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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_with_ann_index
ORDER BY Distance(vectors, Point)
LIMIT N

vectors contains N-dimensional values of type Array(Float32), 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.

An alternative formulation of the nearest neighborhood search problem looks as follows:

SELECT *
FROM table_with_ann_index
WHERE Distance(vectors, Point) < MaxDistance
LIMIT N

While the first query returns the top-N closest points to the reference point, the second query returns all points closer to the reference point than a maximally allowed radius MaxDistance. 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, both queries are 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 ANN Indexes

Syntax to create an ANN index over an Array(Float32) column:

CREATE TABLE table_with_ann_index
(
  `id` Int64,
  `vectors` Array(Float32),
  INDEX [ann_index_name vectors TYPE [ann_index_type]([ann_index_parameters]) [GRANULARITY [N]]
)
ENGINE = MergeTree
ORDER BY id;

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.

ANN indexes support two types of queries:

  • ORDER BY queries:

    SELECT *
    FROM table_with_ann_index
    [WHERE ...]
    ORDER BY Distance(vectors, Point)
    LIMIT N

  • WHERE queries:

    SELECT *
    FROM table_with_ann_index
    WHERE Distance(vectors, Point) < MaxDistance
    LIMIT N
tip

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

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

Restrictions: Queries that contain both a WHERE Distance(vectors, Point) < MaxDistance and an ORDER BY Distance(vectors, Point) clause cannot use ANN indexes. Also, the 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.

Available ANN Indexes

Annoy​

Annoy indexes are currently experimental, to use them you first need to SET allow_experimental_annoy_index = 1. They are also currently disabled on ARM due to memory safety problems with the algorithm.

This type of ANN index is based on the Annoy library which recursively divides the space into random linear surfaces (lines in 2D, planes in 3D etc.).

Syntax to create an Annoy index over an Array(Float32) column:

CREATE TABLE table_with_annoy_index
(
  id Int64,
  vectors Array(Float32),
  INDEX [ann_index_name] vectors TYPE annoy([Distance[, NumTrees]]) [GRANULARITY N]
)
ENGINE = MergeTree
ORDER BY id;

Annoy currently supports 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).

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.

Parameter NumTrees is the number of trees which the algorithm creates (default if not specified: 100). Higher values of NumTree mean more accurate search results but slower index creation / query times (approximately linearly) as well as larger index sizes.

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.

The creation of Annoy indexes (whenever a new part is build, e.g. at the end of a merge) is a relatively slow process. You can increase setting max_threads_for_annoy_index_creation (default: 4) which controls how many threads are used to create an Annoy index. Please be careful with this setting, it is possible that multiple indexes are created in parallel in which case there can be overparallelization.

Setting annoy_index_search_k_nodes (default: NumTrees * LIMIT) determines how many tree nodes are inspected during SELECTs. Larger values mean more accurate results at the cost of longer query runtime:

SELECT *
FROM table_name
ORDER BY L2Distance(vectors, Point)
LIMIT N
SETTINGS annoy_index_search_k_nodes=100;
note

The Annoy 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.

USearch​

This type of ANN index is based on the USearch library, which implements the HNSW algorithm, i.e., builds 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.

Syntax to create an USearch index over an Array column:

CREATE TABLE table_with_usearch_index
(
  id Int64,
  vectors Array(Float32),
  INDEX [ann_index_name] vectors TYPE usearch([Distance[, ScalarKind]]) [GRANULARITY N]
)
ENGINE = MergeTree
ORDER BY id;

USearch currently supports 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).

USearch 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.