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zS*|IzKOw}HKsmjv>Eyp(DxZFkT|OJ%gZN(}`M~O@Smfv&f&v_TyeM>ZvTAZD{|AHA B`2GL@ diff --git a/semester4/dmdb/parts/05_vector-search/01_hsnw-index.tex b/semester4/dmdb/parts/05_vector-search/01_hsnw-index.tex new file mode 100644 index 0000000..967e681 --- /dev/null +++ b/semester4/dmdb/parts/05_vector-search/01_hsnw-index.tex @@ -0,0 +1,14 @@ +\subsection{Hierarchical Navigable Small World Index (HNSW Index)} +This is a layered graph concept, at insert, first all nodes are inserted into layer 0 and each is connected to $M \approx 3 - 4$ neighbours. +Then, the edge count is $\tco{N \cdot M}$. With $N = 100$ million and $M = 16$, we have $1.6B$ edges, with a typical memory footprint of $4-8$GB for $100M$ 32-bit Edge IDs. +Then, some nodes (typically about $N_{L_k} = N / M^k$ to layer $k$) are promoted to layer 1, connected to $M$ nearest neighbours in $L1$ only. +This process is repeated a few times until the number of nodes in the layer is low enough. +This number depends on a number of factors, primarily how coarse grained we want the initial search to be. + +Then, after building, we prune edges, in a process called RNG pruning. +Here we prune an edge $(u, v)$ if there exist edges $(u, w)$ and $(w, v)$, such that $d(u, w) < d(u, v)$ and $d(w, v) < d(u, v)$. +Important is that both conditions have to be met, as the goal is to remove the longest redundant edge from the graph. +This is done using a greedy algorithm. + + +\subsubsection{Search} diff --git a/semester4/dmdb/parts/05_vector-search/main.tex b/semester4/dmdb/parts/05_vector-search/main.tex index 43c6eff..dedff59 100644 --- a/semester4/dmdb/parts/05_vector-search/main.tex +++ b/semester4/dmdb/parts/05_vector-search/main.tex @@ -1,3 +1,4 @@ \section{Vector Search} \input{parts/05_vector-search/00_intro-trees-clustering.tex} +\input{parts/05_vector-search/01_hsnw-index.tex} % \input{parts/05_vector-search/}