb(xb, phi=None): \n", | |
| " norms = (xb ** 2).sum(1)\n", | |
| " if phi is None: \n", | |
| " phi = norms.max()\n", | |
| " extracol = np.sqrt(phi - norms)\n", | |
| " return np.hstack((xb, extracol.reshape(-1, 1)))\n", | |
| "\n", | |
| "def augment_xq(xq): \n", | |
| " extracol = np.zeros(len(xq), dtype='float32')\n", | |
| " return np.hstack((xq, extracol.reshape(-1, 1)))\n", | |
| " " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# reference IP search\n", | |
| "k = 10\n", | |
| "index = faiss.IndexFlatL2(d + 1)\n", | |
| "index.add(augment_xb(xb))\n", | |
| "D, I = index.search(augment_xq(xq), k)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "True" | |
| ] | |
| }, | |
| "execution_count": 12, | |
| "metadata": { | |
| "bento_obj_id": "140595066188536" | |
| }, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "np.all(I == Iref)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "bento_stylesheets": { | |
| "bento/extensions/flow/main.css": true, | |
| "bento/extensions/kernel_selector/main.css": true, | |
| "bento/extensions/kernel_ui/main.css": true, | |
| "bento/extensions/new_kernel/main.css": true, | |
| "bento/extensions/system_usage/main.css": true, | |
| "bento/extensions/theme/main.css": true | |
| }, | |
| "kernelspec": { | |
| "display_name": "faiss", | |
| "language": "python", | |
| "name": "bento_kernel_faiss" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.6.3rc1+" | |
| } | |
| }, | |
| "nbformat": 4, | |
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| } |
Author
IndexFlatIP returns the maximum IP distances.
could i use the new xb with faiss.index_factory(768, "PCA128,IVF16384_HNSW64,Flat") ?
and got the similar results ?
old xb have been L2 norm
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IndexFlatIP finds the minimum IP distance instead of the maximum. What if I want to find maximum IP similarity neighbors? Note that IP can be negative and positive, querying with the opposite vector will return the largest negative ones.