graph_knn_query {rnndescent}

Query a search graph for nearest neighbors

Description

Run queries against a search graph, to return nearest neighbors taken from the reference data used to build that graph.

Usage

graph_knn_query(
  query,
  reference,
  reference_graph,
  k = NULL,
  metric = "euclidean",
  init = NULL,
  epsilon = 0.1,
  max_search_fraction = 1,
  use_alt_metric = TRUE,
  n_threads = 0,
  verbose = FALSE,
  obs = "R"
)

Arguments

query

Matrix of n query items, with observations in the rows and features in the columns. Optionally, the data may be passed with the observations in the columns, by setting obs = "C", which should be more efficient. The reference data must be passed in the same orientation as query. Possible formats are base::data.frame(), base::matrix() or Matrix::sparseMatrix(). Sparse matrices should be in dgCMatrix format. Dataframes will be converted to numerical matrix format internally, so if your data columns are logical and intended to be used with the specialized binary metrics, you should convert it to a logical matrix first (otherwise you will get the slower dense numerical version).

reference

Matrix of m reference items, with observations in the rows and features in the columns. The nearest neighbors to the queries are calculated from this data. Optionally, the data may be passed with the observations in the columns, by setting obs = "C", which should be more efficient. The query data must be passed in the same format and orientation as reference. Possible formats are base::data.frame(), base::matrix() or Matrix::sparseMatrix(). Sparse matrices should be in dgCMatrix format.

reference_graph

Search graph of the reference data. A neighbor graph, such as that output from nnd_knn() can be used, but preferably a suitably prepared sparse search graph should be used, such as that output by prepare_search_graph().

k

Number of nearest neighbors to return. Optional if init is specified.

metric

Type of distance calculation to use. One of:

• "braycurtis"

• "canberra"

• "chebyshev"

• "correlation" (1 minus the Pearson correlation)

• "cosine"

• "dice"

• "euclidean"

• "hamming"

• "hellinger"

• "jaccard"

• "jensenshannon"

• "kulsinski"

• "sqeuclidean" (squared Euclidean)

• "manhattan"

• "rogerstanimoto"

• "russellrao"

• "sokalmichener"

• "sokalsneath"

• "spearmanr" (1 minus the Spearman rank correlation)

• "symmetrickl" (symmetric Kullback-Leibler divergence)

• "tsss" (Triangle Area Similarity-Sector Area Similarity or TS-SS metric)

• "yule"

For non-sparse data, the following variants are available with preprocessing: this trades memory for a potential speed up during the distance calculation. Some minor numerical differences should be expected compared to the non-preprocessed versions:

• "cosine-preprocess": cosine with preprocessing.

• "correlation-preprocess": correlation with preprocessing.

For non-sparse binary data passed as a logical matrix, the following metrics have specialized variants which should be substantially faster than the non-binary variants (in other cases the logical data will be treated as a dense numeric vector of 0s and 1s):

• "dice"

• "hamming"

• "jaccard"

• "kulsinski"

• "matching"

• "rogerstanimoto"

• "russellrao"

• "sokalmichener"

• "sokalsneath"

• "yule"

init

Initial query neighbor graph to optimize. If not provided, k random neighbors are created. If provided, the input format must be one of:

1. A list containing:

   • idx an n by k matrix containing the nearest neighbor indices.

   • dist (optional) an n by k matrix containing the nearest neighbor distances.

   If k and init are specified as arguments to this function, and the number of neighbors provided in init is not equal to k then:

   • if k is smaller, only the k closest values in init are retained.

   • if k is larger, then random neighbors will be chosen to fill init to the size of k. Note that there is no checking if any of the random neighbors are duplicates of what is already in init so effectively fewer than k neighbors may be chosen for some observations under these circumstances.

   If the input distances are omitted, they will be calculated for you.

2. A random projection forest, such as that returned from rpf_build() or rpf_knn() with ret_forest = TRUE.

epsilon

Controls trade-off between accuracy and search cost, as described by Iwasaki and Miyazaki (2018), by specifying a distance tolerance on whether to explore the neighbors of candidate points. The larger the value, the more neighbors will be searched. A value of 0.1 allows query-candidate distances to be 10% larger than the current most-distant neighbor of the query point, 0.2 means 20%, and so on. Suggested values are between 0-0.5, although this value is highly dependent on the distribution of distances in the dataset (higher dimensional data should choose a smaller cutoff). Too large a value of epsilon will result in the query search approaching brute force comparison. Use this parameter in conjunction with max_search_fraction and prepare_search_graph() to prevent excessive run time. Default is 0.1. If you set verbose = TRUE, statistics of the number of distance calculations will be logged which can help you tune epsilon.

max_search_fraction

Maximum fraction of the reference data to search. This is a value between 0 (search none of the reference data) and 1 (search all of the data if necessary). This works in conjunction with epsilon and will terminate the search early if the specified fraction of the reference data has been searched. Default is 1.

use_alt_metric

If TRUE, use faster metrics that maintain the ordering of distances internally (e.g. squared Euclidean distances if using metric = "euclidean"), then apply a correction at the end. Probably the only reason to set this to FALSE is if you suspect that some sort of numeric issue is occurring with your data in the alternative code path. If a search forest is used for initialization via the init parameter, then the metric is fetched from there and this setting is ignored.

n_threads

Number of threads to use.

verbose

If TRUE, log information to the console.

obs

set to "C" to indicate that the input query and reference orientation stores each observation as a column (the orientation must be consistent). The default "R" means that observations are stored in each row. Storing the data by row is usually more convenient, but internally your data will be converted to column storage. Passing it already column-oriented will save some memory and (a small amount of) CPU usage.

Details

A greedy beam search is used to query the graph, combining two search pruning strategies. The first, due to Iwasaki and Miyazaki (2018), only considers new candidates within a relative distance of the current furthest neighbor in the query's graph. The second, due to Harwood and Drummond (2016), puts a limit on the absolute number of distance calculations to carry out. See the epsilon and max_search_fraction parameters respectively.

Value

the approximate nearest neighbor graph as a list containing:

• idx a n by k matrix containing the nearest neighbor indices specifying the row of the neighbor in reference.

• dist a n by k matrix containing the nearest neighbor distances.

References

Harwood, B., & Drummond, T. (2016). Fanng: Fast approximate nearest neighbour graphs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 5713-5722).

Iwasaki, M., & Miyazaki, D. (2018). Optimization of indexing based on k-nearest neighbor graph for proximity search in high-dimensional data. arXiv preprint arXiv:1810.07355.

Examples

# 100 reference iris items
iris_ref <- iris[iris$Species %in% c("setosa", "versicolor"), ]

# 50 query items
iris_query <- iris[iris$Species == "versicolor", ]

# First, find the approximate 4-nearest neighbor graph for the references:
iris_ref_graph <- nnd_knn(iris_ref, k = 4)

# For each item in iris_query find the 4 nearest neighbors in iris_ref.
# You need to pass both the reference data and the reference graph.
# If you pass a data frame, non-numeric columns are removed.
# set verbose = TRUE to get details on the progress being made
iris_query_nn <- graph_knn_query(iris_query, iris_ref, iris_ref_graph,
  k = 4, metric = "euclidean", verbose = TRUE
)

# A more complete example, converting the initial knn into a search graph
# and using a filtered random projection forest to initialize the search
# create initial knn and forest
iris_ref_graph <- nnd_knn(iris_ref, k = 4, init = "tree", ret_forest = TRUE)
# keep the best tree in the forest
forest <- rpf_filter(iris_ref_graph, n_trees = 1)
# expand the knn into a search graph
iris_ref_search_graph <- prepare_search_graph(iris_ref, iris_ref_graph)
# run the query with the improved graph and initialization
iris_query_nn <- graph_knn_query(iris_query, iris_ref, iris_ref_search_graph,
  init = forest, k = 4
)