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Approximate Nearest Neighbor Search Indexes [experimental]

Nearest neighborhood search is the problem of finding the M closest points for a given point in an N-dimensional vector space. The most straightforward approach to solve this problem is a brute force search where the distance between all points in the vector space and the reference point is computed. This method guarantees perfect accuracy, but it is usually too slow for practical applications. Thus, nearest neighborhood search problems are often solved with approximative algorithms. Approximative nearest neighborhood search techniques, in conjunction with embedding methods allow to search huge amounts of media (pictures, songs, articles, etc.) in milliseconds.

Blogs:

In terms of SQL, the nearest neighborhood problem can be expressed as follows:

SELECT *
FROM table
ORDER BY Distance(vectors, Point)
LIMIT N

vectors contains N-dimensional values of type Array(Float32) or Array(Float64), for example embeddings. Function Distance computes the distance between two vectors. Often, the Euclidean (L2) distance is chosen as distance function but other distance functions are also possible. Point is the reference point, e.g. (0.17, 0.33, ...), and N limits the number of search results.

This query returns the top-N closest points to the reference point. Parameter N limits the number of returned values which is useful for situations where MaxDistance is difficult to determine in advance.

With brute force search, the query is expensive (linear in the number of points) because the distance between all points in vectors and Point must be computed. To speed this process up, Approximate Nearest Neighbor Search Indexes (ANN indexes) store a compact representation of the search space (using clustering, search trees, etc.) which allows to compute an approximate answer much quicker (in sub-linear time).

Creating and Using Vector Similarity Indexes

Syntax to create a vector similarity index over an Array(Float32) column:

CREATE TABLE table
(
  id Int64,
  vectors Array(Float32),
  INDEX index_name vectors TYPE vector_similarity(method, distance_function[, quantization, hnsw_max_connections_per_layer, hnsw_candidate_list_size_for_construction]) [GRANULARITY N]
)
ENGINE = MergeTree
ORDER BY id;

Parameters:

  • method: Supports currently only hnsw.
  • distance_function: either L2Distance (the Euclidean distance - the length of a line between two points in Euclidean space), or cosineDistance (the cosine distance- the angle between two non-zero vectors).
  • quantization: either f64, f32, f16, bf16, or i8 for storing the vector with reduced precision (optional, default: bf16)
  • hnsw_max_connections_per_layer: the number of neighbors per HNSW graph node, also known as M in the HNSW paper (optional, default: 32)
  • hnsw_candidate_list_size_for_construction: the size of the dynamic candidate list when constructing the HNSW graph, also known as ef_construction in the original HNSW paper (optional, default: 128)

Values 0 for parameters hnsw_max_connections_per_layer and hnsw_candidate_list_size_for_construction means using the default values of these parameters.

Example:

CREATE TABLE table
(
  id Int64,
  vectors Array(Float32),
  INDEX idx vectors TYPE vector_similarity('hnsw', 'L2Distance') -- Alternative syntax: TYPE vector_similarity(hnsw, L2Distance)
)
ENGINE = MergeTree
ORDER BY id;

Vector similarity indexes are based on the USearch library, which implements the HNSW algorithm, i.e., a hierarchical graph where each point represents a vector and the edges represent similarity. Such hierarchical structures can be very efficient on large collections. They may often fetch 0.05% or less data from the overall dataset, while still providing 99% recall. This is especially useful when working with high-dimensional vectors, that are expensive to load and compare. The library also has several hardware-specific SIMD optimizations to accelerate further distance computations on modern Arm (NEON and SVE) and x86 (AVX2 and AVX-512) CPUs and OS-specific optimizations to allow efficient navigation around immutable persistent files, without loading them into RAM.

USearch indexes are currently experimental, to use them you first need to SET allow_experimental_vector_similarity_index = 1.

Vector similarity indexes currently support two distance functions:

  • L2Distance, also called Euclidean distance, is the length of a line segment between two points in Euclidean space (Wikipedia).
  • cosineDistance, also called cosine similarity, is the cosine of the angle between two (non-zero) vectors (Wikipedia).

Vector similarity indexes allows storing the vectors in reduced precision formats. Supported scalar kinds are f64, f32, f16 or i8. If no scalar kind was specified during index creation, f16 is used as default.

For normalized data, L2Distance is usually a better choice, otherwise cosineDistance is recommended to compensate for scale. If no distance function was specified during index creation, L2Distance is used as default.

Note

All arrays must have same length. To avoid errors, you can use a CONSTRAINT, for example, CONSTRAINT constraint_name_1 CHECK length(vectors) = 256. Also, empty Arrays and unspecified Array values in INSERT statements (i.e. default values) are not supported.

Note

The vector similarity index currently does not work with per-table, non-default index_granularity settings (see here). If necessary, the value must be changed in config.xml.

Vector index creation is known to be slow. To speed the process up, index creation can be parallelized. The maximum number of threads can be configured using server configuration setting max_build_vector_similarity_index_thread_pool_size.

ANN indexes are built during column insertion and merge. As a result, INSERT and OPTIMIZE statements will be slower than for ordinary tables. ANNIndexes are ideally used only with immutable or rarely changed data, respectively when are far more read requests than write requests.

Tip

To reduce the cost of building vector similarity indexes, consider setting materialize_skip_indexes_on_insert which disables the construction of skipping indexes on newly inserted parts. Search would fall back to exact search but as inserted parts are typically small compared to the total table size, the performance impact of that would be negligible.

ANN indexes support this type of query:

WITH [...] AS reference_vector
SELECT *
FROM table
WHERE ...                       -- WHERE clause is optional
ORDER BY Distance(vectors, reference_vector)
LIMIT N
SETTINGS enable_analyzer = 0;   -- Temporary limitation, will be lifted

To avoid writing out large vectors, you can use query parameters, e.g.

clickhouse-client --param_vec='hello' --query="SELECT * FROM table WHERE L2Distance(vectors, {vec: Array(Float32)}) < 1.0"

:::

To search using a different value of HNSW parameter hnsw_candidate_list_size_for_search (default: 256), also known as ef_search in the original HNSW paper, run the SELECT query with SETTINGS hnsw_candidate_list_size_for_search = <value>.

Restrictions: Approximate algorithms used to determine the nearest neighbors require a limit, hence queries without LIMIT clause cannot utilize ANN indexes. Also, ANN indexes are only used if the query has a LIMIT value smaller than setting max_limit_for_ann_queries (default: 1 million rows). This is a safeguard to prevent large memory allocations by external libraries for approximate neighbor search.

Differences to Skip Indexes Similar to regular skip indexes, ANN indexes are constructed over granules and each indexed block consists of GRANULARITY = [N]-many granules ([N] = 1 by default for normal skip indexes). For example, if the primary index granularity of the table is 8192 (setting index_granularity = 8192) and GRANULARITY = 2, then each indexed block will contain 16384 rows. However, data structures and algorithms for approximate neighborhood search (usually provided by external libraries) are inherently row-oriented. They store a compact representation of a set of rows and also return rows for ANN queries. This causes some rather unintuitive differences in the way ANN indexes behave compared to normal skip indexes.

When a user defines an ANN index on a column, ClickHouse internally creates an ANN "sub-index" for each index block. The sub-index is "local" in the sense that it only knows about the rows of its containing index block. In the previous example and assuming that a column has 65536 rows, we obtain four index blocks (spanning eight granules) and an ANN sub-index for each index block. A sub-index is theoretically able to return the rows with the N closest points within its index block directly. However, since ClickHouse loads data from disk to memory at the granularity of granules, sub-indexes extrapolate matching rows to granule granularity. This is different from regular skip indexes which skip data at the granularity of index blocks.

The GRANULARITY parameter determines how many ANN sub-indexes are created. Bigger GRANULARITY values mean fewer but larger ANN sub-indexes, up to the point where a column (or a column's data part) has only a single sub-index. In that case, the sub-index has a "global" view of all column rows and can directly return all granules of the column (part) with relevant rows (there are at most LIMIT [N]-many such granules). In a second step, ClickHouse will load these granules and identify the actually best rows by performing a brute-force distance calculation over all rows of the granules. With a small GRANULARITY value, each of the sub-indexes returns up to LIMIT N-many granules. As a result, more granules need to be loaded and post-filtered. Note that the search accuracy is with both cases equally good, only the processing performance differs. It is generally recommended to use a large GRANULARITY for ANN indexes and fall back to a smaller GRANULARITY values only in case of problems like excessive memory consumption of the ANN structures. If no GRANULARITY was specified for ANN indexes, the default value is 100 million.