Add python tutorial on different indexs refinement and respect accuracy measurement (facebookresearch#3480)

Summary:
Pull Request resolved: facebookresearch#3480

This tutorial summarize the methods to construct different indexs for PQFastScan refinement. It shows how the choice can impact on accuracy.

Reviewed By: junjieqi

Differential Revision: D57799598

fbshipit-source-id: a75c52c60a5217366f3361676da8f03f0c4a9feb

Author: Xiao Fu

tutorial/python/9-RefineComparison.py

@@ -0,0 +1,42 @@
+# Copyright (c) Facebook, Inc. and its affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+import faiss
+
+from faiss.contrib.evaluation import knn_intersection_measure
+from faiss.contrib import datasets
+
+# 64-dim vectors, 50000 vectors in the training, 100000 in database,
+# 10000 in queries, dtype ('float32')
+ds = datasets.SyntheticDataset(64, 50000, 100000, 10000)
+d = 64                           # dimension
+
+# Constructing the refine PQ index with SQfp16 with index factory
+index_fp16 = faiss.index_factory(d, 'PQ32x4fs,Refine(SQfp16)')
+index_fp16.train(ds.get_train())
+index_fp16.add(ds.get_database())
+
+# Constructing the refine PQ index with SQ8
+index_sq8 = faiss.index_factory(d, 'PQ32x4fs,Refine(SQ8)')
+index_sq8.train(ds.get_train())
+index_sq8.add(ds.get_database())
+
+# Parameterization on k factor while doing search for index refinement
+k_factor = 3.0
+params = faiss.IndexRefineSearchParameters(k_factor=k_factor)
+
+# Perform index search using different index refinement
+D_fp16, I_fp16 = index_fp16.search(ds.get_queries(), 100, params=params)
+D_sq8, I_sq8 = index_sq8.search(ds.get_queries(), 100, params=params)
+
+# Calculating knn intersection measure for different index types on refinement
+KIM_fp16 = knn_intersection_measure(I_fp16, ds.get_groundtruth())
+KIM_sq8 = knn_intersection_measure(I_sq8, ds.get_groundtruth())
+
+# KNN intersection measure accuracy shows that choosing SQ8 impacts accuracy
+assert (KIM_fp16 > KIM_sq8)
+
+print(I_sq8[:5])
+print(I_fp16[:5])