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PyNNDescent: Fast Approximate Nearest Neighbors with Numba
Leland McInnes
July 16, 2021
Programming
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PyNNDescent: Fast Approximate Nearest Neighbors with Numba
A PDF version of slides for my SciPy 2021 talk on PyNNDescent.
Leland McInnes
July 16, 2021
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Transcript
Fast Approximate Nearest Neighbour Search with Numba
What are Nearest Neighbours?
Given a set of points with A distance measure between
them…
… and a new “query point” …
Find the closest points to the query point
Why Nearest Neighbors?
Nearest Neighbour computations are at the heart of many machine
learning algorithms
KNN-Classi fi ers KNN-Regressors
Clustering https://commons.wikimedia.org/wiki/File:DBSCAN-Illustration.svg by Chire https://www. fl ickr.com/photos/trevorpatt/41875889652/in/photostream/ by Trevor Patt
HDBSCAN DBSCAN Single Linkage Clustering Spectral Clustering
Dimension Reduction http://lvdmaaten.github.io/tsne/ http://www-clmc.usc.edu/publications/T/tenenbaum-Science2000.pdf t-SNE Isomap Spectral Embedding UMAP
Recommender Systems Query Expansion
Why Approximate Nearest Neighbours?
Finding exact nearest neighbours is hard
Approximate nearest neighbour search trades accuracy for performance
How Do You Find Nearest Neighbors?
Using Trees
Hierarchically divide up the space into a tree
Bound the search using the tree structure (And the triangle
inequality)
KD-Tree
Ball Tree
Random Projection Tree
Using Graphs
How do you search for nearest neighbours of a query
using a graph? Malkov and Yashunin, 2018 Dong, Moses and Li, 2011 Iwasaki and Miyazaki, 2018
Start with a nearest neighbour graph of the training data
Assume we now want to fi nd neighbours of a query point
Choose a starting node in the graph (potentially randomly) as
a candidate node
None
Look at all nodes connected by an edge to the
best untried candidate node in the graph Add all these nodes to our potential candidate pool
None
Sort the candidate pool by closeness to the query point
Truncate the pool to the k best candidates
None
Return to the Expansion step unless we have already tried
all the candidates in the pool
Stop when there are no untried candidates in the pool
None
None
None
None
Looks inef fi cient Scales up well
None
Graph adapts to intrinsic dimension of the data
But how do we build the graph?!
The algorithm works (badly) even on a bad graph
Run one iteration of search for every node Update the
graph with new better neighbours Search is better on the improved graph
None
None
None
None
None
Perfect accuracy of neighbours is not assured We can get
an approximate knn-graph quickly
How Do You Make it Fast?
Algorithm tricks
Query node Expansion node Current neighbour
Neighbour A Neighbour B Common node
Hubs have a lot of neighbours!
None
None
Sample neighbours when constructing the graph Prune away edges before
performing searches
Necessary to fi nd green’s nearest neighbour Necessary to fi
nd blue’s nearest neighbour Not required since we can traverse through blue
For search remove the longest edges of any triangles in
the graph
Initialize with Random Projection Trees
Implementation tricks
None
Pro fi le and inspect llvm code for innermost functions
Type declarations and code choices can help the compiler a lot!
@numba.jit def euclidean(x, y): return np.sqrt(np.sum((x - y)**2)) Query benchmark
took 12s
@numba.jit(fastmath=True) def euclidean(x, y): result = 0.0 for i in
range(x.shape[0]): result += (x[i] - y[i])**2 return np.sqrt(result) Query benchmark took 8.5s
@numba.njit( numba.types.float32( numba.types.Array( numba.types.float32, 1, "C", readonly=True ), numba.types.Array( numba.types.float32,
1, "C", readonly=True ), ), fastmath=True, locals={ "result": numba.types.float32, "diff": numba.types.float32, "i": numba.types.uint16, }, ) def squared_euclidean(x, y): result = 0.0 dim = x.shape[0] for i in range(dim): diff = x[i] - y[i] result += diff * diff return result Query benchmark took 7.6s
Custom data structure implementations to help numba for often called
code
@numba.njit( "i4(f4[ :: 1],i4[ :: 1],f4,i4)", ) def simple_heap_push(priorities, indices,
p, n): ...
Numba has signi fi cant function call overhead with large
parameters Use closures over static data instead
@numba.njit() def frequently_called_function(param, large_readonly_data): ... val = access(large_readonly_data, param) ...
def create_frequently_called_function(large_readonly_data): @numba.njit() def closure(param): ... val = access(large_readonly_data, param) ... return closure
How Does it Compare?
Performance
We can test query performance using ann-benchmarks https://github.com/erikbern/ann-benchmarks
Consider the whole accuracy / performance trade-off space
vs
None
None
None
None
Caveats: •Newer algorithms and implementations •Hardware can makes a big
difference •No GPU support for pynndescent
Features
Out of the box support for a wide variety of
distance measures: Euclidean Cosine Hamming Manhattan Minkowski Chebyshev Jaccard Haversine Dice Wasserstein Hellinger Spearman Correlation Mahalanobis Canberra Bray-Curtis Angular TSSS +20 more measures https://towardsdatascience.com/9-distance-measures-in-data-science-918109d069fa By Maarten Grootendorst
Custom metrics in Python (using numba)
Support for sparse data
Drop-in replacement for sklearn KNeighborsTransformer
Summary
pip install pynndescent conda install pynndescent https://github.com/lmcinnes/pynndescent leland.mcinnes@gmail.com @leland_mcinnes
Questions? leland.mcinnes@gmail.com @leland_mcinnes