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, | |
"nbformat_minor": 2 | |
} |
IndexFlatIP returns the maximum IP distances.
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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.