VLFeat implements the randomized kd-tree forest from FLANN.
This enables fast medium and large scale nearest neighbor queries among high dimensional data points (such as those produced by SIFT).
A kd-tree is a data structure used to quickly solve nearest-neighbor queries. Consider a set of 2D points uniformly distributed in the unit square:
X = rand(2, 100) ;
A kd-tree is generated by using the
kdtree = vl_kdtreebuild(X) ;
kdtree indexes the set of points
Given a query point
Q, the function
its nearest neighbor in
Q = rand(2, 1) ; [index, distance] = vl_kdtreequery(kdforest, X, Q) ;
index stores the index of the column of
is closest to the point
the squared euclidean distance between
A kd-tree is a hierarchal structure built by partitioning the data recursively along the dimension of maximum variance. At each iteration the variance of each column is computed and the data is split into two parts on the column with maximum variance.
The splitting threshold can be selected to be the mean or the median (use the
ThresholdMethod option of
a best-bin first search heuristic. This is a branch-and-bound technique that maintains an estimate of the smallest distance from the query point to any of the data points down all of the open paths.
two important operations: approximate nearest-neighbor search and k-nearest neighbor search. The latter can be used to return the k nearest neighbors to a given query
Q. For instance:
[index, distance] = vl_kdtreequery(kdtree, X, Q, 'NumNeighbors', 10) ;
returns the closest 10 neighbors to
their distances, stored along the columns of
MaxComparisons option is used to run an ANN query. The parameter specifies how many paths in the best-bin-first search of the
kd-tree can be checked before giving up and returning the closest point encountered so far. For instance:
[index, distance] = vl_kdtreequery(kdtree, X, Q, 'NumNeighbors', 10, 'MaxComparisons', 15) ;
does not compare any point in
Q with more than 15 points in
Randomized kd-tree forests
VLFeat supports constructing randomized forests of kd-trees to improve the effectiveness of the representation in high dimensions. The parameter
how many trees to use in constructing the forest. Each tree is constructed independently. Instead of always splitting on the maximally variant dimension, each tree chooses randomly among the top five most variant dimensions at each level. When querying,
best-bin-first across all the trees in parallel. For instance
kdtree = vl_kdtreebuild(X, 'NumTrees', 4) ; [index, distance] = vl_kdtreequery(kdtree, X, Q) ;
constructs four trees and queries them.